The following question have three statements. Study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. Suman borrowed some amount of money at compound interest for 3 years. Find the amount to be paid by her after 3 years. Statement I: Simple interest on the same sum at the same rate of interest in 5 years will be 1/4th of the principal. Statement II: The simple interest on the sum after 6 years will be Rs. 12000. Statement III: The sum borrowed is 5 times the simple interest of 4 years.?

Option 1 : Statement II and either Statement I or Statement III are sufficient to answer the question.

Suppose P, r and T are the principal, rate of interest and time respectively;

Statement I:

Simple interest on the same sum at the same rate of interest in 5 years will be 1/4^th of the principal;

∴ P/4 = (P × r × 5)/100

⇒ r = 5%

Statement III:

The sum borrowed is 5 times the simple interest of 4 years.

P = 5 × (SI of 4 years)

⇒ P = 5 × 4 × (SI of 1 year)

⇒ P = 20 × (SI of 1 year)

⇒ P = 20 × (P × r × 1)/100

⇒ r = 5%

Here we can see that Statement I and III both are giving the same information.

We get the value of r, now we need to find the principal P.

Statement II:

The simple interest on the sum after 6 years will be Rs. 12000.

∴ 12000 = (P × r × 6)/100

Putting r = 5%

⇒ 12000 = 30P/100

⇒ P = 40000

∴ We have principal Rs. 40000, rate of interest 5% and time 3 years, we can find the compound interest.