What will be the ratio of simple interest earned by certain amount for 8 years and that for 12 years?

Answer

Verified

Hint:In this question, we will use a simple interest formula for both time periods and then find the ratio of both the terms.

Complete step-by-step answer:

Let, P be the principal amount that is taken or given on loan. Let, R be the percentage rate of interest per annum on P and let T be the time duration of the loan.Then, the formula to calculate simple interest is,Simple interest $=\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ T}}{100}$. Now, in a given question, let the principle amount be P and the rate of interest on which the amount is given on loan be R.Let, simple interest earned for P, given on rate R for 4 years be ${{S}_{1}}$.Therefore, using formula of simple interest we have,${{S}_{1}}=\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 4}}{100}$.And, let, simple interest earned for P, given on rate R for 6 years be ${{S}_{2}}$.Therefore, using formula of simple interest we have,${{S}_{2}}=\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 6}}{100}$.Now, ratio of ${{S}_{2}}$ to ${{S}_{1}}$is,$\begin{align} & \dfrac{{{S}_{2}}}{{{S}_{1}}}=\dfrac{\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 6}}{100}}{\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 4}}{100}} \\ & =\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 6}}{100}\div \dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 4}}{100} \\ \end{align}$ Changing divide sign to multiply by taking reciprocal, we get, $\dfrac{{{S}_{2}}}{{{S}_{1}}}=\dfrac{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 6}}{100}\times \dfrac{100}{\text{P }\!\!\times\!\!\text{ R }\!\!\times\!\!\text{ 4}}$ Cancelling equal terms, we get, $\dfrac{{{S}_{2}}}{{{S}_{1}}}=\dfrac{6}{\text{4}}=\dfrac{3}{2}$.Hence, the ratio of simple interest earned by a certain amount at the same rate of interest for 6 years and that for 4 years is 3 : 2.Note: In this type of questions, when all the terms, that is P, R, T are the same except one of them for two different cases, then the ratio of the simple interests of both the cases will be the ratio of unequal terms.

Exercise :: Simple Interest - General Questions

11.

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

Answer: Option C

Explanation:

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205.

S.I. for 5 years = Rs.		2205	x 5		= Rs. 3675
3

Principal = Rs. (9800 - 3675) = Rs. 6125.

Hence, rate =		100 x 3675	%	= 12%
6125 x 5

Video Explanation: https://youtu.be/UYwiBCRN39s

12.

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

A.	1 : 3
B.	1 : 4
C.	2 : 3
D.	Data inadequate
E.	None of these

Answer: Option C

Explanation:

Let the principal be P and rate of interest be R%.

Required ratio =

	P x R x 6
100

6PR

= 2 : 3.

	P x R x 9
100

9PR

Video Explanation: https://youtu.be/GaaEDwTWc6w

Page 2

Exercise :: Simple Interest - General Questions

A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

A.	3%
B.	4%
C.	5%
D.	6%
E.	None of these

Answer: Option D

Explanation:

An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes: