A man invested a amount at 8% per annum and another amount at 6% per annum simple interest - Maths - Pair of Linear Equations in Two Variables

Question

A man invested a amount at 8% per annum and another amount at 6%
per annum simple interest Thus, he received Rs248 as annual
interest Had he interchanged the amount invested, he would have
received Rs 34 less What amonts did he invest at different rates
????

Ajanta Trivedi · Accepted Answer

let the amount invested at 8 % per annum be Rs. x and at 6% per annum be Rs. y.

simple interest for one year = amount invested * rate of interest / 100

annual interest = Rs. 248

therefore

$\frac{x * 8}{100} + \frac{y * 6}{100} = 248 8 x + 6 y = 24800 4 x + 3 y = 12400.............. (1)$

if he interchanged the amount invested, he received Rs. 248 - Rs. 34 = Rs. 214

therefore

$\frac{x * 6}{100} + \frac{y * 8}{100} = 214 6 x + 8 y = 21400 3 x + 4 y = 10700.......... (2)$

multiplying eq(1) by 3 and eq(2) by 4 and subtracting:

$12 x + 9 y = 37200 12 x + 16 y = 42800 - 7 y = - 5600 y = \frac{5600}{7} = R s . 800$

put y = 800 in eq(1):

$4 x + 3 * 800 = 12400 4 x + 2400 = 12400 4 x = 12400 - 2400 4 x = 10000 x = \frac{10000}{4} = 2500$

thus he invested Rs 2500 at 8 % per annum and Rs. 800 at 6 % per annum.

hope this helps you.

cheers!!

A man invested a amount at 8% per annum and another amount at 6% per annum simple interest . Thus, he received Rs248 as annual interest. Had he interchanged the amount invested, he would have received Rs 34 less.What amonts did he invest at different rates....????