Question

A sum of money yat simple interest
amounts to & 910 in 6 years and to
₹1015 in 9years find the sum of
money and irate of interest ​

Answer 1

The sum of the money is Rs. 700 and Rate of interest is 5%

Given:  

A sum of the amount at a rate of simple interest amounts to 910 in 6 years

And the same money amounts to Rs. 1015 in 9 years

To find:

The sum of the amount and rate of interest

Solution:

Formula used:

Simple interest = (PTR)/100  

where P = Principal amount, T = time period, and R = Rate of interest

Total Amount = Principal amount + interest

Let P be the principal amount and R be the Rate of interest

From the given problem,

Calculate interest on P, at Rate R for 6 years

=> I₁ = P(6)R/100

=> I₁ = PR(0.06)

And the total amount = P + PR(0.06)  

given that after the amount = Rs. 910  

=>  P + 0.06 PR = 910 --- (1)

Now calculate the interest on P, at Rate R for 9 years

=> I₁ = P(9)R/100

=> I₁ = PR(0.09)

And the total amount = P + PR(0.09)  

given that after the amount = Rs. 1015

=>  P +0.09 PR = 1015 --- (2)

Now solve (1) and (2) to get the P and R-value

=> Do (2) - (1)

=> P + 0.09PR - P + PR(0.06) = 1015 - 910        

=> 0.03 PR = 105

=>  PR = 3500

Substitute PR = 3500 in (2)

=> P +0.09(3500) = 1015  

=> P + 315 = 1015

=> P = 1015 - 315 = 700

=> P = 700

Now substitute P = 700 in (1)  

=> 700 + 0.06 (700) R = 910

=> 700 + 42R = 910

=> 42 R = 210

=> R = 5

Therefore,

The sum of the money is 700 and the Rate of interest is 5%

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