The following tables show the expenditure (in percentage) of two famil

The following tables show the expenditure (in percentage) of two families A and B :
Family A
20% Miscellaneous
30% Entertainment
50% Food
(Monthly income ₹ 20,000)

Family B
20% Entertainment
70% Miscellaneous
10% Food
(Monthly income ₹ 1,00,000)

Which one among the following statements is true?

Family A spends as much on miscellaneous as family B spends on entertainment
The food expense of family B is equal to the total expense of family A
Families A and B spend equally on food
Families A and B spend equally on entertainment
This question was previously asked in
UPSC CAPF – 2013
We are given the percentage expenditure of two families (A and B) in different categories and their monthly incomes. We need to calculate the absolute expenditure for each category for both families and then compare them based on the given statements.

Family A: Monthly income ₹ 20,000
Miscellaneous: 20% of ₹ 20,000 = 0.20 * 20000 = ₹ 4,000
Entertainment: 30% of ₹ 20,000 = 0.30 * 20000 = ₹ 6,000
Food: 50% of ₹ 20,000 = 0.50 * 20000 = ₹ 10,000
Total expenditure for Family A = 4000 + 6000 + 10000 = ₹ 20,000.

Family B: Monthly income ₹ 1,00,000
Miscellaneous: 70% of ₹ 1,00,000 = 0.70 * 100000 = ₹ 70,000
Entertainment: 20% of ₹ 1,00,000 = 0.20 * 100000 = ₹ 20,000
Food: 10% of ₹ 1,00,000 = 0.10 * 100000 = ₹ 10,000
Total expenditure for Family B = 70000 + 20000 + 10000 = ₹ 1,00,000.

Now let’s evaluate each statement:
A) Family A spends as much on miscellaneous as family B spends on entertainment.
Family A Misc: ₹ 4,000
Family B Ent: ₹ 20,000
₹ 4,000 ≠ ₹ 20,000. Statement A is false.

B) The food expense of family B is equal to the total expense of family A.
Family B Food: ₹ 10,000
Total expense of family A: ₹ 20,000
₹ 10,000 ≠ ₹ 20,000. Statement B is false.

C) Families A and B spend equally on food.
Family A Food: ₹ 10,000
Family B Food: ₹ 10,000
₹ 10,000 = ₹ 10,000. Statement C is true.

D) Families A and B spend equally on entertainment.
Family A Ent: ₹ 6,000
Family B Ent: ₹ 20,000
₹ 6,000 ≠ ₹ 20,000. Statement D is false.

The only true statement is C.

To compare expenditures from percentage data for different total amounts (incomes), it is necessary to calculate the absolute values of the expenditures.
This problem highlights the importance of understanding that percentages are relative values. A higher percentage of a smaller total can be less than a lower percentage of a larger total. Comparing percentages directly across different totals is misleading.