Question

a sum of money amount to ₹2600 in 3 years and to ₹2900 in 4.5 years at simple interest. find the sum and rate of interest​?

Answer 1

Answer:

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Answer 2

The sum is ₹2000 and the rate of interest is 10%

Given : A sum of money amount to ₹2600 in 3 years and to ₹2900 in 4.5 years at simple interest.

To find : The sum and the rate of interest.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the sum and the rate of interest)

Total amount after 4.5 years = ₹2900

Total amount after 3 years = ₹2600

It was simple interest, so we can say that

Interest paid in (4.5-3) years = ₹(2900-2600)

Interest paid in 1.5 years = ₹300

Now,

Interest paid in 1.5 years = ₹300

Interest paid in (1.5×2) years = ₹(300×2)

Interest paid in 3 years = ₹600

So,

Sum of money :

= Total amount after 3 years - Interest paid in 3 years

= ₹(2600-600)

= ₹2000

Let, the rate of interest = r%

So,

Interest paid in 3 years = (principal amount × rate × time)/100 = ₹(2000 × r × 3)/100 = ₹60r

Now, comparing the two values of interest paid in 3 years, we get :

60r = 600

r = 600/60

r = 10%

Hence, the sum is ₹2000 and the rate of interest is 10%