Three pipe P, Q and R can fill a tank in 12 minutes, 18 minutes and 24 minutes respectively. The pipe R is closed 12 minutes before the tank is filled. In what time the tank is full?
(a) \(\displaystyle 8(\frac{5}{{13}})hrs\)
(b) \(\displaystyle 8(\frac{4}{{13}})hrs\)
(c) \(\displaystyle 7(\frac{4}{{13}})hrs\)
(d) \(\displaystyle 8(\frac{6}{{13}})hrs\)
(e) None of these
Answer for this MCQ Time and Work is (b)
Let T is the time taken by the pipes to fill the tank
we will get T = \(\displaystyle \frac{{108}}{{13}}=8(\frac{4}{{13}})hrs\)
A, B and C can alone complete a work in 10, 12 and 15 days respectively. A and C started the work and after working for 4 days, A left and B joined. In how many days the total work was completed?
(a) \(\displaystyle 6\frac{5}{9}\) days
(b) \(\displaystyle 6\frac{2}{9}\) days
(c) 6 days
(d) \(\displaystyle 5\frac{4}{9}\) days
(e) \(\displaystyle 7\frac{2}{9}\) days
Answer for this MCQ Time and Work is (b)
(A + C) = \(\displaystyle \frac{1}{{10}}+\frac{1}{{15}}=\frac{1}{6}\). They worked for 4 days so did
\(\displaystyle \frac{1}{6}\times 4=\frac{2}{3}\) of work
Remaining work = \(\displaystyle 1-\frac{2}{3}=\frac{1}{3}\)
Now A left, B and C working
(B + C) = \(\displaystyle (\frac{1}{{12}}+\frac{1}{{15}})=\frac{9}{{60}}=\frac{3}{{20}}\).
They worked for x days and completed \(\displaystyle \frac{1}{3}rd\) of work so \(\displaystyle \frac{3}{{20}}\times x=\frac{1}{3}\)
So x = \(\displaystyle \frac{{20}}{9}days\)
Total = \(\displaystyle 4+\frac{{20}}{9}=\frac{{56}}{9}=6\frac{2}{9}day\)
There are 4 filling pipes and 3 emptying pipes capable of filling and emptying in 12 minutes and 15 minutes respectively. If all the pipes are opened together and as a result they fill 10 litres of water per minute. Find the capacity of the tank.
A and B can do a piece of work in 72 days. B and C can do it in 120 days, A and C can do it in 90 days. In how many days all the three together can do the work ?
(a) 60 days
(b) 80 days
(c) 100 days
(d) 150 days
(e) 200 days
Answer for this MCQ Time and Work is (a)
(A+B)’s 1 day’s work = \(\displaystyle \frac{1}{{72}}\)
(B+C)’s 1 day’s work = \(\displaystyle \frac{1}{{120}}\)
(C+A)’s 1 day’s work = \(\displaystyle \frac{1}{{90}}\)
On adding all three
2 (A + B + C)’s 1 days work = \(\displaystyle \frac{1}{{72}}+\frac{1}{{120}}+\frac{1}{{90}}\)
A particular job can be completed by a team of 10 men in 12 days. The same job can be completed by a team of 10 women in 6 days. How many days are needed to complete the job if the two teams work together?
(a) 4 days
(b) 6 days
(c) 9 days
(d) 18 days
(e) 15 days
Answer for this MCQ Time and Work is (a)
According to question,
10 men’s one day’s work = \(\displaystyle \frac{1}{{12}}\)
Therefore, 1 man one day’s work = \(\displaystyle \frac{1}{{12\times 10}}=\frac{1}{{120}}\)
Similarly,
1 woman one day’s work = \(\displaystyle \frac{1}{{6\times 10}}=\frac{1}{{60}}\)
(1 man + 1 woman)’s one day’s work = \(\displaystyle \frac{1}{{120}}+\frac{1}{{60}}=\frac{{1+2}}{{120}}=\frac{3}{{120}}=\frac{1}{{40}}\)\(\displaystyle \frac{1}{{120}}+\frac{1}{{60}}=\frac{{1+2}}{{120}}=\frac{3}{{120}}=\frac{1}{{40}}\)
10 men + 10 women)’s one day’s work = \(\displaystyle \frac{{10}}{{40}}=\frac{1}{4}\)
Therefore, both the teams can finish the whole work in 4 days.
A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?
(a) 7.5 days
(b) 5.4 days
(c) 3.6 days
(d) 3 days
(e) 5 days
Answer for this MCQ Time and Work is (c)
According to question,
A can finish the whole work in 6 days.
A’s one day’s work = \(\displaystyle \frac{1}{6}\)
Similarly,
B’s one day’s work = \(\displaystyle \frac{1}{9}\)
(A + B)’s one day’s work = \(\displaystyle (\frac{1}{6}+\frac{1}{9})=(\frac{{3+2}}{{18}})=\frac{5}{{18}}\)
Therefore, (A + B)’s can finish the whole work in \(\displaystyle \frac{{18}}{5}\) days i.e., 3.6 days
Alternate Method :
Time taken = \(\displaystyle \frac{{6\times 9}}{{9+6}}=\frac{{54}}{{15}}=3.6days\)
A and B can do a piece of work in 10 days, B and C in 15 days and C and A in 20 days. C alone can do the work in :
(a) 60 days
(b) 120 days
(c) 80 days
(d) 30 days
(e) 70 days
Answer for this MCQ Time and Work is (b)
According to the question Work done by A and B together in one day = \(\displaystyle \frac{1}{{10}}part\)
Work done by B and C together in one day = \(\displaystyle \frac{1}{{15}}part\)
Work done by C and A together in one day = \(\displaystyle \frac{1}{{20}}part\)
So,
A + B = \(\displaystyle \frac{1}{{10}}\) ….(I)
B + C = \(\displaystyle \frac{1}{{15}}\) …(II)
C + A = \(\displaystyle \frac{1}{{20}}\) ….(III)
Adding I, II, III, we get
2 (A + B + C) = \(\displaystyle \frac{1}{{10}}+\frac{1}{{15}}+\frac{1}{{20}}\)
2 (A + B + C) = \(\displaystyle \frac{{6+4+3}}{{60}}=\frac{{13}}{{60}}\)
A + B + C = \(\displaystyle \frac{{13}}{{120}}\) ….(IV)
