An article was sold at 25% loss. Had the article been sold for Rs.60 more there would have been a profit 5%. Find the cost price of the article.

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Solution

(i) Suppose the cost price of the article is Rs.100 at loss of 25% the S.P of the article is $R s . (100 - 25) = R s .75 .$
At profit of 5% the S.P of the article is $R s . (100 + 5) = R s .105$
$∴$ The difference of the two S.Ps is $R s .105 - 75 = R s .30$
If the C.P is Rs.100,
The difference in the two S.Ps is Rs.60 then the C.P is $\frac{100}{30} \times 60 = R s .200$
(ii) Suppose the cost price of article is $x$
At 25% loss,
S.P $= x - \frac{25 x}{100} = \frac{75 x}{100} = R s . \frac{3}{4} x$
At 5% profit,
$S . P = x + \frac{5 x}{100} = \frac{105}{100} x = R s . \frac{21}{20} x$
Accordingly, $\frac{21}{20} x - \frac{3}{4} x = 60$
$\Rightarrow \frac{21 x - 15 x}{20} = 60$
$\Rightarrow \frac{6 x}{20} = 60$
$\Rightarrow x = \frac{60 \times 20}{6} = 200$
$∴$ The cost price of article is Rs.200.

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