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The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A man clears a debt of Rs. 75000 by paying an amount of Rs. 94080. Find the rate of interest. I) He cleared his debt in 2 years. II) He paid an interest of Rs. 19080. III) The interest was compounded annually.

The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. A man clears a debt of Rs. 75000 by paying an amount of Rs. 94080. Find the rate of interest. I) He cleared his debt in 2 years. II) He paid an interest of Rs. 19080. III) The interest was compounded annually. Correct Answer I and III

Considering statement I,

Time = n = 2 years

Statement II is not required, as the interest is already known

Considering statement III,

When the interest is compounded annually,

Amount = Principal × (1 + Rate/100)n      ----(1)

Considering statements I and III,

Substituting values in eq. (1),

⇒ 94080 = 75000 × (1 + Rate/100)2

⇒ 1.2544 = (1 + Rate/100)2

⇒ 1.12 = (1 + Rate/100)

⇒ Rate = 100 × 0.12 = 12%

∴ The question can be answered using statements I and III only

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