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)