Chef X, Chef Y, and Chef Z can prepare 22 dishes individually in 5 hours, 10 hours, and 15 hours respectively. For the presidential brunch, they agreed upon 22 dishes that they would prepare together. All three chefs started cooking at 8 am, but due to some personal emergency, Chef Y had to leave at 10 am. At what time would the brunch be ready?

Solution

Fraction of the dishes prepared by Chef X in 1 hour = 1/5 Fraction of the dishes prepared by Chef Y in 1 hour = 1/10 Fraction of the dishes prepared by Chef Z in 1 hour = 1/15 ∴ Fraction of the dishes prepared by all three chefs in 1 hour = 1/5 + 1/10 + 1/15 = 11/30 Also, Fraction of dishes prepared by Chef X and Chef Z in hour = 1/5 + 1/15 = 4/15 From 8 am to 10 am, all the Chefs were working. They all worked for 2 hours. ⇒ Fraction of the dishes prepared = 2 * 11/30 = 11/15 ∴ Pending fraction of dishes = 1 - 11/15 = 4/15 ∴ Time taken by Chef X and Chef Z to prepare the remaining dishes = (4/15)/(4/15) = 1 hour = 60 min. ⇒ The brunch will be ready at 11:00 am.