Question

The respective ratio of cost price of articles A and B is 7:9. Article A was sold at a profit of 40% and article B was sold at a profit of 10%. If the total profit earned after selling both the articles (A and B) is Rs. 148, what is the difference between cost price of articles A and B?

• A. Rs.120
  
• B. Rs.160
  
• C. Rs.200
  
• D. Rs.80
  
• E. Rs.40

Answer 1

The correct option is D Rs.80


Let, the cost price of articles A be $C{P}_1$
and cost price of Article B be $C{P}_2.$
Cost Price= $\frac{Profit}{Profit\%}\times 100$
$\Rightarrow C{P}_1=\frac{P_1}{40}\times 100\Rightarrow C{P}_1=\frac{P_1}{4}\times 100andC{P}_2=\frac{P_2}{40}\times 100\Rightarrow C{P}_2=P_2\times 10Hence,\frac{C{P}_1}{C{P}_2}=\frac{10P_1}{4}\times \frac{1}{10P_2}=\frac{P_1}{4P_2}\Rightarrow \frac{P_1}{4P_2}=\frac{7}{9}[\because \frac{C{P}_1}{C{P}_2}=\frac{7}{9}(given\left)\right]\Rightarrow P_1=\frac{28P_2}{9}Now,P_1+P_2=148\Rightarrow \frac{28P_2}{9}+P_2=148\Rightarrow 37P_2=148\times 9\Rightarrow P_2=4\times 9=Rs.36and{P}_1=\frac{28P_2}{9}=\frac{28}{9}\times 36=Rs.112$
$C{P}_1=\frac{P_1}{40}\times 100,C{P}_1=\frac{112}{40}\times 100=Rs.280C{P}_2=\frac{P_2}{10}\times 100=\frac{36}{10}\times 100C{P}_2=Rs.360$
Difference of cost price of Article A and B= $C{P}_2-C{P}_1=(360-280)=Rs.80$