Question

on a certain sum of money the difference between the compound interest of a year payable half-yearly and the simple interest for a year is 180 rupees find the sum lent out if the rate of interest in both the cases is 10% per annum.(without using formula)​

Answer 1

Answer:

Let the principal, P = Rs.x, r = 10%, t = 1 year

 

Using S.I. = Prt/100,

S.I. = Rs.(x × 10 × 1)/100 =Rs.x/10

 

No of conversion period, n = 2 × 1 = 2,

r = 10%/2 = 5% per conversion period, P = x,

 

Using C.I. = P [(1 + r/100)n 1],

C.I. = Rs.x [(1 + 5/100)2 1]

= Rs.x(21/20 ×21/20 1)

= Rs.x(441/400 1)

= Rs.(41/400)x

As per problem, C.I. S.I. = Rs.180

Or, Rs.(41/400)x Rs.x/10 = 180

Or, Rs.(41/400 1/10)x = 180

Or, Rs.x/400 = 180

Or, x = Rs.180 × 400 = Rs.7200