Answer :
Sum = P lent out
after one year, Rs 2, 200 = P (1 + r /100 )
After 4 years Rs 2, 800 = P (1 + 4 r /100)
Subtract equation 1 from equation 2 : Rs 2, 800 - RS 2, 200 = 3 P r /100
P r = Rs 20,000
Substituting the value of P r in equation 1 :
2, 200 = P + 200 So P = Rs 2,000.
r = 20,000 / 2,000 = 10
after one year, Rs 2, 200 = P (1 + r /100 )
After 4 years Rs 2, 800 = P (1 + 4 r /100)
Subtract equation 1 from equation 2 : Rs 2, 800 - RS 2, 200 = 3 P r /100
P r = Rs 20,000
Substituting the value of P r in equation 1 :
2, 200 = P + 200 So P = Rs 2,000.
r = 20,000 / 2,000 = 10
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,
[tex]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)[/tex]
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,
[tex]S.I.=\frac{p\times r\times t}{100}\\\;\\I_2=\frac{P\times r\times4}{100}\\\;\\A-P=\frac{4Pr}{100}\;\;........................ii)[/tex]
Comparing Eq. i) and ii)
[tex]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\%[/tex]
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,
[tex]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)[/tex]
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,
[tex]S.I.=\frac{p\times r\times t}{100}\\\;\\I_2=\frac{P\times r\times4}{100}\\\;\\A-P=\frac{4Pr}{100}\;\;........................ii)[/tex]
Comparing Eq. i) and ii)
[tex]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\%[/tex]