A certain sum amounts to ₹81840 in 3 years and to ₹92400 in 5 years at x% p.a under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself ?

10

Sum becomes Rs 81840 in 3 years and Rs 92400 in 5 years at x% per annum

Interest (I) of 2 years = 92400-81840 = Rs 10560

Interest (I) of 1 years = \(\frac{10560}{2}\) = Rs 5280

Interest (I) of 3 years = 5280 × 3 = Rs 15840

Principal = Amount - Interest

P = 81840 - 15840

P = Rs 66000

Rate % = \(\frac{I}{P}\) ×100

Rate % = \(\frac{5280}{66000}\) ×100 = 8%

x=8%

New Rate = x + 2% = 10%

Now, P = 66000

A become double = 66000 × 2 = Rs 132000

T = ?

R = 10%

I = A - P = 66000

I = \(\frac{P×R×T}{100}\)

66000  = \(\frac{66000×10×T}{100}\)

Time = 10 years