Question

Articles are marked at a price which gives a profit of 25%. After allowing a certain discount, the
profit reduces to 12 - %. Find the discount percent.
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Answer 1

Correct question :

Articles are marked at a price which gives a profit of 25%. After allowing a certain discount, the profit reduces to 12 ½ %. Find the discount percent.

Solution :

$\sf \: Let \: the \: C.P. \: of \: an \: artical \: be \: Rs100 \: \\ \\ \sf then \: to \: attain \: of \: profit \: of \: 25 \: {persent} \\ \\ \sf \: marked \: price \: must \: be \: 25 \: {persent} \: more \: \\ \\ \sf \: then \: the \: cost \: price \\ \\ \sf \: marked \: price \: = \: rs \: 100 \: + rs \: 25 \: \\ \\ \: \: \: \: \: \: \: \: \: \sf = rs \: 125 \\ \\ \sf \: after \: allowing \: the \: certain \: discount \: the \: profit \\ \\ \sf \: reduce \: to \: 12 \frac{1}{2} {persent} \\ \\ \sf \: profit \: = \: 12 \frac{1}{2} {persent} \: of \: cp \: \\ \\ \sf = 12 \frac{1}{2} {persent} \: of \: rs \: 100 \: \\ \\ \sf \: = rs \: 12 \frac{1}{2} \\ \\ \sf \: s.p. \: = c.p. \: + \: profit \: \\ \\ \sf = \: rs \: 100 \: + \: rs \: 12 \frac{1}{2} \\ \\ = \sf \: Rs \: 112 \frac{1}{2} \\ \\ \sf \: now \\ \\ \sf \: m.p \: = \: s.p. \: + discount \\ \\ \leadsto \sf \: discount \: = \: m.p. \: - \: s.p. \\ \\ \leadsto \: \sf \: rs \: 125 \: - 112 \frac{1}{2} \\ \\ \sf \leadsto \: rs \: 12 \frac{1}{2} \\ \\ = \: \sf \: discount \: {persent} \: = \: \frac{discount}{m.p.} \times 100 \\ \\ = \sf \frac{ 12\frac{1}{2} }{125} \times 100 \: \\ \\ = \: 10 \\ \\ \sf \: Hence \: discount \: is \: 10 \: persent$