Question

A person invested some amount at the rate of $10\%$ simple interest and some amount at the rate of $12\%$ simple interest. He received a yearly interest of $Rs.130$. But if he had interchanged the amounts invested he would have received $Rs.4$ more as interest. How much amounts did he invest at $12\%$ and $10\%$, respectively?

• A. $Rs.600,Rs.550$
• B. $Rs.800,Rs.450$
• C. $Rs.700,Rs.500$
• D. $Rs.500,Rs.700$

Answer 1

The correct option is D $Rs.500,Rs.700$

Let the amounts invested be $x$ and $y$ respectively at $10$ and $14$.

Now,according to the question,

$10\%ofx+12\%ofy$$=Rs.130$

$10x+12y=13000$ ...(1)

Also,when the principle investments are interchanged then,

$12\%ofx+10\%ofy=134$

$12x+10y=13400$ ...(2)

Multiplying equation (1) by $5$ and (2) by $6$ and then subtracting,

$72x+60y-50x-60y=80400-6500$

$22x=15400$

$x=700$

Putting value of $x$ in (1)

$10\times 700$$+12y=13000$

$12y=6000$

$y=500$

The investments are Rs.$700$ and Rs.$500$