NCERT Solutions Class 5 Mathematics Mela Chapter 13 Animal Jumps

Question. Find the hidden numbers
Numbers put in this box get multiplied by a number and come out. (a) Can you guess the multiplier if you see the 4 numbers coming out of the box? (b) Is there more than one possible multiplier? (c) What numbers might have been put inside the box?
Answer: (a) To discover the multiplier, we need to work out a number that, when we multiply other numbers by it, produces 28, 36, 48 and 72. Let us check: 28 ÷ 4 = 7, 36 ÷ 4 = 9, 48 ÷ 4 = 12, 72 ÷ 4 = 18. When we split each given number by 4, we get 7, 9, 12, 18. We can verify by multiplying back: 7 × 4 = 28, 9 × 4 = 36, 12 × 4 = 48, 18 × 4 = 72. So the multiplier is 4.
(b) Yes, 4 is also a multiple of 2, which means 2 could work as a multiplier too (though the numbers inside the box would be different).
(c) The numbers placed inside the box are 7, 9, 12 and 18, because multiplying each of these by 4 gives us the output numbers: 28, 36, 48 and 72.
In simple words: We need to find the number that makes the inside numbers turn into the outside numbers. When we check, we find that dividing each outside number by 4 gives the inside numbers.

Exam Tip: Always verify your answer by multiplying the inside numbers by the suspected multiplier to confirm you get the outside numbers back.

Question. A number, when arranged in an array, shows the factors of that number. Are there other numbers that are factors of 15? Try to make other arrays for the number 15.
Answer: All the possible arrays we can create for 15 are: 1 row × 15 columns = 15, 3 rows × 5 columns = 15, 5 rows × 3 columns = 15, 15 rows × 1 column = 15. Looking at these arrays, the full list of factors of 15 is: 1, 3, 5, 15.
In simple words: Factors are numbers that divide evenly into another number. For 15, we can split it into different rectangle shapes, and each dimension gives us a factor.

Exam Tip: Remember that factors always come in pairs - when you find one, you can reverse it to find another (e.g., 3 and 5 pair to make 15).

Let Us Do

Question 1. Make different arrays for the following numbers. Identify the factors in each case.
(a) 10
(b) 14
(c) 13
(d) 20
(e) 25
(f) 32
(g) 37
(h) 46
(i) 54

Numbers like 13 and 37 are called prime numbers. Why?
Answer:
(a) 10 - Arrays: 1 × 10, 2 × 5 - Factors: 1, 2, 5, 10
(b) 14 - Arrays: 1 × 14, 2 × 7 - Factors: 1, 2, 7, 14
(c) 13 - Arrays: 1 × 13 only - Factors: 1, 13 - 13 is a prime number because we cannot make any array other than 1 × 13. It has only two factors: 1 and itself.
(d) 20 - Arrays: 1 × 20, 2 × 10, 4 × 5 - Factors: 1, 2, 4, 5, 10, 20
(e) 25 - Arrays: 1 × 25, 5 × 5 - Factors: 1, 5, 25
(f) 32 - Arrays: 1 × 32, 2 × 16, 4 × 8 - Factors: 1, 2, 4, 8, 16, 32
(g) 37 - Arrays: 1 × 37 only - Factors: 1, 37 - 37 is a prime number.
(h) 46 - Arrays: 1 × 46, 2 × 23 - Factors: 1, 2, 23, 46
(i) 54 - Arrays: 1 × 54, 2 × 27, 3 × 18, 6 × 9 - Factors: 1, 2, 3, 6, 9, 18, 27, 54
In simple words: Arrays show us all the different rectangular shapes we can make with a number. Each row and column length is a factor of that number.

Exam Tip: Prime numbers have exactly two factors: 1 and the number itself, which is why they can only form one rectangular array shape.

Question 2. 12 is the first common multiple of 3 and 4. What are some other common multiples of 3 and 4? You can continue the number line or take help from the times tables of 3 and 4.
Answer: The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ... The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, ... The common multiples of 3 and 4 are: 12, 24, 36, 48, 60, 72 and so on. These common multiples are actually multiples of 12. The first one is 12, and each next common multiple is 12 more than the one before it.
In simple words: Common multiples are numbers that appear in the times tables of both numbers. They follow a pattern - they keep increasing by the same amount each time.

Exam Tip: The first common multiple of two numbers is also called the Least Common Multiple (LCM) - knowing this helps you find all other common multiples quickly.

Question 3. A spider takes a jump of 3 every time. A grasshopper takes a jump of 6 each time. Use the number line to find the common multiples of 3 and 6.
Answer: Spider (jumping by 3) lands at: 3, 6, 9, 12, 15, 18, 21, 24... Grasshopper (jumping by 6) lands at: 6, 12, 18, 24, 30, 36... The common multiples of 3 and 6 (where both creatures land) are: 6, 12, 18, 24, 30, 36...
In simple words: Common multiples are the numbers where both creatures touch down. These are numbers that both 3 and 6 divide into evenly.

Exam Tip: When one number is a multiple of another (like 6 is a multiple of 3), the common multiples are just the multiples of the larger number.

Question. 6 and 12 are two common multiples of 3 and 6. You can continue the pattern to find more common multiples. What do you notice about the common multiples of 3 and 6? Discuss.
Answer: From the number line, the common multiples of 3 and 6 shown are: 6, 12, ... Every multiple of 6 is also a multiple of 3. Therefore, the common multiples of 3 and 6 are exactly the multiples of 6. We can verify: 6 = 3 × 2 and 6 × 1, 12 = 3 × 4 and 6 × 2, 18 = 3 × 6 and 6 × 3. This happens because 6 itself is a multiple of 3, so all its multiples automatically work for both numbers.
In simple words: When one number is already a multiple of another, the common multiples are simply the multiples of the bigger number.

Exam Tip: Look for a factor relationship between two numbers - if one divides the other, you can use this shortcut to find common multiples quickly.

Question. 12 and 24 are two of the common multiples of 4 and 6. List a few more.
Answer: The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, ... The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, ... The common multiples of 4 and 6 are: 12, 24, 36 and so on. Additional common multiples beyond 24 include: 48, 60, 72, and further multiples of 12 can be listed by continuing the pattern.
In simple words: To find common multiples, look at both times tables and pick the numbers that show up in both lists.

Exam Tip: The common multiples form a regular pattern - they are all multiples of the LCM (in this case, 12).

Question 1. Find 5 common multiples of the following pairs of numbers.
(a) 2 and 3
(b) 5 and 8
(c) 2 and 4
(d) 3 and 9
(e) 5 and 10
(f) 9 and 12
(g) 8 and 12
(h) 6 and 8
(i) 6 and 9
Answer:
(a) Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, ... | Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ... | Common multiples: 6, 12, 18, 24, 30
(b) Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ... | Multiples of 8: 8, 16, 24, 32, 40, 48, ... | Common multiples: 40, 80, 120, 160, 200
(c) Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, ... | Multiples of 4: 4, 8, 12, 16, 20, 24, 28, ... | Common multiples: 4, 8, 12, 16, 20
(d) Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ... | Multiples of 9: 9, 18, 27, 36, 45, ... | Common multiples: 9, 18, 27, 36, 45
(e) Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ... | Multiples of 10: 10, 20, 30, 40, 50, ... | Common multiples: 10, 20, 30, 40, 50
(f) Multiples of 9: 9, 18, 27, 36, 45, 54, ... | Multiples of 12: 12, 24, 36, 48, 60, ... | Common multiples: 36, 72, 108, 144, 180
(g) Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ... | Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ... | Common multiples: 24, 48, 72, 96, 120
(h) Multiples of 6: 6, 12, 18, 24, 30, 36, ... | Multiples of 8: 8, 16, 24, 32, 40, ... | Common multiples: 24, 48, 72, 96, 120
(i) Multiples of 6: 6, 12, 18, 24, 30, 36, ... | Multiples of 9: 9, 18, 27, 36, 45, ... | Common multiples: 18, 36, 54, 72, 90
In simple words: Write out the times table for each number and pick the numbers that show up in both lists - those are your common multiples.

Exam Tip: List at least 10 multiples of each number to make sure you find enough common ones - sometimes it takes longer to find the pattern.

Question. What do you notice about the common multiples of different pairs of numbers? Discuss in class.
Answer: The common multiples are usually multiples of the least common multiple (LCM) of the two numbers. For instance, the LCM of 2 and 3 is 6, so all common multiples are multiples of 6. Some pairs have only a few common multiples early in the sequence, while others, like 5 and 10, have many overlapping multiples (10, 20, 30, etc.). As numbers grow larger, the common multiples also get larger and become more spread out.
In simple words: Common multiples follow a pattern - they repeat regularly, like counting by the LCM each time.

Exam Tip: The smallest common multiple you find is your LCM - all other common multiples are multiples of this LCM.

Question 2. Food is available at the end of a cobbled road. Robby, the rabbit, takes a jump of 4 each time. Deeku, the deer, takes a jump of 6 each time. They both start at 0. Will both Robby and Deeku reach the food? Who will reach first? How do you know? Explain your answer.
Answer: Robby starts at 0 and jumps by 4 each time, landing at: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64... Deeku starts at 0 and jumps by 6 each time, landing at: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66... Robby will reach the food at position 64 and Deeku will not land on that exact spot. We know this because 64 is a multiple of 4, but it is not a multiple of 6.
In simple words: We need to check if both jump distances divide evenly into 64. Since only 4 divides 64, only Robby lands there.

Exam Tip: When checking if both will reach a location, find the factors of that location number - if the jump size is a factor, they'll land there.

Question 3. Mowgli's friends live along the trail on the marked places below. Which of his friends will he be able to visit, if he jumps by 2 steps starting from 0?
Answer: When Mowgli jumps by 2 steps, he will land on these positions: 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20... From these landing spots, we can see that Mowgli will meet: Ant at position 4, Frog at position 12, Bird at position 14, Bear at position 30, Rabbit at position 50. Since 2 is a common factor of these positions, Mowgli can visit all four of these friends.
In simple words: Mowgli lands on every even number (multiples of 2). His friends are at positions that are all multiples of 2, so he can visit them all.

Exam Tip: Check each friend's position - if it appears in Mowgli's landing list, he can visit them. If not, he skips right past them.

Question. Which of his friends will he be able to meet if he jumps by 3 steps? 3 is a common factor of the numbers 9, 21, 39, and 57.
Answer: The positions where Mowgli can land when jumping by 3 steps are: 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... From these positions, we can see that Mowgli will meet: Spider at position 9, Frog at position 12, Snake at position 21, Bear at position 30, Deer at position 39, Monkey at position 57. Since 3 is a common factor, he can meet all six of these friends.
In simple words: Mowgli lands on every number divisible by 3. His friends are at those positions, so he can meet them all.

Exam Tip: Notice which positions Mowgli skips over - those positions are not multiples of his jump size.

Question. Which numbers will he touch if he jumps by 5 steps? _______ 5 is a common factor of the numbers _______
Answer: The positions where Mowgli can land when jumping by 5 steps are: 5, 10, 15, 20, 25, 30, 35, 40... These are all multiples of 5. So, Mowgli will meet his friends at positions 5, 10, 15, 20, 25 and 30. 5 is a common factor of the numbers: 5, 10, 15, 20, 25, 30, 35, 40...
In simple words: When jumping by 5, Mowgli lands only on numbers that end in 0 or 5.

Exam Tip: Numbers divisible by 5 always end in either 0 or 5 - this is a quick way to check without doing division.

Question. Which numbers will he touch if he jumps by 10 steps? ______ 10 is a common factor of the numbers ______.
Answer: The positions where Mowgli can land when jumping by 10 steps are: 10, 20, 30, 40, 50... These are all multiples of 10. So, Mowgli will meet his friends at positions 10, 20, 30, 40 and 50. 10 is a common factor of the numbers: 0, 10, 20, 30, 40, 50...
In simple words: When jumping by 10, Mowgli lands only on numbers ending in 0.

Exam Tip: Multiples of 10 always have a 0 at the end - this makes them very easy to spot.

Question 4. Let us find some common factors of the numbers 24 and 36. Note that all jumps in the following questions start from 0.
(a) Can we jump by 2 steps at a time to reach both 24 and 36? Yes/No. 2 is/is not a common factor of 24 and 36.
Answer: We can divide both numbers by 2. When we compute 24 ÷ 2 = 12 and 36 ÷ 2 = 18, we see that both divide evenly. So 2 is a common factor of 24 and 36. Yes, we can jump by 2 steps to reach both numbers.
In simple words: If both numbers divide evenly by the same number, that number is a common factor.

Exam Tip: Always verify by dividing both numbers - if both give whole results with no remainder, you have found a common factor.

Question. (b) Can we jump by 3 steps at a time to reach both 24 and 36? Yes/No. 3 is/is not a common factor of 24 and 36.
Answer: We can divide both numbers by 3. When we calculate 24 ÷ 3 = 8 and 36 ÷ 3 = 12, we see that both divide evenly. So 3 is a common factor of 24 and 36. Yes, we can jump by 3 steps to reach both numbers.
In simple words: Both 24 and 36 split into 3 equal parts with nothing left over, so 3 works as a common factor.

Exam Tip: Common factors divide evenly into all given numbers - check by division to confirm.

Question. (c) Can we jump by 4 steps at a time to reach both 24 and 36? Yes/No. 4 is/is not a common factor of 24 and 36.
Answer: We can divide both numbers by 4. When we work out 24 ÷ 4 = 6 and 36 ÷ 4 = 9, we see that both divide evenly. So 4 is a common factor of 24 and 36. Yes, we can jump by 4 steps to reach both numbers.
In simple words: Both numbers divide cleanly by 4, confirming that 4 is a common factor.

Exam Tip: The more common factors two numbers share, the stronger their relationship - look for these shared divisors.

Question. (d) What other jumps can we take to reach both 24 and 36?
Answer: We already know 2, 3 and 4 are common factors. Now let us list all factors: Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factors of 24 and 36 are 1, 2, 3, 4, 6, 12. So, the other jumps we can take to reach both 24 and 36 are 1, 2, 3, 4, 6 and 12 (we already found 2, 3, and 4, so the additional ones are 1, 6, and 12).
In simple words: List all factors of both numbers, then circle the ones that appear in both lists - those are the common factors.

Exam Tip: When listing factors, start with 1 and the number itself, then find the pairs in between systematically.

Question. (e) How many common factors can you find for 24 and 36? List them.
Answer: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. The common factors of 24 and 36 are 1, 2, 3, 4, 6, 12. There are 6 common factors in total.
In simple words: Find all the numbers that divide evenly into both 24 and 36 - count them to get your total.

Exam Tip: Make a comparison table with two columns (one for each number) to make it easy to spot which factors match.

Question. (f) What about jumping by 1 step each time to reach both 24 and 36?
Answer: Yes, we can jump by 1 step to reach both. Since 1 is a factor of every number, it divides both 24 and 36 evenly.
In simple words: Every number can be divided by 1, so 1 is always a common factor of any pair of numbers.

Exam Tip: Remember that 1 is a universal factor - it divides every whole number perfectly.

Question 5. What are the common factors of 12 and 13?
Answer: Factors of 12: 1, 2, 3, 4, 6, 12. 13 is a prime number, which means it has only two factors: 1 and 13. Comparing the two lists, the only common factor of 12 and 13 is 1.
In simple words: Prime numbers like 13 only divide by 1 and themselves, so their only common factor with other numbers is usually just 1.

Exam Tip: When one number is prime, look for 1 as the common factor - that is often the only one unless the prime happens to divide the other number.

Question 6. Find which of the following numbers can be reached by jumps of 4 steps? 4 is the common factor of the numbers _____.
Answer: We can test each number by dividing by 4. When we calculate: 10 ÷ 4 = 2.5 (not whole), 16 ÷ 4 = 4 (whole), 27 ÷ 4 = 6.75 (not whole), 36 ÷ 4 = 9 (whole), 48 ÷ 4 = 12 (whole). The numbers 16, 36 and 48 can be reached by jumps of 4 steps. Therefore, 4 is a common factor of 16, 36 and 48.
In simple words: Check each number by dividing by 4. If you get a whole number with no leftovers, that number works.

Exam Tip: You can also check by seeing if the number appears in the times table of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...

Question 7. Find the common factors of the following pairs of numbers.
(a) 12 and 16
(b) 8 and 12
(c) 4 and 16
(d) 2 and 9
(e) 3 and 5
(f) 12 and 15
(g) 20 and 5
(h) 9 and 21
(i) 6 and 27
Answer:
(a) Factors of 12: 1, 2, 3, 4, 6, 12 | Factors of 16: 1, 2, 4, 8, 16 | Common factors: 1, 2, 4
(b) Factors of 8: 1, 2, 4, 8 | Factors of 12: 1, 2, 3, 4, 6, 12 | Common factors: 1, 2, 4
(c) Factors of 4: 1, 2, 4 | Factors of 16: 1, 2, 4, 8, 16 | Common factors: 1, 2, 4
(d) Factors of 2: 1, 2 | Factors of 9: 1, 3, 9 | Common factors: 1
(e) Factors of 3: 1, 3 | Factors of 5: 1, 5 | Common factors: 1
(f) Factors of 12: 1, 2, 3, 4, 6, 12 | Factors of 15: 1, 3, 5, 15 | Common factors: 1, 3
(g) Factors of 20: 1, 2, 4, 5, 10, 20 | Factors of 5: 1, 5 | Common factors: 1, 5
(h) Factors of 9: 1, 3, 9 | Factors of 21: 1, 3, 7, 21 | Common factors: 1, 3
(i) Factors of 6: 1, 2, 3, 6 | Factors of 27: 1, 3, 9, 27 | Common factors: 1, 3
In simple words: Write all factors of each number, then pick out the ones that match in both lists.

Exam Tip: The number 1 is always a common factor, but look for other shared factors too to show deeper understanding.

Question. What do you notice about the common factors of different pairs of numbers. Discuss in class.
Answer: The number 1 is always a common factor of every pair of numbers because every number divides by 1. Some pairs share more common factors. For example, 12 and 16 both have 1, 2 and 4 as common factors. Number pairs that have no other common factors besides 1 (such as 2 and 9 or 3 and 5) are called coprime numbers or relatively prime numbers. These pairs share only 1 as their common factor.
In simple words: Every pair of numbers has 1 as a common factor. Some pairs are lucky and share other common factors too. Pairs with only 1 in common are called coprime.

Exam Tip: Coprime pairs have no shared prime factors - this is a helpful pattern to recognize for advanced work.

Question 8. State whether the following statements are true (T) or false (F).
(a) Factors of even numbers must be even.
Answer: False (F) Even numbers are divisible by 2, such as 2, 4, 6, 8, etc. However, the factors of an even number include both even and odd numbers. For example, the factors of 6 are 1, 2, 3 and 6. Here, 1 and 3 are odd. So not all factors of even numbers are even.
In simple words: Even numbers can have odd factors like 1 and 3, so this statement is incorrect.

Exam Tip: Always test claims with examples - one counterexample is enough to prove a statement false.

Question. (b) Multiples of odd numbers cannot be even.
Answer: False (F) Odd numbers include 1, 3, 5, 7, etc. However, multiples of odd numbers can be even. For instance, the multiple of 3 is 6 (which is even). When you multiply an odd number by an even number, you get an even result. So multiples of odd numbers can be even.
In simple words: Even though 3 is odd, 3 times 2 gives 6, which is even. So odd numbers can have even multiples.

Exam Tip: Remember the rule: odd × even = even, and odd × odd = odd.

Question. (c) Factors of odd numbers cannot be even.
Answer: True (T) Odd numbers are not divisible by 2. Therefore, their factors must all be odd. For example, the factors of 9 are 1, 3 and 9 - all of them are odd. Since an even number (which is divisible by 2) cannot divide an odd number evenly, odd numbers have no even factors.
In simple words: Odd numbers can only split into odd pieces, never even pieces.

Exam Tip: If a number is odd, every divisor that breaks it into whole pieces must also be odd.

Question. (d) One of the common multiples of two consecutive numbers is their product.
Answer: True (T) Consecutive numbers are numbers that follow each other in order, like 3 and 4 or 10 and 11. The product of two consecutive numbers will always be a common multiple of both. For example, for 3 and 4, their product is 12, and 12 is a multiple of both 3 and 4 (since 3 × 4 = 12 and 4 × 3 = 12).
In simple words: When you multiply two numbers together, the answer is always a multiple of both numbers.

Exam Tip: Multiplying two numbers always produces a common multiple of those numbers - sometimes the smallest, sometimes not.

Question. (e) The only common factor of any two consecutive numbers is 1.
Answer: True (T) Consecutive numbers share no other common factor besides 1. For example, 4 has factors 1, 2 and 4, while 5 has factors 1 and 5. The only number in common is 1. This is always the case because consecutive numbers differ by 1, which means they cannot both be divisible by any number greater than 1. Therefore, the only common factor is always 1.
In simple words: Numbers that sit next to each other on the number line only share 1 as a common factor.

Exam Tip: Consecutive numbers are always coprime - they have no shared prime factors.

Question. (f) 0 cannot be a factor of any number.
Answer: True (T) 0 cannot be a factor of any number because multiplying any number by 0 gives 0, not the original number. Also, division by 0 is not defined or possible in mathematics. Therefore, 0 is not a factor of any number.
In simple words: Since we cannot divide by 0, it cannot be a factor of anything.

Exam Tip: Remember - factors are divisors, and you can never divide by zero. Factors always start from 1.

Question 9. Sher Khan, the tiger, goes hunting every 3rd day. Bagheera, the panther, goes hunting every 5th day. If both of them start on the same day, on which days will they be hunting together?
Answer: Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... Multiples of 5: 5, 10, 15, 20, 25, 30, 35... The first number appearing in both lists is 15. After that, we find 30. So they will hunt together on the 15th, 30th day and so on, following a pattern of every 15 days.
In simple words: Write out when each animal hunts, then find the days they both hunt - those are your answers.

Exam Tip: The first common multiple is the LCM - all other common multiples are multiples of this number.

Question 10. (a) In the trail shown earlier, Sher Khan's house is on number 25 and that of Baloo the bear is on number 30. Mowgli wants to meet his friend Baloo the bear but wants to avoid Sher Khan's house. How long (in steps) could each jump be?
Answer: We need to find a jump size that lands exactly on 30 but skips over 25. First, let us find the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30. Now let us test each one. If Mowgli jumps 1 step, he lands on 1, 2, 3... and reaches 25, then 26, 27... 30. This lands on 25, so it does not work. If he jumps 2 steps, he lands on 2, 4, 6... 24, 26... 30. He skips 25. If he jumps 3 steps, he lands on 3, 6, 9... 24, 27, 30. He skips 25. If he jumps 5 steps, he lands on 5, 10, 15, 20, 25... This lands on 25, so it doesn't work. If he jumps 6 steps, he lands on 6, 12, 18, 24, 30. He skips 25. If he jumps 10 steps, he lands on 10, 20, 30. He skips 25. If he jumps 15 steps, he lands on 15, 30. He skips 25. So Mowgli can choose jump lengths of 2, 3, 6, 10, or 15 steps to reach 30 while avoiding 25.
In simple words: Find a divisor of 30 that does not divide 25 - then Mowgli can use that jump size.

Exam Tip: Test each jump size by listing the landing positions - if 25 appears, that jump does not work.

Question. (b) What number of jumps (in steps) he could choose so that he can meet both Kaa, the snake, at 21 and Akela, the wolf, at 35?
Answer: Kaa is at position 21 and Akela is at position 35. For Mowgli to meet both, he must select a jump size that lands on both 21 and 35. This means finding the common factors of 21 and 35. Factors of 21: 1, 3, 7, 21. Factors of 35: 1, 5, 7, 35. The common factors are 1 and 7. If Mowgli jumps by 1 step, he visits everyone, so that's not helpful. If Mowgli jumps by 7 steps: 7 × 3 = 21 (he meets Kaa) and 7 × 5 = 35 (he meets Akela). Therefore, Mowgli should jump by 7 steps, which allows him to meet both Kaa and Akela.
In simple words: Find a jump size that is a factor of both 21 and 35 - that way, Mowgli lands on both positions.

Exam Tip: To reach two locations with one jump size, find a common factor of both position numbers.

Question 11. Sort the following numbers into those that are divisible by 2 only, divisible by 5 only, divisible by 10 only, and divisible by 2, 5, and 10.
Answer:
(a) Divisible by 2 only: This means the number divides by 2 but not by 5 or 10. Such numbers have an even last digit but do not end in 0 or 5. From the given set (90, 22, 38, 30, 75, 45, 66, 78, 62, 40, 84, 56, 25, 95, 55), the numbers divisible by 2 only are: 22, 38, 62, 66, 78, 84, 56.
(b) Divisible by 5 only: This means the number divides by 5 but not by 2 or 10. Such numbers end in 5 (not 0). The numbers divisible by 5 only are: 25, 45, 55, 75, 95.
(c) Divisible by 10 only: This means the number divides by 10 but not solely by 2 or 5. This is not possible because any number divisible by 10 must also be divisible by both 2 and 5.
(d) Divisible by 2, 5, and 10: A number is divisible by 2 if its last digit is even (0, 2, 4, 6, 8). A number is divisible by 5 if its last digit is 0 or 5. A number is divisible by 10 if its last digit is 0. For a number to be divisible by all three, it must end in 0. The numbers divisible by 2, 5 and 10 are: 30, 40, 90.
In simple words: Check the last digit of each number - this tells you whether it is divisible by 2, 5, or 10.

Exam Tip: A quick divisibility trick: last digit even means divisible by 2; last digit 0 or 5 means divisible by 5; last digit 0 means divisible by 10.