Question

A man had invested an amount of 10% per annum and another amount at 8% per annum simple interest. Thus he received ₹1350 as annual interest. Had he interchanged the amounts invested, he would have received ₹45 less as interest. What amounts did he invest at different rates?

Answer 1

$\rule{200}3$

$\tt\Large{\red{Question:-}}$

A man had invested an amount of 10% per annum and another amount at 8% per annum simple interest. Thus he received ₹1350 as annual interest. Had he interchanged the amounts invested, he would have received ₹45 less as interest. What amounts did he invest at different rates?

$\tt\Large{\green{Answer:-}}$

Let the amounts invested at 10% and 8% be Rs.x and Rs.y respectively.

Then as per the question

x × 10 × 1/ 100 = y × 8 × 1/ 100 = 1350

10x + 8y = 135000 …………..(i)

After the amounts interchanged but the rate being the same, we have

x × 8 × 1/ 100 = y × 10 × 1/ 100 = 1350 – 45

8x + 10y = 130500 …………….(ii)

Adding (i) and (ii) and dividing by 9, we get

2x + 2y = 29500 ……………(iii)

Subtracting (ii) from (i), we get

2x – 2y = 4500

Now, adding (iii) and (iv), we have

4x = 34000

x = 34000/4

= 8500

Putting x = 8500 in (iii), we get

2 × 8500 + 2y = 29500

2y = 29500 – 17000 = 12500

y = 12500/2 = 6250

Hence, the amounts invested are Rs. 8,500 at 10% and Rs. 6,250 at 8%.

$\tt\Large{\blue{Thank\:you}}$

$\rule{200}3$