NCERT Solutions for Class 5th Maths Chapter 4 Making Sums Equal — Making Sums Equal
Book page 42 Updated on2026-09-19
Q1.
Think what will happen to the sums if we interchange 2 and 5? Try interchanging other pairs of numbers and find the one that will make the sums equal.
Answer
If we swap 2 and 5, the two sums move further apart, not closer.
Left group now: 1 + 5 + 7 + 9 = 22 Right group now: 3 + 4 + 2 + 9 = 18 Before the swap the sums were 19 and 21. Now they are 22 and 18.
Why it happens: When you move a small number out and a bigger number in, the left group gains the difference between them. 5 − 2 = 3, so the left sum went up by 3 (19 → 22) and the right sum came down by 3 (21 → 18). The gap grew from 2 to 4.
So we must swap the other way round — send a number out and bring in one that is only a little bigger.
Here is how to find the right pair in 3 steps.
Add both sums: 19 + 21 = 40. Share it equally: 40 ÷ 2 = 20. Each group must reach 20.
The left group must gain 20 − 19 = 1. So the number coming in must be exactly 1 more than the number going out.
Look for such a pair: 2 is in the left group and 3 is in the right group, and 3 − 2 = 1.
One move is enough: 2 goes right, 3 comes left, and both sums become 20.
Tip: Always halve the total first. That tells you the target sum, and then you know exactly how much the smaller group has to gain.
Q2.
(a) Interchange pairs of numbers between the two groups to make their sums equal, using the least number of moves. Left group: 1, 2, 7, 9 (sum 19). Right group: 3, 4, 5, 9 (sum 21).
Answer
Interchange 2 and 3. One move is enough.
Total of both groups: 19 + 21 = 40.
Each group must have 40 ÷ 2 = 20.
The left group needs 20 − 19 = 1 more, so bring in a number that is 1 bigger than the one you send out.
2 goes out, 3 comes in.
Left: 1 + 3 + 7 + 9 = 20 Right: 2 + 4 + 5 + 9 = 20 Check: 20 + 20 = 40, the same total we started with ✓
Q3.
(b) Interchange pairs of numbers between the two groups to make their sums equal, using the least number of moves. Left group: 5, 7, 12, 15 (sum 39). Right group: 9, 11, 13, 14 (sum 47).
Answer
Interchange 5 and 9. One move is enough.
Total: 39 + 47 = 86.
Each group must have 86 ÷ 2 = 43.
The left group needs 43 − 39 = 4 more. So the number coming in must be 4 bigger than the one going out.
Another correct answer: Swapping 7 and 11 also works, because 11 − 7 = 4 as well. Left: 5 + 11 + 12 + 15 = 43. Right: 9 + 7 + 13 + 14 = 43.
Q4.
(c) Interchange pairs of numbers between the two groups to make their sums equal, using the least number of moves. Left group: 11, 15, 19, 23 (sum 68). Right group: 13, 17, 21, 25 (sum 76).
Answer
Here one move is not possible. You need two moves: interchange 11 and 13, and interchange 15 and 17.
Total: 68 + 76 = 144. Each group must have 144 ÷ 2 = 72.
The left group needs 72 − 68 = 4 more.
Try one swap. Look for a right-hand number that is exactly 4 bigger than a left-hand number: 11 needs 15, 15 needs 19, 19 needs 23, 23 needs 27. None of these is in the right group. So one move cannot work.
Now use two swaps. Send out 11 and 15 (that is 26) and bring in 13 and 17 (that is 30). The left group gains 30 − 26 = 4.
Why one move can never work here: Each left number leaves a remainder of 3 when divided by 4 (11, 15, 19, 23), and each right number leaves a remainder of 1 (13, 17, 21, 25). So the difference between any right number and any left number is 2, 6, 10 … — always 2 more than a multiple of 4. It can never be exactly 4.
Other correct answers: Swapping 11 with 13 and 19 with 21 also gives 72 and 72. Any two swaps whose numbers gain the left group exactly 4 will do.
Q5.
(d) Interchange pairs of numbers between the two groups to make their sums equal, using the least number of moves. Left group: 77, 78, 79, 80 (sum 314). Right group: 81, 82, 83, 84 (sum 330).
Answer
Again two moves are needed: interchange 77 and 81, and interchange 78 and 82.
Total: 314 + 330 = 644. Each group must have 644 ÷ 2 = 322.
The left group needs 322 − 314 = 8 more.
For one swap the incoming number would have to be 8 bigger than the outgoing one. But the biggest possible gap is 84 − 77 = 7. So one move is impossible.
Send out 77 and 78 (that is 155) and bring in 81 and 82 (that is 163). The gain is 163 − 155 = 8.
Other correct answers: 79 ↔ 83 with 80 ↔ 84 also works, and so does 77 ↔ 81 with 78 ↔ 82 in any order. Each pair of swaps must together add exactly 8 to the left group.