Question : A sum of Rs. 7,930 is divided into three parts and given on loan at 5% simple interest to A, B, and C for 2, 3, and 4-year periods, respectively. If the amounts of all three are equal after their respective periods of loan, then A received a loan of:
Option 1: Rs. 3,050
Option 2: Rs. 2,760
Option 3: Rs. 2,750
Option 4: Rs. 2,800
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Correct Answer: Rs. 2,760
Solution :
Let the loans taken by A, B, and C be Rs. $p$, Rs. $q$, and Rs. $r$ respectively.
$⇒p + q + r = 7930$
$\text{Simple interest} = \frac{\text{Principal × Time × Rate}}{100}$
$⇒p + \frac{p \times 2 \times 5}{100} = q + \frac{q \times 3 \times 5}{100} = r + \frac{r \times 4 \times 5}{100}$
$⇒110p = 115q = 120r$
$⇒22p = 23q = 24r$
The least common multiple (LCM) of 22, 23, and 24 is 6072.
$⇒22p = 23q = 24r = 6072$
$⇒p = \frac{6072}{22} = 276$
Similarly for $q$ and $r.$
The $p: q: r$ is $276: 264: 253$.
The sum of the terms of the ratio is $276 + 264 + 253 = 793$.
A’s loan =$\frac{276}{793}\times 7930= 2760$
Hence, the correct answer is Rs. 2,760.
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