A sum of money burrowed at a particular rate of interest amounts to Rs 8320 in 2 years and Rs 9685 in 3 and a half years. Find the sum burrowed.
To find the sum borrowed, we need to use the formula for simple interest:
Simple Interest = (Principal Amount) × (Rate of Interest) × (Time)
Let's assign variables to the given values:
Principal Amount = P
Rate of Interest = R
Time = T
Now we can use the formula to set up two equations based on the given information:
Equation 1: P × R × 2 = 8320
Equation 2: P × R × (3.5) = 9685
We have two equations and two unknowns (P and R), so we can solve them simultaneously.
First, let's solve Equation 1 for P:
P = 8320 / (2 × R) [Dividing both sides by 2R]
Substitute this value of P in Equation 2:
(8320 / (2 × R)) × R × (3.5) = 9685
(4160 / R) × (3.5) = 9685 [Simplifying]
Now, cross multiply and simplify:
(4160 × 3.5) = 9685 × R
14560 = 9685R
Divide both sides by 9685:
R = 14560 / 9685 ≈ 1.504
Now substitute this value of R back into Equation 1 to find P:
P = 8320 / (2 × 1.504)
P ≈ 2755.35
Therefore, the sum borrowed is approximately Rs 2755.35.