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?

1235

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/-