Direction: In each of the following questions, a question is asked followed by three statements. You have to study the questions and all the three statements given and decide whether any information provided in the statement(s) is/are redundant and can be dispensed with while answering the questions.
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The difference between the compound interest and the simple interest at the same rate on a certain amount at the end of two years is $ 12.50. What is the rate of interest?
A. Simple interest for two years is $ 500.
B. Compound interest for two years is $ 512.50.
C. Amount on simple interest after two years becomes $ 5500.
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- A or B only
- A or C only
- C only
- C and either A or B
- Any two of (A), (B) and (C)
Correct Option: E
As per the given all details in above question , we can say that
Anyone of the three statements is alone sufficient to answer the question. So, any two can be dispensed with.
From (A) alone:
| Rate = | (CI - SI) x 2 | x 100 = | 25 | x 100 = 5% |
| SI |
From (B) alone :
CI = $512.5
∴ SI = $512.5 − $12.5 = $ 500
Again,
| Rate = | (CI - SI) x 2 | x 100 |
| SI |
| Rate = | 25 | x 100 = 5% |
| 500 |
From (C) alone :
Suppose Principal = P and Rate of Interest = r%
| Then, P |  | 1 + | r |  | 2 | = 5500 + 12.5 = 5512.5 ...(1) |
| 100 |
| and, P + | 2rP | = 5500 |
| 100 |
| or, P |  | 1 + | 2r |  | = 5500 ...(2) |
| 100 |
Dividing (1) by (2) we have
[1 + ( r / 100 )]2 /[1 + ( 2r / 100 )] = 5512.5 / 5500 ....(3)
This is a quadratic equation which has only one variable, r. It can be solved. Hence, value of r can be obtained.
Note : is satisfied with the value r = 5.
So, it confirms that equation is solvable.
