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.
Answers
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