Question

Find the Rate of Interest for a Given Sum of Money
A sum of money amounts to Rs. 5,200 in 5 years and Rs. 5,680 in 7 years at simple interest. What was the rate of interest charged per annum? a) 3% b) 4% c) 5% d) 6%

Answer 1

The rate of interest charged is 6% and the amount is Rs. 4000.

Let us look at how to arrive at this.

If x is the principal amount and r is the rate of interest, then,

Interest in 5 years, i1 = 5xr/100 and T1 = x+i1 = x + 5xr/100 = 5200

On similar lines, we get i2 = 7xr/100 and T2 = x+7xr/100 = 5680

So, we have a sequence of two equations and two unknowns, x and r.

Let us solve for x and r.

From T2 and T1, we get

5680 = x+7xr/100 ---- (1)
5200 = x+5xr/100 ---- (2)

Subtracting (2) from (1), we get

480 = 2xr/100

Or xr = 24000

or r = 24000/x

Substituting the value of r = 24000/x in (2), we get

5200 = x + 5*x*24000/x/100

5200 = x + 5*240 = x+1200

Therefore x = 5200 - 1200 = 4000

Substituting the value of x = 4000 in r = 24000/x, we get

r = 24000/4000 = 6%.

Hence, the rate of interest is 6% and principal amount is Rs. 4000.

Please mark it as brainly.