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The question below is followed by three statements I, II and III. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. What is the rate of interest per annum? I. An amount doubles itself at simple interest in 8 years. II. The difference between the compound interest and the simple interest on an amount of Rs. 20,000 in two years is Rs. 200. III. The Simple interest accrued in 10 years is more than the amount (principal).

The question below is followed by three statements I, II and III. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. What is the rate of interest per annum? I. An amount doubles itself at simple interest in 8 years. II. The difference between the compound interest and the simple interest on an amount of Rs. 20,000 in two years is Rs. 200. III. The Simple interest accrued in 10 years is more than the amount (principal). Correct Answer Only either I or II

Statement I,

Let, rate of interest = r%

Principal = p

Time = 8 years

Amount = 2p

According to problem,

⇒ 2p - p = p × r × 8/100

⇒ r = 100/8

⇒ r = 12.5%

∴ We get the value of rate of interest from (I)

Statement II.

Let, rate of interest = r%

No. of years = 2

Principal = Rs. 20000

∴ Simple interest earned,

⇒ 20000 × 2 × r/100

⇒ 400r

∴ Compound interest earned,

⇒ 20000 × (1 + r/100)2 - 20000

⇒ 20000 + 400r + 2r2 - 20000

⇒ 400r + 2r2

According to problem,

⇒ 400r + 2r2 - 400r = 200

⇒ r2 = 100

⇒ r = 10

∴ We get the value of rate of interest from (II)

Statement III.

Let, rate of interest = r%

Principal = p

No. of years = 10

∴ Interest accrued,

⇒ p × r × 10/100

⇒ pr/10

According to problem,

⇒ pr/10 > p

⇒ r > 10

We do not get any conclusive value of r from III.

∴ We get the value of r from either I or II only.

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