Question : A sum of Rs. 5,000 is divided into two parts such that the simple interest on the first part for $4 \frac{1}{5}$ years at $6 \frac{2}{3} \%$ p.a. is double the simple interest on the second part for $2 \frac{3}{4}$ years at 4% p.a. The ratio of the second part to the first part is:
Option 1: 11:14
Option 2: 11 : 13
Option 3: 14 : 11
Option 4: 13 : 11
Correct Answer: 14 : 11
Solution :
Let the first part of the sum as $x$ and the second part as $5000 - x$.
Given that the simple interest on the first part is double the simple interest on the second part.
$x \times \frac{21}{5} \times \frac{20}{3} \% = 2 \times (5000 - x) \times \frac{11}{4} \times 4 \%$
$⇒x \times \frac{7}{5} \times \frac{1}{15} = (5000 - x) \times 11 \times \frac{1}{50}$
$⇒14x= 55000 - 11x$
$⇒x = 2200$
The second part of the sum = 5000 – 2200 = 2800
So, the ratio of the second part to the first part = 2800 : 2200 = 14 : 11
Hence, the correct answer is 14 : 11.
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