Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. In the last four years, a man donated 5%, 8%, 10% and 12% of his income respectively. He had also received an increment of 15%, 20% and 25% in the second, third and fourth year respectively. Quantity A: What is the percentage increase in his donation in second year as compared to the first year? Quantity B: What is the percentage increase in his donation in third year as compared to the second year? Quantity C: What is the percentage increase in his donation in fourth year as compared to the third year?

Given below are three quantities named A, B and C. Based on the given information, determine the relation among the three quantities. In the last four years, a man donated 5%, 8%, 10% and 12% of his income respectively. He had also received an increment of 15%, 20% and 25% in the second, third and fourth year respectively. Quantity A: What is the percentage increase in his donation in second year as compared to the first year? Quantity B: What is the percentage increase in his donation in third year as compared to the second year? Quantity C: What is the percentage increase in his donation in fourth year as compared to the third year? Correct Answer Quantity A > (Quantity B = Quantity C)

Let his income in first year be Rs. ‘x’

⇒ Donation in first year = 5% of x = 0.05x

Income in second year = x + 15% of x = 1.15x

⇒ Donation in second year = 8% of 1.15x = 0.092x

Income in third year = 1.15x + 20% of 1.15x = 1.38x

⇒ Donation in third year = 10% of 1.38x = 0.138x

Income in fourth year = 1.38x + 25% of 1.38x = 1.725x

⇒ Donation in fourth year = 12% of 1.725x = 0.207x

Solving for Quantity A:

Increase in donation in second year as compared to first year = 0.092x – 0.05x = 0.042x

⇒ Quantity A = Percentage increase = (0.042x/0.05x) × 100 = 84%

Solving for Quantity B:

Increase in donation in third year as compared to second year = 0.138x – 0.092x = 0.046x

⇒ Quantity B = Percentage increase = (0.046x/0.092x) × 100 = 50%

Solving for Quantity C:

Increase in donation in fourth year as compared to third year = 0.207x – 0.138x = 0.069x

⇒ Quantity C = Percentage increase = (0.069x/0.138x) × 100 = 50%

∴ Quantity A > (Quantity B = Quantity C)

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