Question

A sum of money doubles in 12 years. in how many years, it will triple at s.i.

Answer 1

the sum of money double in twelve years

so let the money be x


a/q

2x=12
x=6

.then we need to find that in how many time if will be triple

3x=3×6 =18

Answer 2

Given,

The given sum of money gets doubled after 12 years at simple interest.

To Find,

The time period in which the amount will be tripled at simple interest.

Solution,

Let the principal amount be P.

It takes twelve years for the principal to get doubled.

Thus, the amount of simple interest earned in twelve years is equal to the principal amount.

∴ Simple Interest = $\frac{PTR}{100} = P$

Where $P$ = Principal amount

            $T$ = Time period

            $R$ = Rate of interest.

On substitution of T = 12,

⇒$P = \frac{PR(12)}{100}$

⇒$100P = 12PR$

⇒ $R = \frac{100P}{12P} =\frac{25}{3}$

Thus the rate of interest is $\frac{25}{3}$%.

For the amount to be tripled, the simple interest earned must be double the principal amount.

⇒ S.I = $2P$

Then sum of amount = $P+2P = 3P$.

∵ S.I. = $\frac{PTR}{100}$,

On substitution,

$\frac{PTR}{100} = 2P$

⇒ $\frac{PT(\frac{25}{3}) }{100} = 2P$ (∵$R$ = $\frac{25}{3}$)

⇒$\frac{25PT}{300} = 2P$

⇒$\frac{PT}{12} = 2P$

⇒$T = \frac{(2P)(12)}{P}$

⇒$T = 24$

Henceforth, the time period required for the sum of the amount to be tripled at S.I. is 24 years.