Question

Rajan invests an amount of Rs. 15860 in the names of his three sons Rohan, Sohan and Mohan in such a way that they get the same amount after 2, 3 and 4 years respectively. If the rate of simple interest is 5%, then the ratio of amounts invested among Rohan, Sohan and Mohan will be
A) 10 : 15 : 20
B) 22 : 23 : 24
C) 6 : 4 : 3
D) 2 : 3 : 4

Answer 1

Hint: In the given question, first we let the amount invested by them. Later using the simple interest formula i.e. \[\dfrac{P\times R\times T}{100}\], we will equating the ratios of the simple interest of the three amount that is to be invested and it is given that the rate of simple interest is 5%. Then we will simplify the ratio and we will get the required ratio.

Complete step-by-step solution:
Let the amount invested be ‘x’, ‘y’ and ‘z’ respectively.
Total amount given i.e. principal amount = Rs. 15860
Rate of simple interest = 5%
Formula of the simple interest is given by;
Simple interest = \[\dfrac{P\times R\times T}{100}\]
Where,
P = principal amount
R = rate of interest given
T = time period given,
Now,
According to the question,
It is given the principal amount invested to Rohan, Sohan and Mohan in such a way that they get the same amount after 2, 3 and 4 years respectively.
Therefore,
\[\dfrac{x\times 5\times 2}{100}=\dfrac{y\times 5\times 3}{100}=\dfrac{z\times 5\times 4}{100}=k\]
Solving the above, we get
\[\Rightarrow \dfrac{10x}{100}=\dfrac{15y}{100}=\dfrac{20z}{100}=k\]
Solving the above expression for the value of ‘x’, ‘y’ and ‘z’, we get
\[\Rightarrow x=10k\]
\[\Rightarrow y=\dfrac{20}{3}k\]
\[\Rightarrow z=5k\]
Therefore,
\[\Rightarrow x:y:z=10k:\dfrac{20}{3}k:5k=30k:20k:15k\]
Thus, the ratio of the amount invested by Rohan, Sohan and Mohan will be
\[\Rightarrow 30:20:15\]
Dividing the ratio by 5, we obtain
\[\Rightarrow 6:4:3\]

Hence, the correct answer is option ‘C’.

Note: In order to solve the question, students should remember the formula of calculating a simple interest. They should be very careful while doing the calculation part to avoid making any error. Simple interest is the interest that is not compound as the interest is always given only on the principal amount i.e. interest is the same for every year.