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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: Difference of two numbers is 672. If 7.5% of one number is 12.5% of the other number is equal, then what is the smaller number? Quantity B: Out of his total income, Sachin spends 35% on taxes and rent, from the remaining 40% on food and shopping. Half of the remaining he spends on his children’s school fee and saves remaining which is equal to Rs. 17550, then how much amount he spend on food and shopping?

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: Difference of two numbers is 672. If 7.5% of one number is 12.5% of the other number is equal, then what is the smaller number? Quantity B: Out of his total income, Sachin spends 35% on taxes and rent, from the remaining 40% on food and shopping. Half of the remaining he spends on his children’s school fee and saves remaining which is equal to Rs. 17550, then how much amount he spend on food and shopping? Correct Answer Quantity A < Quantity B

Quantity A: 

Let the two numbers be x and y.

∴ x – y = 672

⇒ 0.075 × x = 0.125 × y

∴ x = 5/3 × y

⇒ 5/3y – y = 672

⇒ 2/3y = 672

⇒ y = 3/2 × 672 = 1008

Quantity B: 

Let the income of Sachin be 100x.

Amount spend on taxes and rent = 35% of 100x = 35x

Amount spend on food and shopping = 40% of (100x - 35x) = 26x

Amount spend on School’s fee = (65x - 26x)/2 = 19.5x

Savings = 19.5x = 17550

x = 900

⇒ 26x = 900 * 26 = 23400

∴ Quantity A < Quantity B

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