Answer
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.
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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? | |||||||||||||||||||||||||||
Answer: Option C Explanation:
Let the principal be P and rate of interest be R%.
Video Explanation: //youtu.be/GaaEDwTWc6w |
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Exercise :: Simple Interest - General Questions
6. | 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? | |||||||||
Answer: Option D Explanation: |
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7. | 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: | |||||||||||||||||||
Answer: Option B Explanation:
Let the sum be Rs. 100. Then,
So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25 |
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