On simple interest, a certain sum becomes ₹59,200 in 6 years and ₹72,000 in 10 years. If the rate of interest had been 2% more, then in how many years would the sum have become ₹76,000 ?

9

Principal(P) becomes 59200 in 6 years and 72000 in 10 years

So, Interest of 4 years = 72000-59200 = Rs.12800

Interest of 1 year = \(\frac{12800}{4}\) = Rs.3200

Interest of 6 years = 3200 × 6 = Rs.19200

P = A - I = 59200-19200 = Rs.40000

Rate% = \(\frac{I}{P}\) × 100 = \(\frac{3200}{40000}\) × 100 = 8%

ATQ,

Rate increase by 2% = 8 + 2 = 10%

Now, Amount= 76000, Principal = 40000

I = A - P = 76000-40000 = 36000

⇒ Interest = \(\frac{P\;×\;R\;×\;T}{100}\)

⇒ 36000 = \(\frac{40000\;×\;10\;×\;T}{100}\)

⇒ Time = 9 Years