The compound interest on a certain sum at $16\frac{2}{3}\%$ p.a. for 3 years is ₹6,350. What will be the simple interest on the same sum at the same rate for $5\frac{2}{3}$ years ?

₹10,200

Rate = 16\(\frac{2 }{3}\)% = \(\frac{1 }{6}\)

Time = 3 years

Compound interest = Principal × ( 1 + \(\frac{rate }{100}\) )^t - Principal

6250 = Principal × [  ( 1 + \(\frac{1 }{6}\) )3 - 1 ]

6250 = Principal × [  ( \(\frac{7 }{6}\) )³ - 1 ]

6250 = Principal × [  ( \(\frac{343 }{216}\) ) - 1 ]

6250 = Principal × ( \(\frac{127}{216}\) )

Principal = 10800

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

Time = 5\(\frac{ 2 }{3}\)  = \(\frac{17 }{3}\) years

= \(\frac{ 10800 × 1 × 17 }{6× 3× 100}\)  

= Rs.10200