Question

In 4 years, 6500 amounts to 8840 at a certain rate of interest. In what time will 1600 amounts to 1816 at the same rate?​

Answer 1

Step-by-step explanation:

Given :-

In 4 years, 6500 amounts to 8840 at a certain rate of interest.

To find :-

In what time will 1600 amounts to 1816 at the same rate?

Solution :-

Given that :

Principle (P) = Rs. 6500

Amount (A) = Rs. 8840

Time (T) = 4 years

Let the rate of interest be R%

We know that

Simple Interest = PTR/100

On Substituting these values in the above formula

=> SI = (6500×4×R)/100

=> SI = 65×4×R

=> SI = 260R

Simple Interest = Rs. 260R

We know that

Amount = Principle + Interest

=> Simple Interest = Amount - Principle

=> SI = 8840-6500

=> SI = 2340

So According to the given problem

Simple Interest = Rs. 2340

=> 260 R = 2340

=> R = 2340/260

=> R = 234/26

=> R = 117/13

=> R = 9%

So, Rate of Interest = 9%

Now ,

Given Principle = Rs. 1600

Amount = Rs. 1816

Rate of Interest = 9%

Let the time be T years

Amount = Principle + Interest

=> Simple Interest = Amount - Principle

Simple Interest = 1816 -1600

=> SI = Rs. 216

We know that

Simple Interest = PTR/100

=> 216 = (1600×T×9)/100

=> 216 = 16×T×9

=> 216 = 144×T

=> T×144 = 216

=> T = 216/144

=> T = (72×3)/(72×2)

=> T = 3/2 years or

=> T = 1 1/2 years or

=> T = 1.5 years or

=> T = 18 months

Answer:-

The required time for the given problem is

18 months or 1.5 years or 1 1/2 years or 3/2 years

Used formulae:-

• Simple Interest = PTR/100

• Amount = Principle + Interest

• P = Principle

• T = Time

• R = Rate of Interest