Question

A man buys two articles at Rs 410. He sells both at the same price. On one he makes a profit of 15% and on the other a loss of 10%. Find the cost price of both.

Answer 1

Let x and y be the cost price of first and second article respectively and z be the selling price of both/
Therefore, x + y = 410     ..........(i)
For first article: profit = 15%

`("z" - x)/x` = 0.15
⇒ z - x = 0.15x
⇒ z = 1.15x..........(ii)
For second article: loss = 10%

`(y - "z")/y` = 0.10
⇒ y - z = 0.10y
⇒ z = 0.9y..........(iii)
Selling price of both are equal, therefore
0.9y = 1.15x

y = `(1.15x)/(0.9)`.......(iv)

Substituting (iv) in (i)

`x + (1.15x)/(0.9)` = 410
⇒ 0.9x + 1.15x = 410 x 0.9
⇒ 2.05x = 369
⇒ x = 180
Substituting value of x in (i)
180 + y = 410
⇒ y = 410 - 180
= 230.
Therefore, cost price of two articles = Rs. 180 and Rs.230.