P’s 1 day’s work = \(\displaystyle \frac{1}{{10}}-\frac{1}{{15}}=\frac{{3-2}}{{30}}=\frac{1}{{30}}\)
Therefore, P alone will complete the work in 30 days.
A and B together can do a piece of work in 5 days and A alone can do it in 8 days. B alone can do the same piece of work in
(a) \(\displaystyle 11\frac{1}{3}days\)
(b) \(\displaystyle 12\frac{3}{5}days\)
(c) \(\displaystyle 13\frac{1}{3}days\)
(d) \(\displaystyle 16\frac{4}{5}days\)
(e) \(\displaystyle 16\frac{2}{3}days\)
Answer for this MCQ Time and Work is (c)
(A + B)’s 1 day’s work = \(\displaystyle \frac{1}{5}\)
A’s 1 day’s work = \(\displaystyle \frac{1}{8}\)
B’s 1 day’s work = \(\displaystyle \frac{1}{5}-\frac{1}{8}=\frac{{8-5}}{{40}}=\frac{3}{{40}}\)
B alone will complete the work in \(\displaystyle \frac{{40}}{3}=13\frac{1}{2}days\)
Alternate Method:
Time taken by B = \(\displaystyle \frac{{5\times 8}}{{8-5}}=\frac{{40}}{3}=13\frac{1}{3}days\)
A, B and C together can complete a piece of work in 30 minutes. A and B together can complete the same work in 50 minutes. C alone can complete the work in
(a) 60 minutes
(b) 75 minutes
(c) 80 minutes
(d) 150 minutes
(e) 120 minutes
Answer for this MCQ Time and Work is (b)
Work done by (A + B + C) in 1 minute = \(\displaystyle \frac{1}{{30}}\)
Work done by (A + B) in 1 minute = \(\displaystyle \frac{1}{{50}}\)
Work done by C alone in 1 minute = \(\displaystyle \frac{1}{{30}}-\frac{1}{{50}}=\frac{{5-3}}{{150}}=\frac{2}{{150}}=\frac{1}{{75}}\)
Therefore, C alone will complete the work in 75 minutes.
Alternate Method:
C alone can do in = \(\displaystyle \frac{{xy}}{{x-y}}=\frac{{50\times 30}}{{50-30}}=75\min utes\)
A, B and C individually can do a work in 10 days, 12 days and 15 days respectively. If they start working together, then the number of days required to finish the work is
Ronald and Elan are working on an Assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 110 pages ?
(a) 7 hrs. 30 min.
(b) 8 hrs.
(c) 8 hrs. 15 min.
(d) 8 hrs. 25 min.
(e) 8 hrs. 45 min.
Answer for this MCQ Time and Work is (c)
Ronald’s 1 hour’s work = \(\displaystyle \frac{{32}}{6}=\frac{{16}}{3}pages\)
[Pages typed in 6 hrs. = 32
Therefore, pages typed in 1 hr = \(\displaystyle \frac{{32}}{6}\)]
Elan’s 1 hour’s work = 8 pages
1 hour’s work of the both = \(\displaystyle \frac{{16}}{3}+8=\frac{{40}}{3}pages\)
Required time = \(\displaystyle \frac{{110\times 3}}{{40}}=\frac{{33}}{4}hours\)
