Find the capital investment by Anil if annual simple interest earned is Rs. 4824, when Anil invested 3/5th of its capital at 8% p.a., 1/4th @ 15% p.a. and the remaining amount @10 % p.a. for 2 years each.
Solution
Correct Answer: Option B
We know that, SI = (P × R × T)/100
Where, SI = Simple interest, P = principal, R = % rate of interest, T = time in years
Let the principal invested by Anil be p.
Anil invests 3/5th of p at 8% per annum for 2 years.
⇒ SI1 \(= \;p\; \times \;\frac{3}{5} \times \frac{8}{{100}} \times 2 = 0.096p\) ……….. (1)
Anil invests 1/4th of p at 15% per annum for 2 years.
⇒ SI2 \(= p\; \times \;\frac{1}{4} \times \frac{{15}}{{100}} \times 2 = 0.075p\) …………. (2)
Remaining principle \(= \;p\; - \;\frac{{3p}}{5} - \frac{p}{4} = \frac{{3p}}{{20}}\)
Anil invests 3/20th of p at 10% per annum for 2 years.
⇒ SI3 \(= \;p\; \times \;\frac{3}{{20}} \times \frac{{10}}{{100}} \times 2 = 0.03p\) ……….(3)
∴ As per given information:
SI1 + SI2 + SI3 = 2 × 4824 = 9648
⇒ 0.096p + 0.075p + 0.03p = 9648
⇒ 0.201p = 9648
⇒ p = 48000
Hence, Anil have a principal amount is Rs. 48000
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