Question

Rahul gave a certain amount to Mohit for 4 years at certain rate of simple interest. But due to financial problem Mohit was not able to return the amount in time so he promised Rahul to return the amount in next 2 years. Now, Rahul applied same rate of compound interest for remaining time on the total amount at the end of 4 years. If total interest at the end of 4 years is Rs.14400 and total interest at the end of 6 years is Rs.26784, then find the amount lent by Rahul to Mohit​

Answer 1

Answer:

the amount lent by Rahul to Mohit​ = Rs 24000

Step-by-step explanation:

Let say Amount lent by Rahul to Mohit = Rs 100P

Let say Interest Rate = R % Per annum

Simple interest = P * R * T /100

Simple Interest in 4 Years = 4PR   Rs

4PR = 14400

=> PR = 3600

Amount after 4 Years  = 100 P + 14400 Rs

Interest in 5th Years = ( 100 P + 14400)R/100 =  PR + 144R = 3600 + 144R

Amount after 5 year = 100 P + 14400 + 3600 + 144R

= 100P + 18000 + 144R

Interest in 6th Year =(100P + 18000 + 144R)R/100 = PR + 180R + 1.44R²

= 3600 + 180R + 1.44R²

Interest in 6 years = 14400 + 3600 + 144R + 3600 +180R + 1.44R² = 26784

=> 1.44R² + 324R - 5184 = 0

=> R² + 225R - 3600 = 0

=> R² + 240R - 15R - 3600 = 0

=> R(R + 240) - 15(R + 240) = 0

=> (R -15)(R + 240) = 0

=> R = 15

PR = 3600

P = 240

100P = Rs 24000

the amount lent by Rahul to Mohit​ = Rs 24000