RBSE Solutions Class 6 Maths Chapter 12 Algebra More Ques

Question 1. Let y denote age in year. Write down the value of y for your 10 friends.
Answer: If 'y' is the age of one friend, then the ages of 10 friends can be shown with different expressions involving 'y'. This helps represent various ages based on a starting age 'y'.
1. \( (y - 2) \) years
2. \( (y + 3) \) years
3. \( (y + 1) \) years
4. \( (y - 1) \) years
5. \( y \) years
6. \( (2y - 10) \) years
7. \( (y + 2) \) years
8. \( (y - 3) \) years
9. \( (y + 3) \) years
10. \( (y - 2.5) \) years
In simple words: If one friend's age is 'y', we can write down other friends' ages by adding or subtracting from 'y', or multiplying 'y'.

🎯 Exam Tip: When expressing ages or other quantities relative to a variable, clearly define what the variable represents (e.g., 'y' years) and then apply the operations as described.

Question 1. Write algebraic expression given instructions about how to form it.
(i) Sum of 5 and a variable
(ii) Difference between 7 and a number
(iii) 3 times of a variable
(iv) 12 less than 6 times of a variable
(v) Half of a variable
(vi) 200 less than one third of a variable
Answer: Let's use 'x' as the variable for each instruction. We will translate the words into mathematical symbols to form the algebraic expressions. This helps in writing mathematical statements in a shorter way.
(i) Sum of 5 and a variable: \( 5 + x \)
(ii) Difference between 7 and a number: \( 7 - x \)
(iii) 3 times of a variable: \( 3x \)
(iv) 12 less than 6 times of a variable: \( 6x - 12 \)
(v) Half of a variable: \( \frac{x}{2} \)
(vi) 200 less than one third of a variable: \( \frac{x}{3} - 200 \)
In simple words: We take a letter like 'x' for the unknown number. Then we write down the sum, difference, or multiplication using numbers and 'x'.

🎯 Exam Tip: Pay close attention to keywords like "sum," "difference," "times," "less than," and "half." "Less than" usually means subtraction, and the number after "less than" comes first in the expression.

Question 2. Shweta secured 75 marks in mathematics. Her score in Science is not known. Let her science score be x. What is her total score?
Answer: Shweta's marks in mathematics are 75. Her science score is unknown, so we use 'x' to represent it. To find her total score, we add her marks from both subjects. This shows how to combine known and unknown values.
Marks of Shweta in mathematics = 75
Marks of Shweta in science = \( x \)
Therefore, total marks = \( x + 75 \)
In simple words: Shweta got 75 marks in Math. Her Science marks are 'x'. So, her total marks are 75 plus 'x'.

🎯 Exam Tip: When finding a total, always add up all the individual components, even if some are represented by variables.

Question 3. Sakshi has some candies with her. Ashu has 4 times as many candies as Sakshi. How many candies are there in total?
Answer: Let's say Sakshi has 'x' candies. Ashu has 4 times as many candies as Sakshi, which means Ashu has \( 4 \times x \) candies. To find the total number of candies, we add Sakshi's candies and Ashu's candies together. This helps find the combined quantity when one amount is a multiple of another.
Sakshi has = \( x \) candies
According to the question,
Ashu has = \( 4 \times x \) candies = \( 4x \) candies
Therefore, total candies = \( x + 4x = 5x \)
In simple words: Sakshi has 'x' candies. Ashu has 4 times 'x' candies. Together, they have 'x' plus '4x' candies, which is '5x' candies.

🎯 Exam Tip: Clearly define the variable for the base quantity (like Sakshi's candies). Then express other quantities (like Ashu's candies) in terms of that variable before adding them up.

Question 1. Match the algebraic expressions with appropriate situations in the following
(i) \( x + 4 \)
(ii) \( x - 4 \)
(iii) \( 4 - x \)
(iv) \( 4y \)
(v) \( \frac{y}{4} \)
(A) Prashant has 4 times as many wealth as Kamli.
(B) Malti has Rs. 4 more than Seema.
(C) My weight is 4 kgs less than Nancy.
(D) I had Rs. 4 from which I spend some money. How much I am left with ?
(E) Banshi had some marbles. He distributed them between his 4 friends equally. How marbles each friend get ?
Answer: We need to match each algebraic expression to the situation that it correctly represents. This involves understanding how words like "more than," "less than," "times," and "distributed equally" translate into mathematical operations.
(i) \( x + 4 \) = (B) Malti has Rs. 4 more than Seema. (If Seema has Rs. x, Malti has Rs. x + 4)
(ii) \( x - 4 \) = (C) My weight is 4 kgs less than Nancy. (If Nancy's weight is x kgs, my weight is x - 4 kgs)
(iii) \( 4 - x \) = (D) I had Rs. 4 from which I spend some money. How much I am left with? (If I had Rs. 4 and spent Rs. x, I am left with Rs. 4 - x)
(iv) \( 4y \) = (A) Prashant has 4 times as many wealth as Kamli. (If Kamli has wealth y, Prashant has wealth 4y)
(v) \( \frac{y}{4} \) = (E) Banshi had some marbles. He distributed them between his 4 friends equally. How marbles each friend get? (If Banshi had y marbles and divided them among 4 friends, each friend gets \( \frac{y}{4} \) marbles)
In simple words: We connect the math problem with the story that fits it. For example, "more than" means add, "less than" means subtract, and "times" means multiply.

🎯 Exam Tip: For matching questions, read each statement and expression carefully. Look for keywords like 'sum', 'difference', 'product', 'quotient' to correctly identify the operation involved.