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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: A sum amounts to Rs. 13760 after 3 years and Rs. 17200 after 6 years, when interest is compounded annually. How much will it amount to at the same rate of interest after 9 years? Quantity B: A man borrowed a sum of  Rs. 12500 at a rate of 8% simple interest per annum for 1 year and 73 days. How much amount did he pay to clear his debt?

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: A sum amounts to Rs. 13760 after 3 years and Rs. 17200 after 6 years, when interest is compounded annually. How much will it amount to at the same rate of interest after 9 years? Quantity B: A man borrowed a sum of  Rs. 12500 at a rate of 8% simple interest per annum for 1 year and 73 days. How much amount did he pay to clear his debt? Correct Answer Quantity A > Quantity B

Quantity A: 

Suppose P = principal, R = rate of interest and N = Time

Amount = P(1 + R/100)N

Given,

⇒ 13760 = P(1 + R/100)3      ----(1)

⇒ 17200 = P(1 + R/100)6      ----(2)

Dividing and solving the above equations,

⇒ (1 + R/100)3 = 5/4

Then,

⇒ 13760 = P × 5/4

⇒ P = 11008

Required amount after 9 years = 11008 × (1 + R/100)9

= 11008 × (5/4)3 = Rs. 21500

Quantity B: 

Time = 1 + 73/365 = 1 + 1/5 = 6/5 yrs.

Now,

Simple interest = (Principal × rate × time)/100 = (12500 × 8 × 6/5)/100 = Rs. 1200

∴ Amount paid to clear debt = 12500 + 1200 = Rs. 13700

∴ Quantity A > Quantity B

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