Page 31 - Math Genius C5

E:\Working\Orange_Education\Math_Genius_5\Open_Files\CHAP_02
\\October 8, 2025 12:09 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

1. In 2025, a toy factory produced 22,466 toys in September, 1,90,895 toys in October
and 2,05,725 toys in November. What was the total number of toys produced in those
three months?
2. The population of a town is 72,31,572, of which, 47,97,237 are men. What is the
population of women of the town?
3. A textile factory produces 30,425 bedsheets per day. How many bedsheets will it
produce in 1 year?

4. A wholesaler purchased 1895 kg of rice for `53,060. Find the rate of rice per kg.

Making SuMS Equal

Sometimes two groups of numbers have unequal sums. By interchanging numbers from
the groups we can make the sums equal.
Let us try

Group A: 23, 49, 59, 80 (sum 211)
Group B: 34, 54, 62, 47 (sum 197)

Swap 59 (from A) with 54 (from B) Fast Check
• New sum of A = (211 – 59 + 54) = 206 Group A: 12, 65, 78, 90 (sum 245)

• New sum of B = (197 – 54 + 59) = 202 Group B: 25, 54, 61, 47 (sum 187)

Here, the sums are not equal. Can you balance the sums with a
Try swapping 49 and 47 single swap? Why or why not?
• New sum of A = 206 – 49 + 47 = 204

• New sum of B = 202 – 47 + 49 = 204

Now, both groups have equal sums.
So, we swap 49 and 59 from group A with 54 and 47 from group B to make their sums
equal.

Alternative way:
• Sum of the numbers of group A = 211

• Sum of the numbers of group B = 197
Difference of the sums = 211 – 197 = 14

14 ÷ 2 = 7
So, we need to interchange numbers from both groups, so that the sum of the numbers of

group A decreases by 7 and the sum of the numbers of group B increases by 7.
So, interchange 59 and 49 of group A with 54 and 47 of group B.
Then, the sum of group A = 23 + 47 + 54 + 80 = 204

and the sum of group B = 34 + 59 + 62 + 49 = 204.

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