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 A sum of money triples itself in 15 years on simple interest. In how many years will it become five times at the same rate of interest on simple interest?

  1. 30 years
  2. 25 years
  3. 15 years
  4. 20 years
  5. 10 years

Answer (Detailed Solution Below)

Option 1 : 30 years

Free

Syllogism (Clear Your Basics)

10 Questions 10 Marks 10 Mins

Given:

Time = 15 years; Amount = 3 × principal

Formula used:

Amount = Principal + simple Interest

Simple interest = [(Principal× Rate× Time)/100]

Calculation:

3P = P + (P × R × 15)/100

 ⇒ 2p = (p × R × 15)/100

 ⇒ (2× 100)/15 = R

 ⇒ 40/3 % = R

Now, 5P = P + (P × 40/3 × t)/100

 ⇒ 4P = (P × 40/3 × t)/100

 ⇒ (3 × 100)/10 = t

 ⇒ 30 years = t

∴ A sum of money becomes five times in 30 years.

A sum of money at simple interest trebles itself in 15 years. it will become 5 times of itself in
Shortcut Trick 

Initial sum Final sum Difference  
P 3P(Triple of initial sum) 2P in 15years 
P 5P(five times of Initial sum) 4P in 30 years

Time taken to for 2P is 15 years hence time taken for 4P will be 30 years ( just double of it). 

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Updated On: 27-06-2022

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40 years 36 years 30 years 25 years

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