Question

A sum of money lent out at simple interest amounts 2880 in 2 years and to 3600 in 5 years find the sum of money and the rate of interest.​

Answer 1

Answer:

Answer: Sum of money is Rs.2,400 and interest is 10 per cent per year

Step-by-step explanation:

P = initial amount

R = rate of interest per cent per year

T = time period in years

A = final amount at the end of period T

SI = Simple Interest = (P*R*T)/100

A = P + SI

Given:

When T = 2, A = 2880

=> 2880 = P + (P*R*2)/100

=> 2880 = P + (2PR/100)

=> 2880 = (100P + 2PR)/100

=> 288000 = 100P + 2PR ...(i)

When T = 5, A = 3600

=> 3600 = P + (P*R*5)/100

=> 3600 = P + (5PR/100)

=> 3600 = (100P + 5PR)/100

=> 360000 = 100P + 5PR ...(ii)

From (i),

100P = 288000 - 2PR

From (ii)

100P = 360000 - 5PR

=> 288000 - 2PR = 360000 - 5PR

=> 3PR = 72000

=> PR = 24000 ....(iii)

Using (iii) in (i), we get:

288000 = 100P + 2*24000

100P = 288000 - 48000

100P = 240000

P = 2400 .....(iv)

Using (iv) in (iii), we get:

2400*R = 24000

=> R = 10 ...(v)

Answer: Sum of money is Rs.2,400 and interest is 10 per cent per year