Solve the Time and Work Questions check the solutions:
A and B together can do a piece of work in 36 days, B and C together can do it in 24 days. A and C together can do it in 18 days. The three working together can finish the work in
(a) 8 days
(b) 16 days
(c) 30 days
(d) 32 days
(e) 45 days
Answer for this MCQ Time and Work is (b)
(A + B)’s 1 day’s work = \(\displaystyle \frac{1}{{36}}\)
(B + C)’s 1 day’s work = \(\displaystyle \frac{1}{{24}}\)
(A + C)’s 1 day’s work = \(\displaystyle \frac{1}{{18}}\)
On adding all three,
2 (A + B + C)’s 1 day’s work = \(\displaystyle \frac{1}{{36}}+\frac{1}{{24}}+\frac{1}{{18}}=\frac{{2+3+4}}{{72}}=\frac{9}{{72}}=\frac{1}{8}\)
(A + B + C)’s 1 day’s work = \(\displaystyle \frac{1}{{16}}\)
Required time = 16 days
A can do as much work in 4 days as B can do in 5 days, and B can do as much work in 6 days as C in 7 days. In what time will C do a piece of work which A can do in a week ?
(a) \(\displaystyle 10\frac{5}{{24}}days\)
(b) \(\displaystyle 4\frac{4}{5}days\)
(c) \(\displaystyle 6\frac{8}{{15}}days\)
(d) \(\displaystyle 12\frac{6}{{19}}days\)
(e) \(\displaystyle 16\frac{5}{9}days\)
Answer for this MCQ Time and Work is (a)
A’s 4 days’ work = B’s 5 days’ work
\(\displaystyle \Rightarrow \) A : B = 4 : 5
Again, B : C = 6 : 7
Therefore,
A : B : C = 4 × 6 : 5 × 6 : 5 × 7 = 24 : 30 : 35
Time taken by A = 7 days
Hence, Time taken by C = \(\displaystyle \frac{{35}}{{24}}\times 7=\frac{{245}}{{24}}=10\frac{5}{{24}}days\)
A can do a piece of work in 10 days, B can do it in 12 days and C can do it in 15 days. In how many days will A, B and C finish it, working all together?
(a) 6 days
(b) \(\displaystyle 5\frac{1}{4}days\)
(c) \(\displaystyle 4\frac{4}{{11}}days\)
(d) 4 days
(e) 11 days
Answer for this MCQ Time and Work is (d)
A’s 1 day’s work = \(\displaystyle \frac{1}{{10}}\)
B’s 1 day’s work = \(\displaystyle \frac{1}{{12}}\)
C’s 1 day’s work = \(\displaystyle \frac{1}{{15}}\)
Therefore,
(A + B + C)’s 1 day’s work = \(\displaystyle \frac{1}{{10}}+\frac{1}{{12}}+\frac{1}{{15}}=\frac{{6+5+4}}{{60}}=\frac{{15}}{{60}}=\frac{1}{4}\)
Required time = 4 days.
A and B can do a piece of work in 72 days. B and C can do it in 120 days and A and C can do it in 90 days. A alone can do it in :
(a) 120 days
(b) 130 days
(c) 150 days
(d) 100 days
(e) 180 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 day’s work = \(\displaystyle \frac{1}{{72}}+\frac{1}{{120}}+\frac{1}{{90}}=\frac{{5+3+4}}{{360}}=\frac{{12}}{{360}}=\frac{1}{{30}}\)
Therefore,
(A + B + C)’s 1 day’s work = \(\displaystyle \frac{1}{{60}}\)
A can do a piece of work in 12 days and B can do it in 18 days. They work together for 2 days and then A leaves. How long will B take to finish the remaining work ?
(a) 6 days
(b) 8 days
(c) 10 days
(d) 13 days
(e) 15 days
Answer for this MCQ Time and Work is (d)
(A+B)’s 2 days’ work = \(\displaystyle 2(\frac{1}{{12}}+\frac{1}{{18}})=\frac{{10}}{{36}}\)
Remaining work = \(\displaystyle 1-\frac{{10}}{{36}}=\frac{{26}}{{36}}\)
Time taken by B to complete \(\displaystyle \frac{{26}}{{36}}\) part of work
A and B can do a piece of work in 28 and 35 days respectively. They began to work together but A leaves after sometime and B completed remaining work in 17 days. After how many days did A leave ?
A and B together can complete a work in 8 days. B alone can complete that work in 12 days. B alone worked for four days. After that how long will A alone take to complete the work ?
(a) 15 days
(b) 18 days
(c) 16 days
(d) 20 days
(e) 25 days
Answer for this MCQ Time and Work is (c)
Time taken by A = \(\displaystyle \frac{{8\times 12}}{4}=24days\)
Work done of by B = \(\displaystyle \frac{4}{{12}}=\frac{1}{3}\)
Remaining work = \(\displaystyle 1-\frac{1}{3}=\frac{2}{3}\)
A can complete a work in 24 days
A can complete \(\displaystyle \frac{2}{3}\) part of work in 16 days
