Question

Two articles are sold for the same price, losing $10\%$ on one and gaining $20\%$ on the other. Find the cost price of each article, if $Rs.40$ is gained on the whole transaction.

• A. $Rs.654$ and $Rs.510$
• B. $Rs.725$ and $Rs.546$
  
• C. $Rs.800$ and $Rs.600$
• D. None of these
  

Answer 1

The correct option is C $Rs.800$ and $Rs.600$

Let selling price of each article $=xRs$
Then, selling price of first article $=xRs$
Loss $=10\%$

C.P of first article$=\frac{100}{90}\times x=\frac{10}{9}\times x$
S.P of second article$=xRs$
Profit $=20\%$

C.P. of second article$=\frac{100}{120}\times x=\frac{5}{6}\times x$

C.P. of both articles $=\frac{10}{9}\times x+\frac{5}{6}\times x=\frac{35x}{18}Rs$

S.P. of both article $=2xRs$
Profit $=2x-\frac{35x}{18}=\frac{x}{18}Rs.$

Then according to the question
$\frac{x}{18}=40$
$x=720$
C.P.of first article $=\frac{100}{90}\times 720=800Rs$
C.P. of second article $=\frac{100}{120}\times 720=600Rs$

Hence, option C.