Question

A printer A can print 1 lakh books in 16 hours, printer B can print the same number of books in 20 hrs while printer C can print them in 24 hrs. All the printers are started at 5 p.m. while printer A is closed at 10 p.m. and the remaining two printers complete the work. Approximately at what time will the work be finished?

• A. 11:30 a.m.
• B. 12 midnight
• C. 12:30 p.m.
• D. 12:30 a.m.

Answer 1

The correct option is D

12:30 a.m.

A's 1 hour's work = $\frac{1}{16}$
B's 1 hour's work = $\frac{1}{20}$
C's 1 hour's work = $\frac{1}{24}$
(A + B + C)`s 1 hour`s work
= $\frac{1}{16}+\frac{1}{20}+\frac{1}{24}=\frac{37}{240}$ [LCM of 16, 20, and 24 = 240]

Work done by A, B, and C in 5 hours = $\frac{37}{240}\times 5=\frac{37}{48}$

Remaining work = 1- $\frac{37}{48}$ = $\frac{11}{48}$

(B + C)`s 1 hour`s work
= $\frac{1}{20}+\frac{1}{24}=\frac{11}{120}$ [LCM of 20 and 24 = 120]

Now, $\frac{11}{120}$ work is done by B and C in 1 hour

So, $\frac{11}{48}$ work will be done by B and C in $\frac{120}{11}\times \frac{11}{48}=2.5$ hours

So, the work will be finished in 2 hours 30 mins after 10 p.m i.e. at 12:30 a.m