If a sum triples in 4 years at simple interest, find the time that it would take to become 5 times itself at the same rate of interest.

8 years

Sum triple in  4 years .

Let sum = P , then  Amount = 3P 

Simple interest of 4 years= 3P - P = 2P

Simple interest of 1 year = \(\frac{2P }{4}\)  = 0.5P

We know ,

Simple  Interest = \(\frac{Principal ×Rate × Time }{100}\)

0.5P = \(\frac{P × Rate × 1 }{100}\) 

Rate = 50%

ATQ ,

Amount = 5P

Simple interest = 5P - P = 4P

4P = \(\frac{P × 50 × Time }{100}\) 

Time = 8 years