Question

The difference between true discount and banker’s discount on 6 months hence at 4% p.a. is ₹ 80. Find the true discount, banker’s discount and amount of the bill.

Answer 1

Given, B.D. – T.D. = ₹ 80,

n = `6/12 = 1/2` year

r = 4% p.a.

Since, B.G. = B.D. – T.D.

∴ B.G. = ₹ 80

But, B.G. = Interest on T.D. for 6 months `(1/2  "years")` at 4% p.a.

∴ 80 = `"T.D." xx 1/2 xx 4/100`

∴ T.D. = `(80xx2xx100)/4`

∴ T.D. = ₹ 4000 

∴ True discount is ₹ 4,000

Also, B.G. = B.D. – x

∴ 80 = B.D. - 4,000

∴ B.D. = 4,000 + 80

∴ B.D. = ₹ 4,080

∴ Banker’s discount is ₹ 4,080.

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

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

∴ 4080 = `("F.V" xx 1/2 xx 4)/100`

∴ 4080 × 100 = F.V. × 2

∴ F.V. = `(4080 xx 100)/2`

∴ F.V. = ₹ 204000

∴ True discount, Banker’s discount and Amount of the bill is ₹ 4,000, ₹ 4,080 and ₹ 2,04,000 respectively.