a sum of money kept in a bank amounts to rs.1500 in 5 years and rs.2000 in 10 years at simple interest. find the sum. options are (a) 1250 (b) 1200 (c) 1150 (d) 1000
Answers
Answer:
Option (d): The sum = Rs.1000
Step-by-step explanation:
Let
P the required sum/principle
R be the rate of interest in % per year
T be the time period in years
A be the final amount after T years.
Then:
A = P + PRT/100
= P(1 + RT/100)
We are given that:
Amount = Rs.1500 after 5 years
=> 1500 = P(1+5R/100) .......Eqn1
Also, amount becomes Rs.2000 after 10 years
=> 2000 = P(1 + 10R/100) ......Eqn2
We can simplify Eqn 1 as:
1500 = P(100 + 5R)/100 .........Eqn 3
Similarly, Eqn 2 becomes:
2000 = P(100 + 10R)/100 ............Eqn 4
Dividing Eqn 4 by Eqn 3, we get:
2000/1500 = (100 + 10R) / (100 + 5R) ............(P and 100 get cancelled)
=> (4/3) = (100 + 10R) / (100 + 5R)
=> 4*(100 + 5R) = 3*(100 + 10R)
=> 400 + 20R = 300 + 30R
=> 20R - 30R = 300 - 400
=> -10R = -100
=> 10R = 100
=> R = 10
Substituting for R in Eqn1, we get:
1500 = P(1 + 5*10/100)
=> 1500 = P(1.5)
=> P = 1500/1.5
=> P = 1000
The required initial amount is Rs.1,000