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

Let cost price of article A be ₹ x and article B be ₹ y.

Given,

Two articles A and B are sold for ₹ 1,167 making 5% profit on A and 7% profit on B.

$\Rightarrow \dfrac{105}{100}x + \dfrac{107}{100}y = 1167 \\[1em] \Rightarrow \dfrac{105x + 107y}{100} = 1167 \\[1em] \Rightarrow 105x + 107y = 116700 \\[1em] \Rightarrow 105x = 116700 - 107y \\[1em] \Rightarrow x = \dfrac{116700 - 107y}{105} …..(1)$

Given,

Two articles A and B are sold for ₹ 1,165 making 7% profit on A and 5% profit on B.

$\Rightarrow \dfrac{107}{100}x + \dfrac{105}{100}y = 1165 \\[1em] \Rightarrow \dfrac{107x + 105y}{100} = 1165 \\[1em] \Rightarrow 107x + 105y = 116500 …..(2)$

Substituting value of x from equation (1) in equation (2),

$\Rightarrow 107 \times \dfrac{116700 - 107y}{105} + 105y = 116500 \\[1em] \Rightarrow \dfrac{12486900 - 11449y}{105} + 105y = 116500 \\[1em] \Rightarrow \dfrac{12486900 - 11449y + 11025y}{105} = 116500 \\[1em] \Rightarrow 12486900 - 424y = 116500 \times 105 \\[1em] \Rightarrow 12486900 - 424y = 12232500 \\[1em] \Rightarrow 424y = 254400 \\[1em] \Rightarrow y = \dfrac{254400}{424} \\[1em] \Rightarrow y = 600$

Substituting value of y in equation (1), we get :

$\Rightarrow x = \dfrac{116700 - 107 \times 600}{105} \\[1em] = \dfrac{116700 - 64200}{105} \\[1em] = \dfrac{52500}{105} \\[1em] = 500.$

Hence, cost of article A = ₹ 500 and cost of article B = ₹ 600.