A sum of ₹5500 is lent out in two parts in such a way that the interest on one part at 12% for 4 years is equal to that on another part at 8% for 5 years. What will be the two parts of the sum?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹2500 and ₹3000
Simple interest is \(\displaystyle \frac{P\times R\times T}{100}\). Setting the two interests equal gives the ratio of the two parts, and the sum of ₹5500 is then shared in that ratio.
The ratio of the two parts (the two interests are equal):
\(\displaystyle \frac{P_1\times12\times4}{100}=\frac{P_2\times8\times5}{100}\)
So \(48P_1=40P_2\)
The part at the higher rate and time must be the smaller one: \(P_1:P_2=40:48=5:6\)
Sharing ₹5500 (split into \(5+6=11\) shares):
\(\displaystyle P_1=5500\times\frac{5}{11}=2500\)
\(\displaystyle P_2=5500\times\frac{6}{11}=3000\)