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A sum when invested at 1221% simple interest per annum amounts to ₹17,500 after 2 years. What is the simple interest?
₹3,700
₹3,450
₹3,650
₹3,500
₹3,500
Since SI = (R × T)% of P, the total interest is 12.5% × 2 = 25% of P. The Amount is 125% of P. Thus, 125% of P = 17500, so P = 17500 / 1.25 = 14000. SI = 17500 - 14000 = 3500.
Amount (A) = ₹17,500, Rate (R) = 12.5% p.a. (or 25/2%), Time (T) = 2 years
A=P(1+100RT), SI=A−P
Since SI = (R × T)% of P, the total interest is 12.5% × 2 = 25% of P. The Amount is 125% of P. Thus, 125% of P = 17500, so P = 17500 / 1.25 = 14000. SI = 17500 - 14000 = 3500.
Confusing 'Amount' for 'Principal'. Students often calculate 25% of 17,500 instead of finding the Principal first.
Define the relationship
The amount A is the sum of the Principal P and the Simple Interest SI. The interest is given by SI=P×100R×T. Substituting, we get A=P+100PRT=P(1+100RT).
A=P(1+100RT)
Substitute values and solve for P
Substitute A=17500, R=12.5, and T=2. Then 17500=P(1+10012.5×2)=P(1+0.25)=1.25P. Thus, P=17500/1.25.
P=1.2517500=14000
Calculate Simple Interest
Finally, subtract the principal from the total amount to find the interest: SI=A−P=17500−14000.
SI=3500
D is correct because the calculated principal is ₹14,000, leading to a simple interest of ₹3,500.
This is fundamentally a base-value percentage problem; always remember that Amount=Principal+Interest and never mistake the amount for the base principal.
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