Question

An amount becomes 4 times in 7 years when invested under simple interest at a certain rate in how many years will the amount become 16 times of the original amount oat the same rate

Answer 1

Answer:

The amount takes 35 years to become 16 times of the original amount at the same rate.

Step-by-step explanation:

$\text{Simple interest(S.I)}=\frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100}$  ............(1)

Also, $\text{Amount}=\text{Principal}+\text{Simple interest}$   ....(2)

Let original principal be x,

then according to question,

Amount becomes 4 times that is 4x. then using (2)

SI becomes 4x -x = 3x

Given: Time = 7 years

Putting values  in (1) , We get,

$3x=\frac{x \times \text{Rate} \times 7}{100}$

On solving further,

$3 \times 100=\text{Rate} \times 7}$

$\frac{3 \times 100}{7} =\text{Rate}$

$\frac{300}{7} =\text{Rate}$

Thus rate is $\frac{300}{7}$

Also, We have to find in how many years will the amount become 16 times of the original amount at the same rate.

Here, original principal is x, then amount becomes 16x

Thus, Simple interest becomes 15x

and  rate =$\frac{300}{7}$

Putting values in (1),

$15x=\frac{x \times\frac{300}{7} \times \text{time}}{100}$

On solving further,

$15 \times 100=\frac{300}{7} \times \text{time}$

$1500=\frac{300}{7} \times \text{time}$

$\frac{1500 \times 7}{300}=\text{time}$

${5 \times 7}=\text{time}$

$35=\text{time}$

Thus, the amount takes 35 years to become 16 times of the original amount at the same rate.