At what rate of interest will a sum becomes three times itself in 25 by 2 years?

Answer

Hint: We will assume the sum invested as x rupees. We have been given that it becomes triple after 3 years which means it becomes 3 x. Now, we know that the final amount = principal amount + simple interest. So, we will find the simple interest from that and using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$, we will find the rate of interest.

Complete step-by-step answer:
We are given the time period as 16 years and that the sum becomes triple after 16 years. So, we will first assume the sum invested as Rs. x. We have been given that after 16 years, it becomes triple, so,
Final amount = $3\times x=3x$.
Now, we know that the final amount is the summation of the principal amount and simple interest,
Final amount = principal amount + simple interest, which can be written as,
3 x = x + simple interest, so we get the simple interest as = 3 x - x = 2 x.
Now, we have the principal amount, time and the simple interest, so we will find the rate using the formula, $\text{simple interest}=\dfrac{\text{principal amount}\times \text{time}\times \text{rate}}{100}$. So, by substituting the values of the parameters we get,
$\begin{align}
  & \dfrac{2x}{1}=\dfrac{x\times 16\times rate}{100} \\
 & \Rightarrow \dfrac{2}{1}=\dfrac{16\times rate}{100} \\
\end{align}$
On cross-multiplying, we get,
$\begin{align}
  & rate=\dfrac{2\times 100}{16} \\
 & \Rightarrow rate=12.5\% \\
\end{align}$
Hence, we get the rate of interest as 12.5 %.

Note: There is a possibility that the students think that the simple interest becomes triple of the principal amount, that is simple interest is 3 x. So, in further calculations for finding the rate of interest, they will end up with, $rate=\dfrac{3\times 100}{16}\Rightarrow 18.75\%$. But students should read the question carefully to understand that the sum becomes triple, which means the principal amount becomes triple after 16 years.

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Solution : Principal amount be P.<br> Amount= principal amount+simple interest<br> 3P=P +simple interest<br> =>simple interest=2P<br> =>`2P=(P xx R xx T)/100` given R=25%<br> =>`2 xx 4=8 yrs=T`

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Multiple Choice Questions

31.

The simple interest on ₹ 4000 in 3 yr at the rate of x% per annum equals to the simple interest on ₹ 5000 at the rate of 12% per annum in 2 yr. The value of x is

• 6%

• 8%

• 9%

• 10%

D.

10%

Two simple interest are equal.
According to the question,

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32.

Simple interest on a certain sum is 16/25 of the sum. The rate of per cent, if the rate per cent and time (in yr) are equal to

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• 10%

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B.

8%

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33.

The interest on a certain sum of money is ₹ 22 and the discount on the same sum for the same time and at the same rate is ₹ 20, find the sum.

• ₹ 220

• ₹ 200

• ₹ 210

• ₹ 212

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34.The rate of simple interest at which a sum of money becomes three times in 25 yr is8%5%4%6%

A.

8%

Let principal  = ₹ P
∴    S.I. = 3P - P = ₹ 2P
According to the question,
    

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35.

The simple interest on a sum for 5 yr is one-fourth of the sum. The rate of interest per annum is

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36.

₹ 800 becomes ₹ 956 in 3 yr at a certain rate of simple interest. If the rate of interest is increased by 4%. What amount will ₹ 800 become in 3 yr?

• ₹ 1020.80

• ₹ 1025

• ₹ 1052

• ₹ 1050

C.

₹ 1052

Simple interest (SI) for 3yr  = ₹ 956  - ₹ 800 = ₹ 156 

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37.

A person lent certain sum of money at 5% per annum simple interest and in 15 years the interest amounted to ₹ 250/- less than the sum lent. What was the sum lent (in ₹)?

• ₹ 1,000/-

• ₹ 1,500/-

• ₹ 2,400/-

• ₹ 3,000/-

A.

₹ 1,000/-

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