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On simple interest, a certain sum of money amounts to ₹1,250 in 2 years and to ₹2,000 in 5 years. Find the rate of interest per annum (rounded off to two places of decimal).
33.33%
27.27%
16.67%
11.11%
33.33%
Calculate the annual interest by finding the difference in amounts for the 3-year gap (5-2=3), then find the principal by subtracting 2 years of interest from the 2-year total, then calculate the rate.
Sum after 2 years = ₹1,250, Sum after 5 years = ₹2,000
R=P×TI×100
Calculate the annual interest by finding the difference in amounts for the 3-year gap (5-2=3), then find the principal by subtracting 2 years of interest from the 2-year total, then calculate the rate.
Using the 5-year amount as the principal or failing to calculate the principal before finding the rate.
Calculate Interest for 3 years
The amount grows from ₹1,250 in 2 years to ₹2,000 in 5 years. The interest for the difference of 3 years is 2000−1250=750.
SI3yr=750
Calculate annual interest
Since simple interest is constant every year, interest for 1 year is 750/3=250.
SI1yr=250
Calculate the principal sum
The amount after 2 years is P+SI2yr=1250. Since SI2yr=2×250=500, then P=1250−500=750.
P=750
Calculate the rate of interest
Using the formula R=(SI1yr×100)/P, we get R=(250×100)/750=100/3=33.333... percent.
R=33.33%
A is correct because the calculated rate of interest is approximately 33.33% per annum.
This type of 'amount in time T1 and T2' question is common in banking and competitive exams; always find the principal first using the linear nature of SI.
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