| Directions: Each question consists of a question and two statements I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the questions. Read both the statements and choose the appropriate option. [IBPS (PO) 2014] |
| What is the rate of interest per cent per annum? |
| I. An amount invested on simple interest becomes four times in 24 yr. |
| II. The difference between compound interest and simple interest for 2 yr on an amount of Rs. 10000 at that rate is Rs. 156.25. |
A) The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
B) The data either in statement I alone or in statement II alone are sufficient to answer the question
C) The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
D) The data in both statements I and II together are necessary to answer the question
E) The data even in both statements I and II together are not sufficient to answer the question
Correct Answer: B
Solution :
| From I, Let the principal be Rs. P. |
| Then, amount [a] = 4P |
| \[\therefore \]\[SI=4P-P=3P\]\[\Rightarrow \]\[T=24\,\,yr\] |
| \[\therefore \]\[\text{Rate}=\frac{SI\times 100}{P\times T}=\frac{3P\times 100}{P\times 24}=12.5%\] |
| From II, \[\text{Difference}=\frac{P{{R}^{2}}}{{{(100)}^{2}}}\] |
| \[\Rightarrow \]\[{{R}^{2}}=\frac{156.25\times 100\times 100}{10000}\]\[\Rightarrow \]\[{{R}^{2}}=156.25\] |
| \[\Rightarrow \]\[R=\sqrt{156.25}\]\[\Rightarrow \]\[R=12.5%\] |
| Hence, either I alone or II alone are sufficient to answer the question. |
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