Discussion
In what time will Rs.4000 lent at 3% per annum on simple interest earn as much interest as Rs.5000 will earn in 5 years at 4% per annum on simple interest?
Answer: A
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Work out the target interest first.
\[ \frac{5000 \times 4 \times 5}{100} = \text{Rs. } 1000 \]
Now find how long Rs. 4000 at 3% takes to earn the same:
\[ 1000 = \frac{4000 \times 3 \times T}{100} = 120\,T \]
\[ T = \frac{1000}{120} = 8\tfrac{1}{3} \text{ years} \]
The smaller principal at the lower rate needs longer, so the answer must exceed the 5 years - a quick sanity check.
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