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Given below are two quantities named A and 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: A sum of Rs. 22500 amounts to Rs. 34500 in 5 years at simple interest. What is the rate of interest? Quantity B: A sum amount of money amounts to Rs. 12000 in a year and to Rs. 15000 in 2 years on simple interest. Find the rate of interest.

Given below are two quantities named A and 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: A sum of Rs. 22500 amounts to Rs. 34500 in 5 years at simple interest. What is the rate of interest? Quantity B: A sum amount of money amounts to Rs. 12000 in a year and to Rs. 15000 in 2 years on simple interest. Find the rate of interest. Correct Answer Quantity A < Quantity B

Quantity A:

Principal = Rs. 22500

Amount = Rs. 34500

Simple Interest = 34500 – 22500 = 12000

Time period = 5

Let P = Principal, R = rate of interest per annum and N = time

Simple Interest = PNR/100

12000 = (22500 × R × 5)/100

12000 = 1125R

R = 12000/1125

R = 10.66%

Rate of interest is 10.66% per annum.

Quantity B:

Let amount of money be Rs. a

Given,

Let rate of interest per annum be R.

Amount = Rs. 12000 and N = 1

Simple interest = 12000 – a

12000 – a = (a × R × 1)/100

1200000 – 100a = aR

Amount = Rs.15000 and N = 2

(15000 – a) = (a × R × 2)/100

750000 – 50a = aR

1200000 – 100a = 750000 – 50a

450000 = 50a

a = 9000

Put this value in any equation then R,

9000 × R = 750000 – 50 × 9000

9R = 750 – 50 × 9

9R = 300

R = 33.33%

From above solution,

Relation between Quantity A < Quantity B is established.

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