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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.
Solution
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.
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