Question

a certain sum of money triples itself in 16 years. In how many years will it becomes 5 times at the same rate?

Answer 1

1st case
let p= ₹100 & amt= ₹300
therefore SI= ₹300 - 100 = ₹200
given t = 16yrs
therefore R= 100× SI ÷ p×t
=100 × 200 ÷ 100×16 = 12.5%

2nd case
p =₹100 amt= ₹500
therefore SI = ₹500-100 = ₹400
r =12.5%
therefore T = 100 × SI ÷ p×r
=100 × 400 ÷ 100× 12.5 = 32yrs

hope u understood >_<

Answer 2

In 32 years the amount will become 5 times the principle

Given:

A certain sum of money triples itself in 16 years.

Find:

In how many years will it becomes 5 times at the same rate

Solution:

• Case 1
• First we have to find out the rate of simple interest
• Let the sum be x
• Given, after 3 years it becomes three times itself
• Amount after three years = 3x
• Interest = Amount - principle = 3x - x = 2x
• Time required = 16 years
• Let the rate be r
• Interest (I) = $\frac{PTR}{100}$
• 2x = $\frac{x*16*r}{100}$
• 2 = $\frac{16*r}{100}$
• or
• r =12.5%
• Case 2
• p=x,  Amount = 5x
• Interest = 5x-x =4x
• Rate = 12.5%
• Time required for the amount to become 5 times = $\frac{100*I}{PR}$
•                                                                                   =$\frac{100*4X}{X*12.5}$
•                                                                                   =$\frac{400}{12.5}$
•                                                                                   = 32 YEARS

• It takes 32 years for the amount to become 5 times the principle

#SPJ2