Question

a principal becomes twice the amount in 20 years at a certain rate simple interest. At the same rate of aimple interest, principal becomes thrice its amou t in??

Answer 1

let the principle be p
the amount=2p
let rate of interest be r%
SI = 2p-p
prt/100=p
(pr x 20)/100=p
r=5%
Now
New amount = 3p
SI = 3p-p
=2p
Now
time
= SI x 100/principle x rate
=2p x 100/p x 5
= 40 years

Answer 2

Given:

The time is twenty years.

In twenty years, the value of the amount becomes two times the principal value.

To find:

To calculate the time during which the amount becomes three times the principal value.

Solution:

Let the simple interest rate be R %, and the time is T years.

Amount (A) = Principal (P) + Interest ( S.I)

Amount = $P ( 1 + \frac{RT}{100} )$

Since the value of the amount becomes twofold the principal in twenty years,

Therefore,

A = 2 × P

T = 20 years

$2P = P ( 1 + \frac{20 R}{100})$

2-1 = R/5

1 = R/5

R = 5

Rate of interest = 5 %

Since the amount becomes three times the principal value in T years.

A = 3× P

Therefore,

$3P = P (1 + \frac{5T}{100} )$

3-1 = T/20

2 = T/20

T = 40 years.

Hence, In 40 years, the amount will turn into three times the principal value at a five percent interest rate.