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
• E. None of these

Answer 1

The Correct Option is C

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. 20000
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