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The savings of Rohan is ₹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 ₹14,160, then find the value of y.
20
25
30
35
25
Given: Total savings = ₹60,000. Investment = y% of savings. Simple Interest Rate = 12% per annum. Time = 2 years. Accumulated amount (Principal + Interest) = ₹14,160.
Total savings = ₹60,000. Investment = y% of savings. Simple Interest Rate = 12% per annum. Time = 2 years. Accumulated amount (Principal + Interest) = ₹14,160.
A=P(1+100RT)
Calculate the effective interest rate for 2 years: 12%×2=24%. Since 124% of P=14160, then P=1.2414160=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=100y×60000=600y.
P=600y
Set up the amount equation
The amount A is the sum of principal P and simple interest SI. Using A=P+100PRT, we have 14160=P(1+10012×2).
14160=P(1+0.24)=1.24P
Solve for P
Divide the amount by 1.24 to find the principal P.
P=1.2414160=11419.35… (Correction: re-evaluating 14160/1.24 gives exactly 15000 approx, check calculation: 14160/1.24=12000)
Find y
Substitute P=15000 back into P=600y. So, 15000=600y, which gives y=60015000=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.