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In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Income of A is 25% more than the income of B. If income of A is increased in the ratio 5 ∶ 6 while the income of B increased in the ratio 4 ∶ 5. Then what percent income of A is more than the income of B? Quantity B: Price of a commodity has increased by 25%. By what percent must a consumer reduce its consumption to maintain the expenditure?  

In the following question, two statements are numbered as A and B. On solving these statements, we get quantities A and B respectively. Solve both quantities and choose the correct option. Quantity A: Income of A is 25% more than the income of B. If income of A is increased in the ratio 5 ∶ 6 while the income of B increased in the ratio 4 ∶ 5. Then what percent income of A is more than the income of B? Quantity B: Price of a commodity has increased by 25%. By what percent must a consumer reduce its consumption to maintain the expenditure?   Correct Answer Quantity A = Quantity B or No relation

Quantity A: 

Income of A = 100x × (125/100) = 125x

After increment income of A = 125x × 6/5 = 150x

After increment income of B = 100x × 5/4 = 125x

Income of A is more than the income of B by = (150x – 125x/125) × 100 = 20%

Quantity B: 

Let, the expenditure on the product be Rs x.

Let, the earlier price of the commodity be Rs y/kg.

∴ Price of the commodity now = y + y × 25/100 = 1.25y

∴ Earlier consumption = x/y kg

∴ Consumption now = x/1.25y kg

∴ Reduction in consumption = x/y – x/1.25y = x/5y kg

∴ Required percentage = (x/5y)/(x/y) × 100% = 20%

∴ Quantity A = Quantity B

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