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A machine X can print one lakh books in 8 hours, machine Y can print the same number of books in 10 hours while machine Z can print them in 12 hours. All the machines are started at 8 A.M. while the machine X is closed at 10 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished?

A machine X can print one lakh books in 8 hours, machine Y can print the same number of books in 10 hours while machine Z can print them in 12 hours. All the machines are started at 8 A.M. while the machine X is closed at 10 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished? Correct Answer 12 noon

Given:

X can print one lakh books = 8 hours

Y can print the same number of books = 10 hours

Z can print = 12 hours

Calculation:

(X + Y + Z)'s 1 hour's work = (1/8 + 1/10 + 1/12) = 37/120    

Work done by X, Y and Z in 2 hours = (37/120 × 2) = 37/60  

Remaining work = (1 – 37/60) = 23/60

(Y + Z)'s 1 hour's work = (1/10 + 1/12)

⇒ 11/60

∴ 11/60 work is done by Y and Z in 1 hour.

∴ 23/60 work will be done by Y and Z = (60/11 × 23/60)

⇒ 23/11 hours ≈ 2 hours

∴ the work will be finished approximately 2 hours after 10 A.M., i.e., around 12 P.M.

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