Working together, a chef and his assistant can make a pastry dessert in 18 minutes. When the chef makes it himself, it takes him 27 minutes less than it takes his assistant working alone. How long does it take the chef to make the dessert?

let the assistant takes = x minutes

assistant does in one minute = 1/x

chef takes = x - 27 minutes

chef does in one minute = 1/(x-27)

both does in one minute = 1/x + 1/(x-27)

= (2x-27)/(x)(x-27)

both does complete work in x(x-27)/(2x-27) minutes

=> 18(2x-27) = x^2 - 27x

=> x^2 - 63x + 486 = 0

=> x = 63 + 45 = 108

=> x = 63-45 = 18 cannot be 18

x = 108 minutes

assistant in 108 minutes

chef in 81 minutes