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At simple interest, a man made a deposit of some money in...

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?

A.

15 years

B.

25 years

C.

20 years

D.

30 years

Correct answer is C

Amount (A) = Principal (P) + Interest (I) i.e. A = P + I

1 = PTR100

A = 3P; T = 10 years (Given)

Since A = P + I

3P=P+P×10×R100

3P=P+10PR100

3P=P+PR10

3PP=PR10

2P=PR10

2P1=PR10

PR = 20P

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