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 ?
Answer & explanation
Correct answer: option 2
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