A shopkeeper sells a table at 8% profit and a chair at 10% discount, thereby getting ₹1008. If he had sold the table at 10% profit and chair at 8% discount, he would have got ₹20 more. Find the cost price of the table and the list price of the chair.

Let the cost price of table be ₹x and list price of chair be ₹y.

According to first condition,

$\Rightarrow \dfrac{108}{100}x + \dfrac{90}{100}y = 1008 \\[1em] \Rightarrow \dfrac{108x + 90y}{100} = 1008 \\[1em] \Rightarrow 108x + 90y = 100800 \\[1em] \Rightarrow 18(6x + 5y) = 100800 \\[1em] \Rightarrow 6x + 5y = \dfrac{100800}{18} \\[1em] \Rightarrow 6x + 5y = 5600 ……(i)$

According to second condition,

$\Rightarrow \dfrac{110}{100}x + \dfrac{92}{100}y = 1028 \\[1em] \Rightarrow \dfrac{110x + 92y}{100} = 1028 \\[1em] \Rightarrow 110x + 92y = 102800 \\[1em] \Rightarrow 2(55x + 46y) = 102800 \\[1em] \Rightarrow 55x + 46y = 51400 ……(ii)$

Multiplying (i) by 55 and (ii) by 6, we have

⇒ 330x + 275y = 308000 ……..(iii)

⇒ 330x + 276y = 308400 ……..(iv)

Subtracting eq. (iii) from (iv) we get,

⇒ (330x + 276y) - (330x + 275y) = 308400 - 308000

⇒ 330x - 330x + 276y - 275y = 400

⇒ y = 400.

On substituting value of y in (i) we get,

⇒ 6x + 5(400) = 5600

⇒ 6x + 2000 = 5600

⇒ 6x = 3600

⇒ x = 600.

Hence, cost of table = ₹600 and cost of chair = ₹400.