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प्रश्न
If the difference between true discount and banker's discount on a sum due 4 months hence is Rs 20, find true discount, banker's discount and amount of the bill, the rate of simple interest charged being 5% p.a .
उत्तर
Given the difference B.D - T.D = Rs 20
N = 4 months = `4/12 = 1/3` year
And r = 5% p.a.
Since. B.G = B.D -T.D
∴ B.G = Rs 20.
Let true discount be Rs x
Now, B.G = interest on. T.D for
4 months `(1/3 "year")` at 5 % p.a.
`=> 20 = "x" xx 1/3 xx 5/100`
`=> "x" = (20 xx 100 xx 3)/5 = 1200`
∴ x = Rs 1200
∴ True discount = Rs 1,200
B.G = B.D - T.D
⇒ 20 = B.D - 1,200
∴ BD = Rs. 1,200
Banker's discount is Rs 1,220.
Also, B.D = interest on Face value (F.V) for n years at r% p.a.
Let y be the face value
i.e. B.D = `("y" xx "n" xx "r")/100`
`=> 1220 = ("y" xx 1/3 xx 5)/100`
`=> 1220 xx 100 = "5y"/3`
`=> "y" = (122000 xx 3)/5 = 73200`
∴ y = Rs 73,200
∴ Amount of the bill (face value) is Rs 73,200.
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