Question

A certain sum of money becomes three times of itself in 20 years at simple interest.in how many years does it become double of itself at the same rate of simple interest

Answer 1

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check it out.
it will take 10 years to become double of itself at the same rate of interest.
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Answer 2

10 years required for to double the principal amount itself.

Given:

A certain sum of money becomes three times of itself in 20 years at simple interest.  

To find:

Number of years it becomes double to itself at the same rate of simple interest = ?

Solution:

Let certain sum of money = P (principal),  

Time in interval T = 20 Years -----(1)

Triple the amount means

Principal + Interest = 3 Principal.  

Interest I = 2 Principal.  

I  = 2P-------(2)  

We know that, from simple interest formula.

$I=\frac{P T R}{100}$

By substituting equation 1 and 2 in the formulae,

$\begin{array}{l}{2 P=\frac{p T R}{1000}} \\ {200=T R} \\ {R=\frac{200}{T}} \\ {R=\frac{200}{20}} \\ {R=10}\end{array}$

Such that, the0 Rate of interest for principal amount 0 becomes three times of itself in 20 years’ time is 10.

Similarly by using R = 10, we need to find in how many years the amount would be double of itself for the same rate of interest.

i.e., amount of double of itself  

Principal (P) + Interest (I) = 2 Principal (P)

P+I = 2P  

I = P---------(3)  

By using the simple interest formula

$I=\frac{P T R}{100}$

By substituting I = P, R= 10 then we get T value

$\begin{aligned} I &=\frac{P T R}{100} \\ P &=\frac{P T R}{100} \\ T R &=100 \\ T &=\frac{100}{10} \\ T &=10 \end{aligned}$

Hence, it requires 10 years of time by considering the same interest as the amount becomes triple itself in the span of 20 years