2. A certain sum at certain rate of
SI becomes Rs. 1344 in 4 years.
The same sum becomes Rs. 1416
in 6 years at the same rate of
interest, find the sum.
Answers
Solution:
Simple Interest=>
A = P (1 + rt)
whereas,
A = final amount
P = initial principal balance
r = annual interest rate
t = time (in years)
Situation 1 =>
A = Rs. 1344
t = 4 year
r = ?
P = ?
A = P (1 + rt)
1344 = P (1 + 4r)
1344 = P + 4Pr
P = 1344 - 4Pr [Equation 1]
Situation 2 =>
A = Rs. 1416
t = 6 year
r = ?
P = ?
A = P (1 + rt)
1416 = P (1 + 6r)
1416 = P + 6Pr
P = 1416 - 6Pr [Equation 2]
Both Situation 1 and 2 have same Principal(P) and Rate(r) so, equating them
1344 - 4Pr = 1416 - 6Pr
2Pr = 72
Pr = 36
Put value of Pr in Equation 1
P = 1344 - 4Pr
P = 1344 - 4(36)
P = 1344 - 144
P = 1200
The certain sum is Rs. 1200 i.e. the principal sum.
Given :
Amount in 4 years = ₹ 1344
Amount in 6 years = ₹ 1416
To find :
The value of sum .
Solution :
Let sum be P and the rate of interest be R .
Amount = P + ( P * R * Time ) / 100
Now , according to the question ,
1344 = P + ( P * R * 4 ) / 100 ......(i)
1416 = P + ( P * R * 6 ) / 100 ......(ii)
Subtraction (i) from (ii) ,
72 = P * R / 50
=> P * R = 3600 .....(iii)
putting (iii) in (i) ,
1344 = P + ( 3600 * 4 ) / 100
=> P = 1344 - 144
=> P = 1200
The sum is ₹ 1200 .