You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question.
In how many years will a sum of money put at simple interest treble itself?
A. The interest earned in 4 years is half the sum.
B The rate of interest is 12%
C. The sum doubles itself in 8 years at simple interest.
Choose the correct answer from the options given below:
(1) A and B only
(2) B and C only
(3) A and C only
(4) Either of A or B or C
(1) 1
(2) 2
(3) 3
(4) 4
EXPLANATION
Let’s denote the principal amount as P, the rate of interest as R, and the time as T.
The formula for simple interest is given by: Simple Interest = (P * R * T) / 100
Now, we want to find the time (T) it takes for the sum to treble itself.
Trebling the principal means the final amount is three times the initial amount. So, the formula for the final amount is: Final Amount = P + Simple Interest = P + (P * R * T) / 100
Now, we can evaluate each statement:
A. The interest earned in 4 years is half the sum. This statement does not provide information about the rate of interest or the time required for the sum to treble itself. It is not sufficient.
B. The rate of interest is 12%. This statement provides the rate of interest (R), but we still need information about the principal amount and time. It is not sufficient.
C. The sum doubles itself in 8 years at simple interest. This statement provides information about the time (T) it takes for the sum to double. It is not directly related to trebling the sum, but it gives information about the time, which is crucial. It is not sufficient on its own.
Combining statements A and C: Statement A provides information about the interest earned in 4 years, and statement C provides information about the time it takes for the sum to double. Combining these, we can potentially calculate the rate of interest and then use that to find the time needed to treble the sum. So, together, they are sufficient.
Therefore, the correct answer is (3) A and C only.
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