Question : A sum of Rs 27,000 is divided into two parts A and B such that the simple interest at the rate of 15% p.a. on A and B after two years and four years, respectively, is equal. The total interest (in Rs) received together from A and B is:
Option 1: 9,600
Option 2: 5,400
Option 3: 18,000
Option 4: 10,800
Correct Answer: 10,800
Solution :
Let $x$ be the principal for part A and $y$ be the principal for part B.
So, according to the question
$\frac{x×15×2}{100}$ = $\frac{y×15×4}{100}$
⇒ $x: y$ = 2 : 1
Divide 27000 in the ratio of 2 : 1
⇒ $x$ = $\frac{2}{3}$ × 27000 = 18000
and, $y$ = $\frac{1}{3}$ × 27000 = 9000
Now,
Total Interest = $\frac{18000×15×2}{100}$ + $\frac{9000×15×4}{100}$ = 10,800
Hence, the correct answer is 10,800.
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