Question

Two articles A and B are sold for Rs. 1,167 making 5% profit on A and 7% profiton A and 7% profit on B. IF the two articles are sold for Rs. 1,165, a profit of 7% is made on A and a profit of 5% is made on B. Find the cost prices of each article.

Answer 1

Let the cost price of article A = Rs. x
and the cost price of articles B = Rs. y

According to the question,
( x + 5% of x ) +( y + 7% of y ) = 1167

`[ x + 5/100 x ] + [ y + 7/100 y ] = 1167`

`(21x)/(20) + (107y)/100 = 1167`

105x + 107y = 116700                     ...(1)
and,
`[107x]/100 + [105y]/100 = 1165
107x + 105y = 116,500                ...(2)

Adding (1) and (2)
    105x + 107y = 116700
+  107x + 105y = 116500  
     212x + 212y = 233200
Dividing by 212,
x + y = 1100                               ...(3)

subtracting (2) from (1)
    105x + 107y = 116700 
-   107x + 105y = 116500  
     -        -            -             
    - 2x + 2y = 200
Dividing by 2,
- x + y = 100                              ...(4)

Adding equation (4) and (3)
       - x + y = 100
   +    x + y = 1100  
              2y = 1200
                y = 600

from (3)
x +600 = 1100
x = 500
Thus, cost price of article A is Rs. 500 and that of article B is Rs. 600.