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प्रश्न
The true discount on a sum is `3/8` of the sum due at 12% p.a. Find the period of the bill.
बेरीज
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उत्तर
Given, T.D. = `3/8 xx` S.D.
∴ T.D. = `3/8 xx ("P.W." + "T.D.")`
∴ `8/3` T.D. = P.W. + T.D.
∴ P.W. = `8/3` T.D. − T.D. ...[Multiply both sides by 8]
8T.D. = 3(P.W. + T.D.)
8T.D. = 3P.W. + 3T.D.
Now bring like terms together:
8T.D. − 3T.D. = 3P.W.
5T.D. = 3P.W.
∴ P.W. = `5/3` T.D.
Also, T.D. = `("P.W." xx "n" xx "r")/100`
∴ T.D. =`(5/3 "T.D." xx"n" xx 12)/100`
∴ T.D. = `(5 "T.D." xx "n" xx 12)/(3 xx 100)`
∴ n = `("T.D." xx 3 xx 100)/(5 "T.D." xx 12)`
∴ n = 5 years
∴ The bill has a 5-year term.
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