Question

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.

Answer 1

(i) Suppose the cost price of the article is Rs.100 at loss of 25% the S.P of the article is $Rs.(100-25)=Rs.75.$
At profit of 5% the S.P of the article is $Rs.(100+5)=Rs.105$
$\therefore$ The difference of the two S.Ps is $Rs.105-75=Rs.30$
If the C.P is Rs.100,
The difference in the two S.Ps is Rs.60 then the C.P is $\frac{100}{30}\times 60=Rs.200$
(ii) Suppose the cost price of article is $x$
At 25% loss,

S.P $=x-\frac{25x}{100}=\frac{75x}{100}=Rs.\frac{3}{4}x$
At 5% profit,
$S.P=x+\frac{5x}{100}=\frac{105}{100}x=Rs.\frac{21}{20}x$
Accordingly, $\frac{21}{20}x-\frac{3}{4}x=60$

$\Rightarrow \frac{21x-15x}{20}=60$
$\Rightarrow \frac{6x}{20}=60$

$\Rightarrow x=\frac{60\times 20}{6}=200$
$\therefore$ The cost price of article is Rs.200.