Question

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

Answer 1

Given, B.D. – T.D. = ₹ 20,

n = `4/12 = 1/3` years and r = 5% p.a.

Since, B.G. = B.D. – T.D.

∴ B.G. = ₹ 20

Let True discount be ₹ x

Now, B.G. = Interest on T.D. for 4 months `(1/3 "years")` at 5% p.a.

∴ `20 = x xx 1/3 xx 5/100`

∴ x = `(20 xx 100 xx 3)/5`

∴ x = ₹ 1,200

∴ True discount is ₹ 1,200.

∴ B.G. = B.D. – T.D.

∴ 20 = B.D. – 1,200

∴ B.D. = 20 + 1,200

∴ B.D. = ₹ 1,220

∴ Banker’s discount is ₹ 1,220.

Also, B.D. = Interest on F.V. for n years at r % p.a.

Let the face value ₹ y

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

∴ `1,220 = (y xx 1/3 xx 5)/100`

∴ `1,220 xx 100 = y xx 5/3`

∴ y = `(1,22,000 xx 3)/5`

∴ y = ₹ 73,200

∴ True discount, Banker’s discount and Amount of the bill (face value) is ₹ 1,200, ₹ 1,220 and  ₹ 73,200 respectively.