Let the cost price of one table and one chair be ₹ x and ₹ y, respectively. 

So, 

The selling price of the table, when it’s sold at a profit of 10% = ₹ x + 10x/100 = ₹ 110x / 100 

The selling price of the chair, when it’s sold at a profit of 25% = ₹ y + 25y/100 = ₹ 125y / 100 

Hence, according to the question 

110x / 100 + 125y / 100 = 1050 … (i) 

Similarly, 

The selling price of the table, when it’s sold at a profit of 25% = ₹ (x + 25x/100) = ₹ 125x/ 100 

The selling price of the chair, when it’s sold at a profit of 10% = ₹ (y + 10y/100) = ₹ 110y / 100 

Hence, again from the question 

125x / 100 + 110y / 100 = 1065 … (ii) 

Re- written (i) and (ii) with their simplest coefficients, 

11x/10 + 5y/4 = 1050…….. (iii) 

5x/4 + 11y/10 = 1065…….. (iv) 

Adding (iii) and (iv), we get 

(11/ 10 + 5/ 4)x + (5/ 4 + 11/ 10)y = 2115 

47/ 20x + 47/ 20y = 2115 

x + y = 2115(20/ 47) = 900 

⇒ x = 900 – y ……. (v) 

Using (v) in (iii), 

11(900 – y)/10 + 5y/4 = 1050 

2(9900 -11y) + 25y = 1050 x 20 [After taking LCM] 

19800 – 22y + 25y = 21000 

3y = 1200 

⇒ y = 400 

Putting y = 400 in (v), we get 

x = 900 – 400 = 500 

Therefore, the cost price of the table is ₹ 500 and that of the chair is ₹ 400.