Question

A certain sum of money amounts to ₹6,500 in 3 years and ₹5,750 in 1 1/2years
respectively . Find the principal and the rate percent.

Answer 1

Let principal = P
rate = R% 

for t=3 years, A = 6500
A = P + PTR/100
⇒6500 = P + 3PR/100
⇒6500 = P + 0.03PR
⇒ R = (6500-P)/0.03P

for t=1.5 years, A = 5750
A = P + PTR/100
⇒5750 = P + 0.015PR
⇒ 5750 = P + 0.015P[(6500-P)/0.03P]
⇒ 5750 = P + (6500-P)/2
⇒ 5750 = P + 3250 - 0.5P
⇒ 5750 - 3250 = 0.5P 
⇒ 0.5P = 2500
⇒ P = 2500/0.5 = Rs. 5000

R = (6500-P)/0.03P = (6500-5000)/(0.03×5000) = 1500/150 = 10

Principal is Rs. 5000 and rate is 10%.

Answer 2

t=3 a=65oo
a=P+PTR/100
6500=P+3PR/100
P=5000
R=1500/150 = 10%
PRINCIPAL=5000
RATE PERCENT=10%