At simple interest, a man made a deposit of some money in the bank. The amount in his bank account after 10 years is three times the money deposited. If the interest rate stays the same, after how many years will the amount be five times the money deposited?
- 15 years
- 25 years
-
20 years
- 30 years
The correct answer is: C
Explanation
Amount (A) = Principal (P) + Interest (I) i.e. A = P + I
1 = \(\frac {PTR}{100}\)
A = 3P; T = 10 years (Given)
Since A = P + I
\(\implies 3P = P + \frac {P\times 10 \times R}{100}\)
\(\implies 3P = P + \frac {10PR}{100}\)
\(\implies 3P = P + \frac {PR}{10}\)
\(\implies 3P - P = \frac {PR}{10}\)
\(\implies 2P = \frac {PR}{10}\)
\(\implies \frac {2P}{1} = \frac {PR}{10}\)
\(\implies\) PR = 20P
\(\therefore\) R = 20%
Since the rate stays the same
A = 5P; R = 20%;T =?; A =P + I
\(\implies 5P = P + \frac {p \times T \times 20}{100}\)
\(\implies 5P - P = \frac {2PT}{10}\)
\(\implies 4P = \frac {2PT}{10}\)
\(\implies 2P = \frac {PT}{10}\)
\(\implies\) PT = 20P
\(\therefore\) T = 20 years
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