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Given below are two quantities named A & B. Based on the given information; you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: The ratio of expenditure and savings is 3 : 2. If the income increases by 15% and the savings increase by 6%, then by how much percent should his expenditure increases? Quantity B: In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 litres of pure milk, the percentage of water in the mixture becomes m%. Find the value of m if the total quantity of mixture is 91 litres.

Given below are two quantities named A & B. Based on the given information; you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers. Quantity A: The ratio of expenditure and savings is 3 : 2. If the income increases by 15% and the savings increase by 6%, then by how much percent should his expenditure increases? Quantity B: In a mixture of milk and water, there is only 26% water. After replacing the mixture with 7 litres of pure milk, the percentage of water in the mixture becomes m%. Find the value of m if the total quantity of mixture is 91 litres. Correct Answer Quantity A < Quantity B

Quantity A:

The ratio of expenditure and savings is 3 : 2;

Suppose the income = x

∴ Expenditure = 3x/5 = 0.6x and

Savings = 2x/5 = 0.4x;

∵ The Income increases by 15% and the savings increases by 6%;

∴ New income = 1.15x and New savings = (0.4x) × 1.06 = 0.424x

∴ New expenditure = 1.15x – 0.424x = 0.726x

∴ Percentage increase in the expenditure = (0.726x – 0.6x)/0.6x = 21%

Quantity B:

Suppose total quantity = 91 litres

Initially the quantity of milk = 74% and water = 26%

Finally the quantity water = m% and milk = n% (Suppose)

∵ 7 litre of the mixture is replaced with pure milk;

⇒ 91 × 0.74 – 7 × 0.74 + 7 = 91 × n/100

⇒ 67.34 – 5.18 + 7 = 91n/100

⇒ 69.16 = 91n/100

⇒ n = 76%

∴ m = 100 – 76 = 24%

∴ Quantity A < Quantity B

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