[Solved] In how much time will a sum of money double itself at 12% p. (2024)

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  1. 6 years 2 months
  2. 8 years 1 month
  3. 6 years 4 months
  4. 8 years 4 months

Answer (Detailed Solution Below)

Option 4 : 8 years 4 months

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Detailed Solution

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Given:

Rate of interest = 12%

Concept used:

1 years = 12 months

Simple Interest, SI = (P × R × T)/100

Amount = P + SI

where, P = Principal, R = Rate of interest, T = time in years

Calculation:

Let the principal amount and time be P and T respectively.

According to the question,

P + (P × 12 × T)/100 = 2× P

⇒(P × 12 × T)/100 = P

12T/100 = 1

⇒ T = 25/3

Now, 25/3 years = 25/3×12

⇒ 25× 4 months

⇒ 100 months

⇒8 years 4 months

∴ It will take 8 years and 4 months.

[Solved] In how much time will a sum of money double itself at 12% p. (2)Shortcut Trick

Let the principal be Rs. 'a'

According to the question,

The sum becomes double itself,

Amount = 2a

Simple interest = 2a - a = a

Also, SI = PRT/100

a = a× 12× T/100

T = 100/12

T =\(8 \frac{1}{3}\)

T = 8 years 4 months.

Hence, the correct answer is 8 years and 4 months.

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[Solved] In how much time will a sum of money double itself at 12% p. (2024)
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