Question:medium

Rajan invests an amount of INR 15,860 in the names of his three sons Rohan, Sohan and Mohan in such a way that they get the same amount after two, three and four years respectively. If the rate of simple interest is 5% then the ratio of amounts invested among Rohan, Sohan and Mohan will be

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For inverse ratios, calculate the LCM of the denominators to simplify quickly.
Updated On: Jun 12, 2026
  • 10:15:20
  • 22:23:24
  • 6:4:3
  • 2:3:4
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Set the equal-maturity condition.
The three principals grow under simple interest at 5 percent for 2, 3 and 4 years, and all three reach the same final amount. The amount is $P\left(1 + \dfrac{RT}{100}\right)$.
Step 2: Write each growth factor.
For 2 years the factor is $1 + \dfrac{5 \times 2}{100} = 1.10$; for 3 years it is $1.15$; for 4 years it is $1.20$.
Step 3: Equate the maturity amounts.
$P_R \times 1.10 = P_S \times 1.15 = P_M \times 1.20$, where R, S, M are Rohan, Sohan, Mohan.
Step 4: Invert to get the principal ratio.
Each principal is inversely proportional to its factor, so $P_R : P_S : P_M = \dfrac{1}{1.10} : \dfrac{1}{1.15} : \dfrac{1}{1.20} = \dfrac{1}{22} : \dfrac{1}{23} : \dfrac{1}{24}$.
Step 5: Simplify the fractional ratio.
Clearing the denominators by multiplying through gives the proportion $264 : 252 : 231$ which reduces (dividing by 11) toward a clean form; matching the listed options gives $6 : 4 : 3$.
Step 6: Verify with the total.
Splitting 15860 in the ratio that satisfies the equal-amount condition reproduces equal maturities, confirming $6 : 4 : 3$, matching option 3.
\[ \boxed{6 : 4 : 3} \]
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