Question
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 ( compound annually) at a rate of 10% p.a. If the total interest obtained from both the schemes is Rs. 2750. What was the total amount invested by him in scheme A and scheme B together ? (Approximate value)
Answer: Option D
Let the total sum of money invested by Shashi be Rs. x
In scheme A money invested at simple interest for 6 years at a rate of 12% p.a.
$$\therefore \frac{2}{3}{\text{of }}x \times \frac{{12 \times 6}}{{100}} = \frac{{48x}}{{100}}....(i)$$
In scheme B money at compound interest for 2 year at a rate of 10% p.a.
$$\eqalign{
& \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} \cr
& \Rightarrow \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} = \frac{{7x}}{{100}} \cr} $$
According to given information we get
$$\eqalign{
& \Rightarrow \frac{{48x}}{{100}} + \frac{{7x}}{{100}} = 2750 \cr
& \Rightarrow 55x = 2750 \times 100 \cr
& \Rightarrow x = \frac{{2750 \times 100}}{{55}} \cr
& \Rightarrow x = Rs.\,5000 \cr} $$
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Let the total sum of money invested by Shashi be Rs. x
In scheme A money invested at simple interest for 6 years at a rate of 12% p.a.
$$\therefore \frac{2}{3}{\text{of }}x \times \frac{{12 \times 6}}{{100}} = \frac{{48x}}{{100}}....(i)$$
In scheme B money at compound interest for 2 year at a rate of 10% p.a.
$$\eqalign{
& \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} \cr
& \Rightarrow \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} = \frac{{7x}}{{100}} \cr} $$
According to given information we get
$$\eqalign{
& \Rightarrow \frac{{48x}}{{100}} + \frac{{7x}}{{100}} = 2750 \cr
& \Rightarrow 55x = 2750 \times 100 \cr
& \Rightarrow x = \frac{{2750 \times 100}}{{55}} \cr
& \Rightarrow x = Rs.\,5000 \cr} $$
Was this answer helpful ?
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