Question

If the difference between true discount and banker's discount on a sum due 4 months hence is Rs 20,  find true discount, banker's discount and amount of the bill, the rate of simple interest charged being 5% p.a .

Answer 1

Given the difference B.D - T.D = Rs 20 

N = 4 months = `4/12 = 1/3` year

And r = 5% p.a.

Since. B.G = B.D -T.D 

∴ B.G = Rs 20. 

Let true discount be Rs x 

Now, B.G = interest on. T.D for 

4 months `(1/3 "year")` at 5 % p.a.

`=> 20 = "x" xx 1/3 xx 5/100`

`=> "x" = (20 xx 100 xx 3)/5 = 1200`

∴ x = Rs 1200

∴ True discount = Rs 1,200 

B.G = B.D - T.D 

⇒ 20 = B.D - 1,200 

∴  BD = Rs. 1,200 

Banker's discount is Rs 1,220.

Also, B.D = interest on Face value (F.V) for n years at r% p.a. 

Let y be the face value 

i.e. B.D = `("y" xx "n" xx "r")/100`

`=> 1220 = ("y" xx 1/3 xx 5)/100`

`=> 1220 xx 100 = "5y"/3`

`=> "y" = (122000 xx 3)/5 = 73200`

∴ y = Rs 73,200

∴  Amount of the bill (face value) is Rs 73,200.