Question

Divide Rs15600 into two parts such that the interest on one at 5 percent for 5 years may be equal to that on the other at 9/2 percent for 6 years

Answer 1

Let one part = n
T = 5 years
R = 5%

Other part = 15600-n
T = 6 years
R = 9/2 %

SI = n×5×5/100 = (15600-n)×6×9/(2×100)
⇒ 25x = 27(15600-n)
⇒ 25x = 27×15600 - 27n
⇒ 52x = 27×15600
⇒ n = 27×15600/52
⇒ n= 8100
Other part = 15600 - 8100 = 7500

Answer 2

Let the principal be x and 15600 - x
now,  S.I. of (x * 5 * 5 /100)= S.I. of ((15600 - x) * 9/2 * 6 /100)
S.I. of 25x = S.I. of 27*15600 - 27x
25x + 27x = 15600 * 27
52x = 15600 * 27
x = Rs. 8100
So, Principals are Rs. 8100 and Rs. 750