A sum amounts to nineteen times itself in five years under simple interest. In how many months will the same sum become four times itself?

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Solution

The correct option is A 10
Simple Interest $S I = \frac{P N R}{100}$
Given, $A m o u n t A = 19 P$
$=> P + S I = 19 P$
$=> P + \frac{P \times 5 \times R}{100} = 19 P$
$=> 0.05 R = 18$
$=> R = 360$ %
So, when $A = 4 P$
$=> P + S I = 4 P$
$=> P + \frac{P \times N \times 360}{100} = 4 P$
$=> 3.6 N = 3$
$=> N = \frac{3}{3.6} = \frac{1}{1.2} = \frac{10}{12}$ years
Or $N = 10$ months

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