Question

A man sells three articles. First article for $Rs24,000$ at $20\%$ profit, second article for $Rs18,900$ at $125\%$ profit and the third for $Rs14,850.$ If on the whole, he gains $3\frac{1}{8}\%,$ find the cost price of the third article.

• A. $27,400$
• B. $27,600$
• C. $27,800$
• D. $28,000$

Answer 1

The correct option is B $27,600$

For $1$^st article

Selling Price of $1$^st article $=24000$

Profit on $1$^st article $=20$%

$S.P=C.P+20$% of $C.P=\left(120/100\right)\times C.P$

$C.P=24000\times \frac{100}{120}=20000$

For $2$^nd article

Selling Price $=18900,$ Profit $=125$%

$S.P=C.P+125$% of$C.P=\frac{225}{100}\times C.P$

$C.P=18900\times \frac{100}{225}=8400$

Selling price of $3$^rd article $=14850$

Total $S.P=24000+18900+14850=57750$

and given total profit he makes is $\frac{25}{3}$%

Total Profit percept $=\frac{Totalprofit}{TotalC.P.}\times 100$

$\Rightarrow \frac{\left(\frac{25}{3}\right)}{100}=\frac{(S.P-C.P)}{C.P}=\left(\frac{S.P}{C.P}\right)-1=\frac{25}{300}\Rightarrow \frac{S.P}{C.P}=\frac{325}{300}\Rightarrow C.P=57750\times \left(\frac{300}{325}\right)$

Hence the correct $C.P$ is $Rs.27,600$.