Direction: In the following question, a questions is followed by information given in three statements. You have to study the question along with the statements and decide, the information given in which of the statements (s) is necessary to answer the question.
What is the rate of interest p.c.p.a.?
I. Simple interest earned per annum is Rs. 5,300
II. The difference between the compound and simple interest on an amount at the above stated interest rate is Rs. 1,060 at the end of 2 years
III. An amount doubles itself in 5 years with simple interest.
Solution
Correct Answer: Option D
We know that simple interest (SI) = principal (P) × rate of interest (r) × time
From statement I:
Given: SI = Rs. 5300
Time = 1 year
⇒ 5300 = P × r ………………. (1)
From statement II:
We know that difference between CI & SI after 2 years if rate of SI & CI are same = \({P} \times {\left( {\frac{r}{{100}}} \right)^{2\;}}\)
According to the statement: \({P} \times {\left( {\frac{r}{{100}}} \right)^{2\;}} = 1060 \ldots \ldots \ldots \ldots \ldots .\left( 2 \right)\)
[CI = compound interest, P = principal; r = rate of interest]
Statement (1) & (2) can be solved simultaneously as there are 2 variables & 2 equations.
From statement III:
Assume that the amount is Q.
The amount doubles itself in 5 years with simple interest.
∴Simple interest = amount – principal = 2Q – Q = Q
\(\Rightarrow \frac{{Q \times 5 \times R}}{{100}} = Q\)
⇒ R = 20%
[R = rate of interest]
∴The question can be answered by using only the 3rd option or using options I and II.
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