Question

Vrushali invested Rs. (X + 3000) on compound interest of r% p.a. compounded annually for 2 years and Tarushi invested Rs. (X - 2000) on simple interest of (r - 2)% p.a. for 3 years. The total interest received by both of them is together Rs. 12360. If Anant invested Rs. (X + 8000) on simple interest for 3 years on 15% and received an interest of Rs. 13500, find the value of ‘r’.

• A. 10
• B. 18
• C. 12
• D. 15

Answer 1

Answer: (C)

12

Answer 2

According to the question,
Simple interest received by Anant = Rs. 13500
(X + 8000) × 15% × 3 = 13500
(X + 8000) = 30000
X = 22000
Amount invested by Vrushali = Rs. 22000 + 3000 = Rs. 25000
Amount invested by Tarushi = 22000 – 2000 = Rs. 2000
The total interest received by Vrushali and Tarushi = Rs. 12360
$[25000 × (1 + \frac{r}{100})^2 - 25000] + [20000 × (r - 2)\% × 3] = 12360$
$25000 × (1 + \frac{r}{100})^2 - 25000 + 600(r - 2) = 12360$
$25000 × (1 + \frac{r^2}{10000} + \frac{r}{50}) - 25000 + 600(r - 2) = 12360$
25000 + 2.5r2 + 500r - 25000 + 600(r - 2) = 12360
2.5r2 + 500r + 600r - 1200 = 12360
2.5r2 + 1100r = 13560
r2 + 440r - 5424 = 0
r² + 452r - 12r - 5424 = 0
r(r + 452) - 12(r + 452) = 0
(r + 452)(r - 12) = 0
r = -452, 12
Rate of interest cannot be negative. So, r = 12
So, the correct option is (C) : 12.