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Question
Find the true discount, banker’s discount and banker’s gain on a bill of ₹ 4,240 due 6 months hence at 9% p.a.
Solution
Given, S.D. = ₹ 4,240,
n = `6/12 = 1/2` years, r = 9% p.a.
Since, B.D. = `("S.D." xx "n" xx "r")/100`
∴ B.D. = `(4,240 xx 1/2 xx 9)/100`
`= (4,240 xx 9)/(100 xx2)`
∴ B.D. = ₹ 190.80
Let true discount be ₹ x
Now, B.D. = T.D. + Interest on T.D. for `1/2` year at 9% p.a.
∴ 190.80 = `x + (x xx 1/2 xx 9/100)`
∴ `190.80 = x + (9x)/200`
∴ `190.80 = (209 x)/200`
∴ x = `(190.80 xx 200)/209`
∴ x = ₹ 182.58
∴ T.D. = ₹ 182.58 ≈ ₹ 182.60
Also, B.G. = B.D. – T.D. = 190.8 – 182.58
∴ B.G. = ₹ 8.22 ≈ ₹ 8.20
∴ True discount, banker’s discount and banker’s gain are ₹ 182.60, ₹ 190.80 and ₹ 8.20 respectively.
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