A sum of Rs.2405 is divided into two parts such that the simple interest on the first part for 10\(\frac{1}{2}\) years at 9\(\frac{1}{3}\)% p.a. is equal to the simple interest on the second part for 3\(\frac{1}{2}\) years at 9% p.a. what is the difference (in Rs.) between two parts?
Answer & explanation
Correct answer: option 3
Rate = 9 \(\frac{1}{3}\)% = \(\frac{28}{3}\)% & 9%
Time = 10 \(\frac{1}{2}\) = \(\frac{21}{2}\) &
3\(\frac{1}{2}\) = \(\frac{7}{2}\)
S.I. = \(\frac{P\;R\;T}{100}\),
Total Principal = P1 + P2
ATQ,
\(\frac{P_1\;×\;28\;×\;21}{100\;×\;3\;×\;2}\) = \(\frac{P_2\;× \;9\;×\;7}{100\;×\;2}\)
P1 × 14 × 2 = P2 × 9
\(\frac{P_1}{P_2}\) = \(\frac{9}{28}\)
P1 = 9R
P2 = 28R
P = P1 + P2 = 9R + 28R = 37R
37R = 2405 (given)
1R = 65
P2 - P1 = 28R - 9R = 19R = 19 × 65 = Rs.1235/-