Direction: Following question consists of a question followed by three statements I, II and III. You have to study the question and the statements and decide which of the statements (s) is/are necessary to answer the question.
Sri Gupta borrowed a sum at compound interest. What is the amount returned in 2 years?
I. The rate of interest is 5% per annum.
II. The simple interest incurred on the sum in 1 year is Rs. 600.
III. The borrowed sum is ten times the amount earned as simple interest in two years.
Solution
Correct Answer: Option D
We have to calculate the amount returned in 2 years.
From the formula of compound interest,
\(A = P \times {\left( {1 + \frac{r}{{100}}} \right)^n} \ldots \ldots \ldots \ldots \ldots \ldots ..\left( 1 \right)\)
A = amount to be returned after n years if principal is P & rate is r% (compounded annually)
The statement(s) which can provide us the values of P, r will give us the answer.
Given: n = 2 years
Using statement 1:
r = 5%
Using statement 2 :
The simple interest incurred on the sum in 1 year is Rs. 600.
We know that, simple Interest (SI) = Principal × rate × number of years ÷ 100
According to the question, SI = Rs. 600; number of years = 1
Using statement 3 :
The borrowed sum is ten times the amount earned as simple interest in two years.
If borrowed sum = P then amount earned as simple interest = P/10
We know that, simple Interest (SI) = Principal × rate × number of years ÷ 100
⇒ (P/10) = P × rate × 2 ÷ 100
⇒ Rate = 5%
∴The data in statement III alone are not sufficient to answer the question.
Combining statement II & III:
Rate = known from statement III
Principal can be calculated from statement II
Amount to be returned after n years can be calculated from formula 1.
Combining statement I & II:
Rate = known from statement I
Principal can be calculated from statement II
Amount to be returned after n years can be calculated from formula 1.
∴ II & Either I or III statements are required.
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