A shopkeeper sold 8 chairs at a profit of 20% and 6 chairs at a profit of 10%. Had he sold all the 14 chairs at a profit of 12%, his profit would have been reduced by 442. What is the cost price of each chair? (cost of each chair is same)

Let C.P. of each chair = $$100x$$

Case 1 : 8 chairs sold at 20% profit

=> S.P. of 8 chairs = $$8 \times \frac{120}{100} \times 100x = 960x$$

6 chairs sold at 10% profit

=> S.P. of 6 chairs = $$6 \times \frac{110}{100} \times 100x = 660x$$

$$\therefore$$ Total S.P. of 14 chairs = $$960x + 660x = 1620x$$

Case 2 : 14 chairs sold at 12% profit

=> S.P. of 14 chairs = $$14 \times \frac{112}{100} \times 100x = 1568x$$

Acc. to ques,

=> $$1620x - 1568x = 442$$

=> $$52x = 442$$

=> $$xx = \frac{442}{52} = 8.5$$

$$\therefore$$ C.P. of 1 chair = $$100 \times 8.5$$ = Rs. 850