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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.
Solution
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.
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