Question

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

Answer 1

Let  the  principle be  P  and rate  of  interest  r.

For  one  year,

Time (t) = 1 year

rate  of interest = r

principle  = P

Simple  interest (I₁) = A - P = 2200 - P

Amount  = Rs. 2200

We know that,

$S.I.=\frac{p\times r\times t}{100}\\\;\\I_1=\frac{P\times r\times1}{100}\\\;\\A-P=\frac{Pr}{100}\\\;\\2200-P=\frac{Pr}{100}\;\;\;................i)$

For  four   year,

Time (t) = 4 year

rate  of interest = r

principle  = P

Simple  interest (I₂) = A - P = 2800 - P

Amount  =  Rs.2800

We know that,

$S.I.=\frac{p\times r\times t}{100}\\\;\\I_2=\frac{P\times r\times4}{100}\\\;\\A-P=\frac{4Pr}{100}\;\;........................ii)$

Comparing  Eq. i) and  ii)

$2200-P=\frac{2800-P}{4}\\\;\\2200-P=\frac{2800}{4}-\frac{P}{4}\\\;\\2200-P=700-\frac{P}{4}\\\;\\2200-700=P-\frac{P}{4}\\\;\\1500=\frac{4P-P}{4}\\\;\\6000=3P\\\;\\P=2000\\\;\\\;\\\text{Putting P=2000 in eq. ii)}\\\;\\\frac{2800-P}{4}=\frac{Pr}{100}\\\;\\\frac{2800-2000}{4}=\frac{2000\times r}{100}\\\;\\\frac{800}{4}\\\;\\200=20r\\\;\\r=10\%$