Question

A sum of money double itself in 8 years at a certain rate . In how many years will it become triple of itself at the rate at the rate of simple interest​

Answer 1

★Given:-

• A sum of money double itself in 8 years at a certain rate.

★To find:-

• In how many years will it become triple of itself at the rate at the rate of simple interest​.

★Solution:-

Let,

→Principal = x

→Time=8 years

Given that,

• amount after 8 years becomes double

Hence,

→Amount = 2x

Simple interest:-

⇒Amount-principal

⇒ 2x - x = x

We know:

✦Rate = S.I×100/PT

Putting the values,

Rate = x(100) / x(8)

        = 100/8

         = 25/2 = 12.5%

Now,

Sum of money triples

Here,

• Principle = x
• Amount = 3x
• SI=A-P=3x-x=2x
• Rate = 12.5%
• Time = ?

Using the formula,

✦Time= (100×SI)/(PR)

Putting the values in the formula,

⇒ Time = (2x)(100) / x(25/2)

⇒200×2/25

⇒ 8×2

⇒ 16 Years

Hence,

It will take 16 years.

____________

Answer 2

Answer:

Correct Question:-

1. A sum of money doubles itself in 8 years. What is the rate of interest.

To find,

•      The rate of Interest

Given as,

• Principal = P
• Rate of Interest = R
• Time = 8 years
• Amount = 2P

Formula used:-

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

Solution:-

  2P = P + SI

= 2P - P = SI

= P = SI

SI = $\frac{\rm P \times T \times R}{100}$

P = $\frac{\rm P \times R \times 8}{100}$

$\rm \frac{P}{P} = \frac{8R}{100}$

$\rm R = \frac{100}{8} = 12.5 %$

So the required answer is 12.5%.

Step-by-step explanation: