A certain sum of money doubles itself in 6 years. How much time (in years) will it take to become five times of itself at the same rate?

Options
a) 30
b) 24
c) 35
d) 28

Solution

As per question
A certain sum of money doubles itself in 6 years
Amount = 2 x P
Time = 6 years
S.I = \frac {P \times R \times T}{100}
Amount = P + S.I
P = x
A = 2x
S.I = x
S.I = \frac {P \times R \times T}{100}
x = \frac {x \times R \times 6}{100}
R = \frac {100}{6} = \frac{50}{3}%

Amount become five times of itself
A = 5x
P = x
A = P + S.I
5x = x + S.I
S.I = 5x – x
S.I = 4x
S.I = \frac {P \times R \times T}{100}
4x = \frac {x \times 50 \times T}{100 \times 3}
4 = \frac {50 \times T}{300}
4 = 6 \times T
T = 6 x 4 = 24 years

Ans: b) 24 years

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