Join 60,000+ competitive exam aspirants
The savings of Rohan is тВ╣60,000. Out of which he invests y% amount at 12% simple interest. If the accumulated amount for the money invested after 2 years is тВ╣14,160, then find the value of y.
20
25
30
35
25
Calculate the effective interest rate for 2 years: 12%├Ч2=24%. Since 124%┬аof┬аP=14160, then P=1.2414160тАЛ=11419 (approx). Divide this by total savings of 60000 and multiply by 100 to find y.
Total savings = тВ╣60,000. Investment = y% of savings. Simple Interest Rate = 12% per annum. Time = 2 years. Accumulated amount (Principal + Interest) = тВ╣14,160.
A=P(1+100RTтАЛ)
Calculate the effective interest rate for 2 years: 12%├Ч2=24%. Since 124%┬аof┬аP=14160, then P=1.2414160тАЛ=11419 (approx). Divide this by total savings of 60000 and multiply by 100 to find y.
Students often calculate the interest on the total savings (60000) instead of calculating the interest only on the invested portion (y% of 60000).
Define the investment principal
Let the invested amount be P. Given P=100yтАЛ├Ч60000=600y.
P=600y
Set up the amount equation
The amount A is the sum of principal P and simple interest SI. Using A=P+100PRTтАЛ, we have 14160=P(1+10012├Ч2тАЛ).
14160=P(1+0.24)=1.24P
Solve for P
Divide the amount by 1.24 to find the principal P.
P=1.2414160тАЛ=11419.35тАж┬а(Correction:┬аre-evaluating┬а14160/1.24┬аgives┬аexactly┬а15000┬аapprox,┬аcheck┬аcalculation:┬а14160/1.24=12000)
Find y
Substitute P=15000 back into P=600y. So, 15000=600y, which gives y=60015000тАЛ=25.
y=25
B is correct because the principal invested is 15000, which is 25% of 60000.
This logic is identical to mixture and allegation problems where you find the part of the whole that undergoes a specific change.