Question

If the interest on 1700 rupees is 340 rupees for 2 years, the rate of interest must be:
a. 12%
b. 15%
c. 4%
d. 10%

Answer 1

Hint: In order to find the solution of this question, we should know about the concept of simple interest, that is, simple interest is given by the formula, $I=\dfrac{P\times R\times T}{100}$, where I represents the interest, P represents the principal amount, R represents the rate of interest and T represents the time for which the interest is applied. By using this concept, we can find the answer to this question.

Complete step-by-step solution -
 In this question, we have been asked to find the rate of interest applied on Rs. 1700 for 2 years, such that the interest becomes Rs. 340. To solve this question, we should know that the simple interest is calculated by, $I=\dfrac{P\times R\times T}{100}$, where I represents the interest obtained over the principal amount, P represents the principal amount on which the interest is applied, R represents the rate of interest and T represents the time for which the interest is applied
So, let us consider the rate of interest as R. Therefore, we can say that according to the question, we have P = Rs. 1700, I = Rs. 340 and T = 2 years. So, we can write the formula of simple interest as follows.
$340=\dfrac{1700\times R\times 2}{100}$
Now, we will keep the variable R on one side and rest all terms on the other side. So, we get,
 $R=\dfrac{340\times 100}{1700\times 2}$
Now, on further simplification, we get,
$R = 10$
Hence, we can say that the rate of interest is 10% on Rs. 1700 for 2 years to obtain the interest of Rs. 340. Therefore, option (d) is the correct answer.

Note: While solving this question, the possible mistakes one can make is either the calculation mistake or by writing the wrong formula. One might think of applying the formula of compound interest, but that is wrong because every time, compound interest is applied, the interest increases, but here the interest is constant. So, we have to apply the formula of simple interest and not compound interest.