Explanation

First, find the rate at which the carpenters work:

6 carpenters make 8 chairs in 10 days.

Step 1: Calculate the rate of work per carpenter per day

Rate = 8 chairs / (6 carpenters * 10 days)

= 8 / 60

= 4/30

= 2/15 chairs per carpenter per day

Step 2: Calculate the number of days for 10 carpenters to make 18 chairs

Let the number of days be x.

10 carpenters * x days * (2/15) chairs/carpenter/day = 18 chairs

(20/15)x = 18

(4/3)x = 18

x = 18 * (3/4)

x = 13.5