Question

Amounts to rs 35 when it was invested at 10% per annum. But when invested at 8% per annum, it amounts to rs 30. Find the investment toime

Answer 1

$\huge\mathfrak\red{HeyAa..!}$

formula for simple interest is f = p + prn

f is the future amount.

p is the present amount.

r is the interest rate per year.

n is the number of years.

when r = .10, f = 35 and the formula becomes 35 = p + p * .10 * n

when r = .08, f = 30 and the formula becomes 30 = p + p * .08 * n

factor out the p in each of these equations to get:

35 = p + p * .10 * n becomes 35 = p * (1 + .10 * n)

30 = p + p * .08 * n becomes 30 = p * (1 + .08 * n)

solve each equation for p to get:

p = 35 / (1 + .10 * n)

p = 30 / (1 + .08 * n)

since p = 35 / (1 + .10 * n) in the first equation, you can replace p in the second equation with 35 / (1 + .10 * n) to get:

35 / (1 + .10 * n) = 30 / (1 + .08 * n)

cross multiply to get 35 * (1 + .08 * n) = 30 * (1 + .10 * n)

distribute the multiplications in this equation to get:

35 * 1 + 35 * .08 * n = 30 * 1 + 30 * .10 * n

simplify to get:

35 + 2.8 * n = 30 + 3 * n

subtract 2.8 * n from both sides of this equation and subtract 30 from both sides of this equation to get:

35 - 30 = 3 * n - 2.8 * n

simplify to get:

5 = .2 * n

divide both sides of this equation by .2 to get:

25 = n

that's your solution.

you can confirm by replacing n in your original equations with 25 and you'll see that the present value will be the same in both equations.

that present value will be 10.

the original investment is 10.

at 10% per year, the future value becomes 10 + 10 * .10 * 25 = 35

at 9% per year, the future value becomes 10 + 10 * .08 * 25 = 30