A sum of ₹3125 amounts to 3515.20 in 3 years at x% p.a., interest being compounded yearly. What will be the simple interest (in ₹) on the same sum and for the same time at (x + 2)% p.a.?

562.50

Amount  = Principal × ( 1 + \(\frac{rate }{100}\) )^t

3515.20 = 3125 × ( 1 + \(\frac{x }{100}\) )³

3515.20 = 3125 × ( \(\frac{100+x }{100}\) )³

\(\frac{3515.20 }{3125}\) = ( \(\frac{100+x }{100}\) )³

\(\frac{26 }{25}\) = ( \(\frac{100+x }{100}\) )

2500 + 25x = 2600

25x = 100

x = \(\frac{100 }{25}\)  = 4%

New rate = ( x + 2 )% = ( 4 +2 )% = 6%

Simple interest = \(\frac{P×R×T}{100}\)

= \(\frac{3125×6×3}{100}\)

= 562.50