Question

A person deposits rsx in savings bank account at the rate of 5% per annum and rs y in fixed deposit at 10% per annum.At the end of the first yearhe gets rs 400 as total interest. He deposits rs y in savings bank account and rsx in fixed deposit he would get rs 350 as total interest. Find the total amount he deposited.

Answer 1

Answer :

Given : A person deposits Rs . x in savings bank account at the rate of 5% per annum and Rs . y in fixed deposit at 10% per annum.
we know
Simple interest = $\frac{P\times r\times t}{100}$
And from given condition " At the end of the first year he gets Rs. 400 as total interest. " we get

$$\begin{gathered} \frac{x\times 5\times 1}{100}+\frac{y\times 10\times 1}{100}=400 \\ \Rightarrow \frac{x}{20}+\frac{y}{10}=400 \\ \Rightarrow \frac{x+2y}{20}=400 \\ \Rightarrow x+2y=8000--------(1) \end{gathered}$$
And from given condition " He deposits Rs . y in savings bank account and Rs . x in fixed deposit he would get Rs. 350 as total interest. " , we get

$$\begin{gathered} \frac{y\times 5\times 1}{100}+\frac{x\times 10\times 1}{100}=350 \\ \Rightarrow \frac{y}{20}+\frac{x}{10}=350 \\ \Rightarrow \frac{y+2x}{20}=350 \\ \Rightarrow 2x+y=7000--------(2) \end{gathered}$$

Now we multiply 2 in equation 1 , we get

2x + 4y = 16000 ----------- ( 3 )

Now subtract equation 2 from equation 3 , we get

3y = 9000

y = 3000 , Substitute that value in equation 1 , we get

x + 2 ( 3000 ) = 8000

x = 8000 - 6000

x = 2000
So,
Total amount he deposits = x + y = 2000 + 3000 = Rs . 5000 ( Ans )