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Question 1014966: A certain sum is invested for certain time. It amounts to Rs. 35 at 10% per annum. But when invested at 8% per annum, it amounts to Rs. 30. Find the time?
Read more: http://www.bankersadda.com/2016/01/test-of-day-for-lic-aao-syndicate-sidbi.html#ixzz3xtcWaHAz
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! answer is 25 years.
i initially assumed compound interest, but that gave me an answer that was around 8 years which wasn't one of the selections.
i then went back and assumed simple interest and that got me the following:
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
they did not stipulate that it was simple interest, which caused me some confusion in the beginning because i assumed it was compound interest.
when i saw the selections from the picture i linked to, i saw that it couldn't be that and assumed simple interest.
that led to the correct solution, i believe.
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