Samacheer Kalvi Class 8 Maths Solutions Chapter 7 Information processing InText Questions

Recap (Text Book Page No. 232 & 233)

 

Question 1. Find the number of all possible triangles that can be formed from the triangle given below.
Answer: To find all possible triangles in the given figure, we can count them based on their size or composition. There are 5 single small triangles, 4 triangles formed by combining two smaller parts, 2 triangles formed by combining three parts, and 1 large overall triangle. Adding these up gives us the total number of triangles. In total, the figure contains 12 triangles.
In simple words: Look at the picture and count all the triangles you can find. There are small ones, medium ones made of two or three small ones, and one big one. Add them all up to get the total.

🎯 Exam Tip: When counting triangles in a complex figure, systematically list triangles by the number of basic regions they cover to avoid missing any and to prevent double-counting.

 

Question 2. Use the numbers given in the figure to form a 3 × 3 magic square.
Answer: To form a magic square with the given numbers (13, 15, 7, 17, 9, 1, 11, 3, 5), arrange them in a 3x3 grid. The standard goal for a magic square is that all rows, columns, and main diagonals sum to the same total. For these numbers, the sum of all numbers is 81, so the magic constant (sum for each row/column/diagonal) would ideally be \( \frac{81}{3} = 27 \). The arrangement that satisfies the row and column sums is:

In simple words: Take all the numbers and place them into a 3x3 grid so that when you add up the numbers in any straight line across or down, they all give the same answer.

🎯 Exam Tip: When checking a magic square, always verify that both the main diagonals also sum to the magic constant, not just rows and columns.

 

Question 3. Convert the tree diagram into a numeric expression.
Answer: A tree diagram shows a sequence of operations. For this diagram, we perform multiplication first and then addition. The first branch multiplies 10 by 5, and the second branch multiplies 9 by 4. These two results are then added together. This process helps visualize the order of operations clearly.
\( (10 \times 5) + (9 \times 4) \)
\( = 50 + 36 \)
\( = 86 \)
In simple words: Follow the branches of the tree diagram. First, multiply the numbers connected by an 'X'. Then, add the results together using the '+' sign.

🎯 Exam Tip: Always remember the order of operations (PEMDAS/BODMAS) when converting diagrams to expressions: Parentheses/Brackets first, then Exponents/Orders, then Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right).

 

Question 4.
(i) Find the total time taken by the bus to reach from A to E via B, C and D.
(ii) Find which is the shortest route from A to E.
Answer:
(i) To find the total time from A to E via B, C, and D, we add up the time taken for each segment of the route. This route is A \( \rightarrow \) B \( \rightarrow \) C \( \rightarrow \) D \( \rightarrow \) E.
Time taken \( = (7 + 5 + 3 + 6) \) hrs \( = 21 \) hrs.
(ii) To find the shortest route from A to E, we need to calculate the total time for all available routes and then compare them. We list out all the possible paths and their total travel times.

The shortest route is A \( \rightarrow \) B \( \rightarrow \) D \( \rightarrow \) E, which takes 17 hours.
In simple words: For the first part, just add up the travel times for the route A to B, B to C, C to D, and D to E. For the second part, check all the different ways to get from A to E, add up the times for each way, and pick the path that has the smallest total time.

🎯 Exam Tip: When finding the shortest path, always draw out or list all possible routes clearly, calculate the total cost/time for each, and then compare them to ensure no route is overlooked.

 

Question 5. Connect the Fibonacci squares through diagonals by curve from corner to corner across each square to draw a Golden Spiral.
Answer: To create a Golden Spiral, start from the smallest square in the Fibonacci sequence layout. Draw a smooth curve from one corner to the opposite corner of that square. Then, continue this curve into the next larger square, connecting its corners diagonally in a flowing motion. Keep extending the curve through the diagonals of successively larger Fibonacci squares. This creates a visually pleasing spiral that expands outwards in a specific mathematical ratio, reflecting natural growth patterns.
In simple words: Imagine squares of different sizes, like building blocks, arranged in a spiral. To draw a Golden Spiral, you connect the corners of these squares with a curved line, starting from the smallest square and gracefully moving into the bigger ones.

🎯 Exam Tip: The Golden Spiral is found in many natural forms, like seashells and galaxies. Understanding how it's built from Fibonacci squares helps appreciate its mathematical beauty and occurrence in the real world.

 

Question 6. When you plan to buy a shirt, one shop offers a discount of ₹ 200 on MRP ₹ 1000 and another shop offers 15% discount on the same MRP. Where would you buy?
Answer: To decide where to buy the shirt, we need to calculate the final price in each shop after the discount. This helps us see which shop offers a better deal.
Price in 1st shop \( = ₹ 1000 - ₹ 200 = ₹ 800 \).
Price in IInd shop \( = ₹ 1000 - (15\% \text{ of } ₹ 1000) \)
\( = ₹ 1000 - \left( \frac { 15 }{ 100 } \times 1000 \right) \)
\( = ₹ 1000 - ₹ 150 \)
\( = ₹ 850 \).
Since ₹ 800 is less than ₹ 850, I would buy the shirt from shop 1.
In simple words: Shop 1 takes off Rs 200, making the shirt Rs 800. Shop 2 takes off 15%, which is Rs 150, making the shirt Rs 850. So, shop 1 is cheaper by Rs 50.

🎯 Exam Tip: Always convert percentage discounts into actual money saved before comparing, as it makes the comparison straightforward and avoids errors.

 

Question 7. Amazing park is offers a package deal of 5 entrance passes for ₹ 130. If one entrance pass normally costs ₹ 30, how much will you save by taking advantage of this special deal?
Answer: To find out how much money is saved, we first need to calculate the normal cost of five passes. Then, we compare this normal cost with the special deal price.
Cost of one entrance pass \( = ₹ 30 \).
Normal cost of 5 entrance passes \( = ₹ 5 \times 30 = ₹ 150 \).
Special deal price for 5 passes \( = ₹ 130 \).
Amount of saving \( = (\text{Normal Cost}) - (\text{Special Deal Price}) \)
\( = ₹ 150 - ₹ 130 = ₹ 20 \).
So, you will save Rs 20 by taking advantage of this special deal. This shows that package deals can often be more economical.
In simple words: One pass usually costs Rs 30, so five passes would be Rs 150. But the special deal lets you buy five passes for only Rs 130. You save Rs 20 by choosing the deal.

🎯 Exam Tip: When evaluating package deals, always calculate the total normal price of the items included in the package to accurately determine the actual savings.

Activity (Text Book Page No. 237)

 

Question 1. Determine the number of two digit numbers that can be formed using the digits 1, 3 and 5 with repetition of digits allowed. The activity consists of two parts (i) Choose a one's digit. (ii) Choose a ten's digit. Complete the table given beside
Answer: To form two-digit numbers using the digits 1, 3, and 5 with repetition allowed, we can systematically list all combinations by choosing a digit for the tens place and a digit for the ones place. Since repetition is allowed, each position can be filled by any of the three digits. The table below shows all the possible two-digit numbers that can be formed.

In simple words: When you can use the same number twice (like 11 or 33), and you have digits 1, 3, and 5, you can make these numbers: 11, 13, 15, 31, 33, 35, 51, 53, and 55. There are 9 such numbers in total.

🎯 Exam Tip: For problems involving digit formation with repetition, if there are 'n' choices for each of 'k' positions, the total number of combinations is \( n^k \). Here, 3 digits for 2 positions is \( 3^2 = 9 \).

 

Question 2. Find the three digit numbers that can be formed using the digits 1, 3 and 5 without repetition of digits. Complete the tree diagram given below to the numbers
Answer: When forming three-digit numbers using digits 1, 3, and 5 without repetition, we must ensure that each digit is used only once in any given number. A tree diagram helps visualize all the possible unique combinations. For the first digit, there are 3 choices. For the second digit, only 2 choices remain (since one is used). For the third digit, only 1 choice is left. Therefore, there are \( 3 \times 2 \times 1 = 6 \) unique three-digit numbers. These numbers are: 135, 153, 315, 351, 513, and 531.
In simple words: If you use the numbers 1, 3, and 5 to make three-digit numbers, and you can't use any number more than once, then you can make these six numbers: 135, 153, 315, 351, 513, and 531.

🎯 Exam Tip: For problems involving digit formation without repetition, the number of choices decreases by one for each subsequent position, which is a factorial calculation (e.g., \( n! \) for \( n \) digits).

Activity (Text Book Page No. 242)

 

Question 1.
(i)
(ii)
(iii)
Answer: This question asks to identify a pattern and complete it visually. The pattern usually progresses in quantity or type of shapes.
(i) The pattern shows two green squares.
(ii) The pattern shows a single green spiral.
(iii) The pattern shows three green squares.
In simple words: You need to look at the pictures and guess what comes next or what the missing picture should be.

🎯 Exam Tip: For visual pattern questions, look for changes in number, color, shape, size, or orientation of the elements. Identify the rule governing the change to predict the next item.

 

Question 2.
(i)
(ii)
(iii)
Answer: This question asks to complete a visual pattern based on the provided images. The patterns involve spirals and stars.
(i) The pattern shows a single green spiral.
(ii) The pattern shows three blue stars.
(iii) The pattern shows three green stars.
In simple words: Watch how the pictures change, like how many stars there are or if they are colored differently. Then, draw the picture that follows the rule.

🎯 Exam Tip: Pay close attention to subtle details like color, line thickness, or the exact arrangement of components, as these often hold the key to the pattern rule.

 

Question 3.
(i)
(ii)
(iii)
Answer: This question involves completing visual patterns with squares and circles. The pattern is about filling in the blanks with the correct number or color of shapes.
(i) The pattern shows three empty squares.
(ii) The pattern shows three orange circles.
(iii) The pattern shows three red circles.
In simple words: Fill in the missing pictures by following the rule, like how many circles or squares are in each row, or what color they are.

🎯 Exam Tip: If the pattern involves multiple attributes (e.g., both color and shape), analyze each attribute independently to find its sequence, then combine them to predict the complete pattern element.

 

Question 4.
(i)
(ii)
(iii)
Answer: This question requires completing a visual pattern featuring circles and spirals. The pattern seems to involve a progression in the number of similar shapes or a change in their form.
(i) The pattern shows one green circle.
(ii) The pattern shows two green circles.
(iii) The pattern shows two green spirals.
In simple words: Look at the circle and spiral pictures. See how they change in number or type, and then choose the right picture to continue the pattern.

🎯 Exam Tip: Some patterns involve a mix of shape changes and quantity changes. Break down complex patterns into simpler components to identify each individual rule.

 

Question 5.
(i)
(ii)
(iii)
Answer: This question asks to complete a visual pattern with squares, stars, circles, and spirals. The pattern shows an arrangement of shapes that needs to be logically continued or completed.
(i) The pattern shows two blue stars.
(ii) The pattern shows one green circle.
(iii) The pattern shows three green spirals.
In simple words: Find the rule for how the shapes change or grow in the pictures, and then pick or draw the picture that fits next.

🎯 Exam Tip: If a pattern includes a 'question mark', it often indicates a missing element that completes a logical sequence or set within the given visual information.

Try These (Text Book Page No. 243)

 

Question 1. Find any five SETs among these set of cards (repetition of cards allowed).
Answer: To find five SETs among the given cards, we look for groups of cards that share common properties, such as shape, number of items, or color. Repetition means we can reuse cards for different sets. Let's describe the cards: (a) single star, (b) empty square, (c) two stars, (d) empty circle, (e) single red circle, (f) three empty squares, (g) two red circles, (h) three stars, (i) single spiral, (j) three red circles.
Here are five possible sets:
(i) (a), (c), (h) - This set includes cards with stars, showing 1, 2, and 3 stars respectively.
(ii) (e), (g), (j) - This set includes cards with red circles, showing 1, 2, and 3 red circles respectively.
(iii) (a), (b), (d) - This set includes cards that show single items (star, square, circle).
(iv) (f), (i), (j) - This set includes cards with three items (squares, spirals, circles).
(v) (f), (i), (h) - This set includes cards with three items (squares, spirals, stars).
In simple words: Group the cards that are similar in some way, like all cards with stars, or all cards with red circles, or all cards that show three of something. You can use the same card in different groups.

🎯 Exam Tip: When forming sets, clearly define the common property that links the elements in each set. This demonstrates a clear understanding of set theory principles like grouping by attributes.

 

Question 2. This is an example for a magic square in SETs. Can you make another two?
Answer: A magic square in SETs uses different visual elements or patterns in a grid so that the rows, columns, and diagonals follow a specific pattern or rule. The example shows a grid with stars, circles, and squares arranged in a certain order. To make another two examples, you can create new 3x3 grids using different combinations or arrangements of these or other simple shapes, ensuring that a visual "magic" rule is maintained. For example, one could arrange them such that each row, column, and diagonal has a unique combination of shapes, or a certain count of a particular shape. A simple approach is to create a square where all cells contain two shapes, and another where all cells contain three shapes. This applies the principle of increasing complexity or repetition based on the given elements.
In simple words: The magic square shows patterns instead of numbers. To make two more, you can draw new grids using the shapes, making sure that there's a pattern in each line going across, down, or corner-to-corner. You can try making all the cells have two items, or all cells have three items, for example.

🎯 Exam Tip: For pattern-based magic squares, the "magic" can be determined by the quantity of elements, their color, shape, or a combination of these attributes in each row, column, and diagonal.

Activity (Text Book Page No. 250)

 

Question 1. Where are the even Fibonacci Numbers? Colour both the term n and where F(n) is even in yellow. Do you find any pattern? Every Third Fibonacci number is a multiple of 2(even).
Answer: Let's look at the Fibonacci sequence and identify the even numbers. The Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...
The even Fibonacci numbers are: F(3) = 2, F(6) = 8, F(9) = 34, F(12) = 144.
We can observe a clear pattern here: every third Fibonacci number in the sequence is an even number. This is a property that arises from the nature of the Fibonacci sequence, where two odd numbers add up to an even number, and then an odd and an even number add up to an odd number, and so on.
The pattern is: Every 3rd Fibonacci number is a multiple of 2 (even).
In simple words: If you list the Fibonacci numbers, you will see that every third number is an even number (a number you can divide by 2). This happens because of how the numbers are added together.

🎯 Exam Tip: Understanding the parity (odd/even) pattern of Fibonacci numbers (Odd, Odd, Even, Odd, Odd, Even, ...) helps quickly identify multiples of 2.

 

Question 2. Where there are Fibonacci numbers which are multiple of 3? Colour both the term n and where F(n) is multiple of 3 in red. Write down the pattern you find Every 4th Fibonacci number is a multiple of 3.
Answer: Let's examine the Fibonacci sequence and find the numbers that are multiples of 3. The Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...
The Fibonacci numbers that are multiples of 3 are: F(4) = 3, F(8) = 21, F(12) = 144.
From this, we can observe a repeating pattern: every fourth Fibonacci number is a multiple of 3. This indicates a deeper divisibility rule within the sequence. This property is part of the Pisano period concept, where the sequence modulo n repeats.
The pattern is: Every 4th Fibonacci number is a multiple of 3.
In simple words: Look at the Fibonacci numbers. If a number can be divided by 3 without any remainder, it's a multiple of 3. You'll notice that this happens for every fourth number in the list.

🎯 Exam Tip: When exploring divisibility patterns in sequences like Fibonacci, extend the sequence to enough terms to confirm the repeating pattern confidently.

 

Question 3. What about the multiple of 5? Colour both the term n and where F(n) is multiple of 5 in blue. ' Write down the pattern you find. Every 5th Fibonacci number i.e a multiple of F(5) or 5 = F(5)
Answer: Let's look at the Fibonacci sequence and pinpoint the numbers that are multiples of 5. The Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...
The Fibonacci numbers that are multiples of 5 are: F(5) = 5, F(10) = 55.
We can see a distinct pattern: every fifth Fibonacci number is a multiple of 5. This is another example of how divisibility rules appear at regular intervals within the Fibonacci sequence. This pattern holds true for all Fibonacci sequences.
The pattern is: Every 5th Fibonacci number is a multiple of 5.
In simple words: Check the Fibonacci numbers again. You will find that every fifth number in the list can be divided by 5 perfectly.

🎯 Exam Tip: Divisibility rules for Fibonacci numbers often align with their position in the sequence, making pattern recognition a key skill for these types of questions.

 

Question 4. What about the multiple of 8? Colour both the term n where F(n) is multiple of 8 in green. Write down the pattern you find. Every 6th Fibonacci number i.e a multiple of F(6) or 8 = F(6)
Answer: Let's check the Fibonacci sequence for numbers that are multiples of 8. The Fibonacci sequence is: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610...
The Fibonacci numbers that are multiples of 8 are: F(6) = 8, F(12) = 144.
Observing these, we can conclude that every sixth Fibonacci number is a multiple of 8. This demonstrates a repeating pattern of divisibility. This principle extends to other divisors as well.
The pattern is: Every 6th Fibonacci number is a multiple of 8.
In simple words: When you look at the Fibonacci numbers, you'll see that every sixth number in the sequence can be divided by 8 with no leftover.

🎯 Exam Tip: Creating a table of Fibonacci numbers and their factors can help visually confirm and generalize these divisibility patterns across different multiples.

From the above activity, we conclude that Every Fibonacci number is a factor of (a term number of) Fibonacci numbers in multiples

Table 2.

 

From the above table, we get a general rule as Every \( k^{th} \) Fibonacci number is a multiple of F(k).

R - Red
Y - Yellow
B - Blue
G - Green

Activity (Text Book Page No. 258)

Code 1: Pigpen

 

Question I. Fill in the blank boxes and decode The Pigpen code looks like meaningless writing, but it is quite easy to catch on to. Each letter is represented by the part of the "Pigpen” that surrounds it. The first code uses the following key. To complete the code, you need to work out how to use the key to decode the message.
Answer: The Pigpen cipher uses a grid-based key where each letter is replaced by the specific lines of the grid that enclose it. By matching the given symbols to their corresponding letters on the Pigpen key, we can decode the hidden messages. This method of substitution makes the message look like random lines until the key is applied. The key divides letters into patterns based on parts of a tic-tac-toe grid and a cross grid.
The decoded messages are:
- WATER BOTTLE
- GIFT VOUCHER
- EXAM PAD
- GEOMETRY BOX
In simple words: The Pigpen code turns letters into unique shapes using a special grid. By looking at these shapes and finding their matching letters on the key, we can read the secret messages.

🎯 Exam Tip: When working with substitution ciphers like Pigpen, carefully draw the key or refer to it to avoid misinterpreting the symbols for letters.

Code 2: Polybius Square Cipher

 

Question II. Fill in the blanks A Polybius Square is a table that allows someone to convert letters into numbers. Use the Polybius square rows and column values to find the code
Answer: A Polybius Square is a table that allows someone to convert letters into numbers, and vice versa. Each letter is assigned a pair of numbers corresponding to its row and column in the square. This numerical representation can then be used in further encoding. By using the provided Polybius square, we can decode the numerical messages back into words. This cipher is fundamental in cryptography, demonstrating how simple mapping can create coded messages.
(4,2) (3,4) (5,5) (3,3) (1,5) (2,3) (5,5) (4,3) (1,4) \( \implies \) THE TREASURE
(4,2) (2,2) (5,5) (1,5) (3,2) (5,2) (2,2) (5,5) (4,5) (4,3) (5,5) (3,2) \( \implies \) ITEM DOES
(3,3) (4,3) (4,2) (3,4) (1,5) (1,1) (5,5) "(2,5)" \( \implies \) NOT HAVE
(1,5) (3,3) (4,5) "(4,5)" \( \implies \) BAND.
The complete decoded message is: THE TREASURE ITEM DOES NOT HAVE BAND D.
Based on the clue that the treasure item does not have the letters 'b' and 'd', from the options (Water bottle, Gift voucher, Exam pad, Geometry box), the only item that fits is "Gift voucher". All other options contain 'b' or 'd'.
In simple words: The Polybius Square turns each letter into two numbers. To solve the code, you find the letter for each pair of numbers using the table. The secret message tells you about the treasure. Since the treasure cannot have letters 'b' or 'd', "Gift voucher" is the only choice from the list.

🎯 Exam Tip: When working with Polybius squares, always remember that each letter corresponds to a unique row-column pair. Double-check your mapping to ensure accurate decoding. Also, the row number is typically listed first, then the column number.

Code 3: Atbash Cipher

 

Question III. Find the code using the key as shown in given figure: Atbash cipher is a substitution cipher with just one specific key where all the letters are reversed that is A to Z and Z to A.
Answer: The Atbash cipher is a simple substitution cipher where each letter in the alphabet is replaced by its "reverse" counterpart. That means A becomes Z, B becomes Y, C becomes X, and so on. This creates a mirrored alphabet, making it easy to encode and decode messages once you know the rule. By applying this key to the coded message, we can reveal the original text. The code is "GSV ILLN MFNYVI RH Z NFOGRKOV LU ULFI ZMW HVEVM THE".
Let's apply the Atbash cipher:
Plain Text: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Cipher Text: Z Y X W V U T S R Q P O N M L K J I H G F E D C B A
Decoding the message "GSV ILLN MFNYVI RH Z NFOGRKOV LU ULFI ZMW HVEVM THE":
GSV \( \implies \) THE
ILLN \( \implies \) ROOM
MFNYVI \( \implies \) NUMBER
RH \( \implies \) IS
Z \( \implies \) A
NFOGRKOV \( \implies \) MULTIPLE
LU \( \implies \) OF
ULFI \( \implies \) FOUR
ZMW \( \implies \) AND
HVEVM \( \implies \) SEVEN
The decoded message is: THE ROOM NUMBER IS A MULTIPLE OF FOUR AND SEVEN. This means the room number is \( 4 \times 7 = 28 \).
In simple words: The Atbash cipher flips the alphabet, so A becomes Z, B becomes Y, and so on. We use this rule to change the secret code back into normal words. The message says the room number is a multiple of four and seven, so it's 28.

🎯 Exam Tip: The Atbash cipher is its own inverse; applying the cipher twice to a message returns the original text. This unique property makes it distinct from other substitution ciphers.

Code 4: Using a Key – Reflection Table

 

Question IV. Use the reflection table which is given below and find the correct word by using a reflected alphabet.
Answer: The reflection table cipher works by substituting each letter with another letter directly opposite it in a specific arrangement. In this case, the first half of the alphabet (A-M) is paired with the second half (N-Z). So, A is replaced by N, B by O, C by P, and so on, and vice versa. This is a form of simple substitution, allowing for straightforward encoding and decoding.
The reflection table is:
A B C D E F G H I J K L M
N O P Q R S T U V W X Y Z
Decoding the given words:
JVAQBJ \( \implies \) WINDOW
PBZCHGREGNOYR \( \implies \) COMPUTER TABLE
PUNVE \( \implies \) CHAIR
PHOOBNEQ \( \implies \) CUPBOARD
These words are the decoded clues for the puzzle. Understanding such simple ciphers helps grasp the basics of cryptography.
In simple words: This code changes letters by swapping them with other letters from a special table. For example, 'A' turns into 'N' and 'N' turns into 'A'. Using this rule, we can change the coded words back into normal words like WINDOW and CHAIR.

🎯 Exam Tip: Always note the specific letter-to-letter mapping for reflection or substitution ciphers. If it's not a standard Atbash, the unique key table is crucial for correct decoding.

After finding the codes, the teacher then asks students to rearrange the clues one by one
CLUES

 

RESULT
(i) The room in which the treasure took place = ______
(ii) The place of the treasure = ______
(iii) The identity of the treasure = ______
(Hint:- If you answered the question number 6 in Exercise 4.3, you can compare and verify your results) The gift voucher contains (20 full marks awarded).
Answer: To find the final answer for the treasure hunt, we combine the clues decoded from the previous cipher puzzles. Each clue provides a piece of information that helps narrow down the possibilities. We must systematically use all the information to reach the correct conclusion.
The 4 clues are:
1. Water bottle, Gift voucher, Exam pad, Geometry box (These are the possible treasure items)
2. The name of the treasure does not have 'b' & 'd' (This clue helps identify the treasure item from the list)
3. The room is a multiple of four and seven = 28 (This clue identifies the room number)
4. Window, Computer table, Chair, Cupboard (These are the possible locations for the treasure)

Based on these clues:
(i) The room in which the treasure took place \( = 28 \) (from Clue 3).
(ii) The place of the treasure \( = \) Chair (This location is chosen from Clue 4, possibly linked to where the item would logically be found).
(iii) The identity of the treasure \( = \) Gift voucher (from Clue 2 applied to Clue 1, as 'Gift voucher' is the only item without 'b' or 'd').
In simple words: We used all the secret messages to find the answers. The room number is 28. The treasure is a gift voucher. It is hidden in the chair.

🎯 Exam Tip: For multi-part treasure hunt questions, ensure each clue is analyzed sequentially and its implications are applied to narrow down the options for the final solution.

Code 2: Polybius Square Cipher

 

Question 1. Use the Polybius square rows and column values to find the code.

Answer: Each pair of numbers points to a letter in the Polybius square. The first number is the row, and the second number is the column. By matching the numbers to the letters in the table, we can decode the message. For instance, (4, 2) stands for T, (3, 4) means H, and (5, 5) represents E. The full message decodes to "THE NAME OF TREASURE DOES NOT HAVE BAND D". Since a clue says the treasure item does not have the letters 'b' and 'd', "exam pad" and "geometry box" cannot be the treasure item. Therefore, the treasure item is "gift voucher".
In simple words: We use the number pairs to find letters in the table. The first number shows the row, and the second shows the column. This helps us spell out the secret message.

🎯 Exam Tip: When decoding ciphers, always keep the key chart handy and work systematically through each letter or number pair to avoid errors.

 

Code 3: Atbash Cipher

Question 1. Find the code using the key as shown in given figure:

Answer: The Atbash cipher works by reversing the alphabet, so A becomes Z, B becomes Y, and so on. We apply this rule to each letter in the given cipher to decode it. The given cipher is: GSV ILLN MFNYVI RH Z NFOGRKOV LU ULFI ZMW HVEVM THE
Decoded Message: THE ROOM NUMBER IS A MULTIPLE OF FOUR AND SEVEN
Since the room number must be a multiple of both 4 and 7, we find the product of these two numbers. This gives us the room number.
The room number is \( 4 \times 7 = 28 \).
In simple words: The Atbash code swaps letters from the start of the alphabet with letters from the end. If A is Z, then G is T, S is H, and so on. We use this to read the secret message. The room number is 28 because it's a multiple of 4 and 7.

🎯 Exam Tip: For Atbash ciphers, remembering that it's a simple reversal helps. Practicing with a few examples makes decoding quick and easy.

 

Code 4: Using a Key – Reflection Table

Question 1. Use the reflection table which is given below and find the correct word by using a reflected alphabet.

JVAQBJ-
PBZCHGREGNOYR-
PUNVE-
PHOOBNEQ-
Answer: We use the reflection table to swap each letter with its opposite. For example, J becomes Q, V becomes E, and A becomes Z. By applying this rule to each coded message, we can find the hidden words. JVAQBJ- WINDOW
PBZCHGREGNOYR- COMPUTER TABLE
PUNVE- CHAIR
PHOOBNEQ- CUPBOARD
In simple words: This code changes letters to their mirror image in the alphabet. If A is the first letter, it changes to Z (the last). This helps us uncover the secret words.

🎯 Exam Tip: Reflection ciphers are similar to Atbash. Always double-check your letter mapping to ensure accuracy when decoding messages.

 

Result

Question 1. Find the following based on the clues:
(i) The room in which the treasure took place =
(ii) The place of the treasure =
(iii) The identity of the treasure =
Answer: We found earlier that the room number is a multiple of 4 and 7, which gives us 28. Also, the treasure item is "gift voucher". We can now fill in the blanks based on all the clues decoded previously. The activity combines different cipher methods to find a final answer.
(i) The room in which the treasure took place = 28
(ii) The place of the treasure = Chair
(iii) The identity of treasure = Gift voucher.
In simple words: By using all the clues we decoded, we figured out the room number, where the treasure was, and what the treasure itself was.

🎯 Exam Tip: When combining multiple clues, ensure each part of the problem is solved correctly before putting them together. One small error can change the entire result.

 

Try These (Text Book Page No. 260)

Question 1. Use Pigpen Cipher code and write the code for your name and your chapter names
(i) LIFE MATHEMATICS
(ii) ALGEBRA
(iii) GEOMETRY
(iv) INFORMATION PROCESSING
Answer: To use the Pigpen Cipher, we first need to set up the criss-cross pattern and fill it with alphabets. Each letter is represented by the outline of the "pigpen" shape that surrounds it. We draw two square grids (one for A-I, J-R) and two X-shaped grids (one for S-Z). For example, the letter A would be the top-left corner of the first square. For your name, you would find the pattern for each letter in your name. For the chapter names, each letter would also be converted to its specific pattern. This creates a secret code for the words. (i) LIFE MATHEMATICS: \( \boxed{\sqcup\urcorner} \ \boxed{\sqcap} \ \boxed{\sqsupset} \ \boxed{\ulcorner} \ \boxed{\square} \ \boxed{_ \_} \ \boxed{\sqcap} \ \boxed{\sqsupset} \ \boxed{\sqcap} \ \boxed{\sqcup\urcorner} \ \boxed{\ulcorner} \ \boxed{\square} \ \boxed{\lrcorner} \ \boxed{\lrcorner} \ \boxed{\ulcorner} \ \boxed{\sqsubset} \ \boxed{\ulcorner} \ \boxed{\square} \ \boxed{_ \_} \) (ii) ALGEBRA: \( \boxed{\sqcup\urcorner} \ \boxed{\sqsupset} \ \boxed{\ulcorner} \ \boxed{\square} \ \boxed{\ulcorner} \ \boxed{\sqcup\urcorner} \ \boxed{\square} \) (iii) GEOMETRY: \( \boxed{\ulcorner} \ \boxed{\square} \ \boxed{_ \_} \ \boxed{\sqsupset} \ \boxed{\sqcap} \ \boxed{\ulcorner} \ \boxed{\lrcorner} \ \boxed{\ulcorner} \) (iv) INFORMATION PROCESSING: \( \boxed{\sqsupset} \ \boxed{\ulcorner} \ \boxed{\square} \ \boxed{\square} \ \boxed{\sqcup\urcorner} \ \boxed{\sqsupset} \ \boxed{\ulcorner} \ \boxed{\sqcup\urcorner} \ \boxed{\sqsupset} \ \boxed{\ulcorner} \ \boxed{\ulcorner} \ \boxed{\square} \ \boxed{\ulcorner} \ \boxed{\ulcorner} \ \boxed{_ \_} \ \boxed{\sqsupset} \ \boxed{\ulcorner} \ \boxed{\square} \ \boxed{\ulcorner} \ \boxed{_ \_} \)In simple words: To make a Pigpen code, you draw a grid and an 'X' shape. You put letters inside these shapes. Then, each letter gets a special pattern based on its shape. You find the pattern for each letter in your name and the chapter names.

🎯 Exam Tip: Always remember the basic grid structure for Pigpen ciphers (two squares and two 'X' shapes) and how letters are assigned to different parts of the outline.

 

Question 2. Decode the following Shifting and Substituting secret codes given below. Which one is easier for you?
(i) Shifting method:- MNS G H M F HRH LONRRHAKD
(ii) Substituting method:- \( \boxed{\ulcorner} \boxed{\lrcorner} \boxed{>} \boxed{\sqcap} \boxed{\sqsupset} \boxed{\Gamma} \boxed{O} \boxed{\neg} \ \boxed{\square} \boxed{<} \boxed{\sqsupset} \boxed{>} \boxed{>} \boxed{\lrcorner} \boxed{L} \boxed{O} \)
Answer: For the shifting method, we try different letter shifts. If we shift each letter in the code (MNSGHMFHRHLONRRHAKD) by a certain number of places, we can decode it. For example, shifting by 13 places (N becomes A, O becomes B, etc.) decodes the message. The substituting method uses the Pigpen code patterns. By matching each symbol to its corresponding letter in the Pigpen key, we can read the message. Both methods lead to the message "NOTHING IS IMPOSSIBLE". Decoded text from Shifting method: NOTHING IS IMPOSSIBLE
Decoded text from Substituting method: NOTHING IS IMPOSSIBLE
The Pigpen cipher (substituting method) can be considered easier because once the key is known, it is a direct one-to-one symbol to letter conversion, making it less trial-and-error than a shift cipher if the shift amount is unknown.
In simple words: We decoded both secret messages. One uses a shifting rule (like moving letters a few steps forward or backward), and the other uses the Pigpen shapes. Both methods revealed the same message: "NOTHING IS IMPOSSIBLE". The Pigpen one is simpler once you know the symbol rules.

🎯 Exam Tip: For shift ciphers, remember that if the shift amount isn't given, you might need to try a few common shifts. For substitution ciphers, always have your key reference handy.

 

Question 3. Write a short message to a friend and get them to decipher it.(Use any one shifting and substituting code method)
Answer: Students should create their own message and code it using either a shifting method (like Caesar cipher) or a substituting method (like Pigpen cipher). Then, they can ask a friend to decode it. This activity helps in understanding how ciphers work by creating and solving them. For example, a simple Caesar cipher shifting 3 letters forward would turn "HELLO" into "KHOOR".
In simple words: Make up a secret message for your friend. Use either a shift code (like moving letters along the alphabet) or a symbol code (like Pigpen). Then, ask your friend to try and read your secret message.

🎯 Exam Tip: When creating your own cipher, make sure your key is clear and consistent. A simple code with a clear key is often more effective for demonstrating the concept.

 

Activity (Text Book Page No. 264)

Question 1. In how many ways can you buy your items? Complete the price lists given below. One is done for you.
Answer: We need to select three items from Rice, Toor Dal, Sugar, and Wheat, keeping in mind the quantities and staying within a budget of Rs 220, without exceeding a total weight of 5kg. We calculate the total cost for different combinations of items to find valid ways to purchase. Many combinations are possible, but only those fitting both the budget and weight limits are valid. The tables below show three possible ways to buy the items based on the given conditions.
In simple words: We need to pick three food items. Each must fit our money limit (Rs 220) and total weight limit (5kg). We calculate the cost for different choices to see which ones work.

🎯 Exam Tip: For problems involving budget and quantity constraints, make sure to check both conditions (total cost and total quantity) for each combination before concluding if it's a valid purchase.

 

Question 2. Which one is the best purchase price list and why?
Answer:

The best purchase price list is the one that has the lowest total cost while still meeting all the criteria (three items, within Rs 220 budget, and total weight not exceeding 5kg). Comparing the given options: - Rs 231 (exceeds budget) - Rs 182.25 (This is the lowest total cost shown and is within budget and weight limits if the quantities are 2.5 kg Rice, 1 kg Toor Dal, 1 kg Wheat, summing to 4.5kg total weight). - Rs 214.50 (within budget, 1 kg Rice, 2 kg Toor Dal, 2 kg Wheat, sum to 5kg total weight) - Rs 207.00 (within budget, 3 kg Rice, 1 kg Toor Dal, 1 kg Sugar, sum to 5kg total weight) - Rs 220.00 (exactly the budget, 2 kg Toor Dal, 1.5 kg Rice, 1.5 kg Wheat, sum to 5kg total weight) The purchase with Rice (2.5 kg), Toor Dal (1 kg), and Wheat (1 kg) for a total of Rs 182.25 is the best option because it has the lowest total bill amount while staying within the budget and weight limits. This option offers the most savings.
In simple words: The best shopping list is the one that costs the least money (Rs 182.25) but still lets us buy what we need without going over budget or carrying too much weight.

🎯 Exam Tip: To find the "best" option in such problems, always compare the final costs and ensure all stated conditions (like budget and weight limits) are strictly met by the chosen solution.

 

Activity (Text Book Page No. 265)

Question 1. Consider that you want to buy 12 litres of the same quality of edible oil at your budget price of Rs 250 per litre. In a supermarket, there are a lot of offers on various oil brands. Some of the offers are given below. Complete the table and find which one is the best offer for you and how much you will save for your total purchase.
Answer: We need to calculate the cost of 12 litres of oil under different offers and compare it to our budget price of Rs 250 per litre. The standard cost for 12 litres would be \( 12 \times 250 = Rs 3000 \). We complete the table by filling in the special prices, savings, and cost per litre for each offer, and then the total cost for 12 litres.

Based on the calculations, the best offer price per litre for you is Rs 137.50 (Oil 6). The amount you saved for your total purchase is Rs \( 3000 - 1650 = Rs 1350 \).
In simple words: We looked at all the oil deals to find the cheapest way to buy 12 litres. The best deal was Oil 6, costing Rs 137.50 per litre. This saved us Rs 1350 compared to the usual price.

🎯 Exam Tip: To identify the best deal, always calculate the unit price (cost per litre in this case) for each offer and then compare them. Don't just look at the total discount.

 

Try These (Text Book Page No. 266)

Question 1. Here is your shopping list:
4 bottles of Protein Milk (200 ml size) 2 packets of Peanut candies(200 gm), 1 packet of Chocolate biscuits, 1 packet of Badam nuts (500 gm)
Answer: We need to compare the costs for the given shopping list at Star Food Mart and Super Provisions. We will calculate the price for each item based on the offers provided by each store.

The total cost for the shopping list at Star Food Mart is Rs 684. The total cost at Super Provisions is Rs 690.
In simple words: We calculated the cost for all the items at both Star Food Mart and Super Provisions. Star Food Mart would cost Rs 684 and Super Provisions would cost Rs 690 for the same shopping list.

🎯 Exam Tip: When comparing prices from different stores, make sure to consider all offers and discounts each store provides to find the true total cost.

Question 2. (i) If you buy all the items in one shop, where will you get the best price?
Answer: Based on the calculations, the best price for buying all items in one shop would be from Star Food Mart. The total cost at Star Food Mart is Rs 684, which is less than Super Provisions' total of Rs 690. It offers a saving of Rs 6.
In simple words: Star Food Mart has the best price if you buy everything from just one shop because it costs less money overall.

🎯 Exam Tip: To find the best deal for a full shopping list, calculate the total cost for the entire list at each store and directly compare the final sums.

Question 3. (ii) If you buy the items from the two shops, how will you do it to spend the least amount of money?
Answer: To spend the least amount of money by buying from both shops, you should purchase items that are cheaper at one store compared to the other. - Protein Milk: Rs 160 (same at both) - Peanut Candies: Star Food Mart Rs 140, Super Provisions Rs 150 (Buy from Star Food Mart) - Chocolate Biscuits: Star Food Mart Rs 84, Super Provisions Rs 90 (Buy from Star Food Mart) - Badam Nuts: Star Food Mart Rs 300, Super Provisions Rs 290 (Buy from Super Provisions) Therefore, you should buy Badam nuts from Super Provisions and all other items (Protein Milk, Peanut Candies, Chocolate Biscuits) from Star Food Mart.
In simple words: To save the most money, buy the Badam nuts from Super Provisions and all the other items from Star Food Mart. This way, you get each item at its lowest price.

🎯 Exam Tip: When mixing purchases from multiple stores, always identify which individual items are cheapest at which store and plan your purchases accordingly to maximize savings.

 

Question 4. II. You have Rs 1000/- to spend to buy the following shopping list:
6 bottles of Protein Milk (200 ml size), 3 packets of Peanut candies(200 gm), 3 packets of Chocolate biscuits, 1 packet of Badam nuts (250 gm)
Answer: We need to calculate the cost of this new shopping list at both Star Food Mart and Super Provisions, and then determine how to stay within a Rs 1000 budget.

The total cost at Star Food Mart is Rs 852. The total cost at Super Provisions is Rs 880. Both totals are below the Rs 1000 budget, so either store is a valid choice.
In simple words: For the new shopping list, both stores are within our Rs 1000 budget. Star Food Mart costs Rs 852 and Super Provisions costs Rs 880.

🎯 Exam Tip: Always calculate the total cost for each store and compare it against the budget limit. If multiple options are within budget, state all valid choices.

Question 5. (i) How can you do this so that you don't go over your budget amount Rs 1000?
Answer: Since both Star Food Mart (total cost Rs 852) and Super Provisions (total cost Rs 880) are under the Rs 1000 budget, you can buy all your items from either store. The best option to stay within budget and save the most would be to buy from Star Food Mart, as it has a lower total cost. You could also buy items from both shops, taking each item from the shop where it's cheaper.
In simple words: Since both stores cost less than Rs 1000, you can buy everything from either shop. To save the most, buy from Star Food Mart.

🎯 Exam Tip: When asked how to stay within a budget, analyze all available options. If multiple options fit, select the one that offers the most savings or efficiency.

Question 6. (ii) Which shop offers you the best value for money on each item?
Answer: We compare the individual item prices after discounts at both stores: - Protein Milk: Rs 40 (same at both) - Peanut candies: Star Food Mart Rs 70, Super Provisions Rs 75 (Star Food Mart is cheaper) - Chocolate biscuits: Star Food Mart Rs 84, Super Provisions Rs 90 (Star Food Mart is cheaper) - Badam nuts (250g): Star Food Mart Rs 150, Super Provisions Rs 145 (Super Provisions is cheaper) Star Food Mart offers better value for money on Peanut candies and Chocolate biscuits, while Super Provisions offers better value for Badam nuts. Protein milk is the same price at both stores. So, for the overall "best value for money on each item", a mix-and-match approach yields the lowest total.
In simple words: Star Food Mart is cheaper for peanut candies and chocolate biscuits. Super Provisions is cheaper for badam nuts. Protein milk costs the same everywhere.

🎯 Exam Tip: Value for money often means getting the lowest price for each specific item. Break down the shopping list and compare each item's price separately at different stores.

Question 7. (iii) Is the “BUY ONE GET ONE” deal at Super Provisions the same as “50% off" deal?
Answer: Yes, a "Buy One Get One" deal is effectively the same as a "50% off" deal when you buy two items. If you buy one item and get another identical item free, you are paying for one item to receive two. This means the cost per item is half of the original price, which is equivalent to a 50% discount on each item when bought in a pair.
In simple words: Yes, "Buy One Get One Free" is the same as getting half price (50% off) if you buy two items together. You pay for one but get two, so each item costs half.

🎯 Exam Tip: Understand common retail promotions. "Buy One Get One Free" always implies a 50% discount per item when purchasing two, making it an excellent saving strategy.

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