Question

a sum of money lent out at simple intrest amounts to ₹2200 in one year and ₹2800 in 4 years. find the sum of money and the rate of intrest

Answer 1

Answer:

Principal = 2000 and rate = 10%

Step-by-step explanation:

Let the sum of money(Principal)  be Rs P

and rate of interest be R%

We know that

Simple interest = PRT/100

For time T = 1 year,

SI = PR/100

Thus amount = P + SI

or 2200 = P + PR/100

or P(1+R/100) = 2200 .............(1)

For time T = 4 years,

SI = 4PR/100 = PR/25

Thus Amount = P + SI

or 2800 = P + PR/25

or P(1+R/25) = 2800................(2)

On dividing equations (1) and (2), P gets cancelled

or (100+R)/4(25+R) = 2200/2800

or  100+R/100+4R = 11/14

or 14(100 + R) = 11( 100 + 4R)

or 14 R + 1400 = 44 R + 1100

or 30 R = 300

or R =10

Substituting R = 10 in equation (1),

P(1 + 10/100) = 2200

or P (11/10)  =  2200

or  P  = 2200 x 10/11 = 2000

Thus, Principal = 2000 and rate = 10%

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