Shashi had a certain amount of money. He invested $\frac{2}{3}$ of the total money in scheme A for 6 years and rest of the money he invested in scheme B for 2 years. scheme A offers simple interest at a rate of 12\% p.a. and scheme B offers compound interest (compounded annually) at a rate of 10\% p.a. if the total interest obtained from both the schemes is ₹ 2,750, what was the total amount invested by him in scheme A and scheme B together? (Approximate value) [IBPS-Bank Spl. Officers (IT) Exam, 2015]
(a)₹ 4500
(b)₹ 4200
(c)₹ 4050
(d)₹ 5000
Answer
Answer (as printed): D
Explanation
Let the total sum of money invested by Shashi be ₹ $x$. In scheme A money invested at simple interest for 6 years at a rate of 12\% p.a. $$\therefore \frac{2}{3} \text { of } x \times \frac{12 \times 6}{100}=\frac{48 x}{100}$$ In scheme B money invested at compound interest for$$\begin{aligned} & 2 \text { years at a rate of } 10 \% \text { p.a. } \frac{x}{3}\left(1+\frac{10}{100}\right)^{2}-\frac{x}{3} \\ & \Rightarrow \frac{x}{3}\left(1+\frac{10}{100}\right)^{2}-\frac{x}{3}=\frac{7 x}{100} \end{aligned}$$ According to given information we get $$\begin{aligned} & \Rightarrow \frac{48 x}{100}+\frac{7 x}{100}=2750 \\ & 55 x=2750 \times 100 \\ & x=\frac{2750 \times 100}{55} \\ & x=₹ 5000 \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.