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…

Solution
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

Solution
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