Time And Work - Study Mode
[#101] Two pipes A and B can fill a cistern in 12 min and 16 min respectively. Both the pipes are opened together for a certain time but due to some obstruction the flow of water was restricted to $$frac{7}{8}$$ of full flow in pipe A and $$frac{5}{6}$$ of full in pipe B. This obstruction is removed after some time and tank is now filled in 3 min from that moment. How long was it before the full flow.
Correct Answer
(D) 4.5 min
Explanation
Solution: Let the obstruction remain for x min. Hence, Part of cistern filled in X min + part of cistern filled in 3 min = full cistern $$left[ {frac{{7{ ext{x}}}}{{8 imes 12}} + frac{{5{ ext{x}}}}{{6 imes 16}}}
ight]$$ xa0xa0 $$ + $$ $$left[ {frac{3}{{12}} + frac{3}{{16}}}
ight]$$ xa0 = 1 $$frac{{12{ ext{x}}}}{{96}} + frac{7}{{16}} = 1$$ Thus, X = 4.5 min.
[#102] Three pipes A,B and C attached to a cistern. A can fill it in 10 min, B in 15 min, C is a waste pipe for emptying it. After opening both the pipes A and B, a man leaves the cistern and returns when the cistern should have been just full. Finding, however, that the waste pipe had left open, he closes it and the cistern now gets filled in 2 min. In how much time the pipe C, if opened alone, empty the full cistern?
Correct Answer
(C) 18 min
Explanation
Solution: Let pipe C alone can empty the cistern in x min. A fills cistern in 1 min = $$frac{1}{{10}}$$ B fills cistern in 1 min = $$frac{1}{{15}}$$ A and B together fill in 1 min $$ = frac{{10 imes 15}}{{10 + 15}} = frac{{150}}{{25}} = 6,{ ext{min}}$$ Since, waste pipe was left open for 6 min then, 6 min, $$frac{6}{x}$$ part of cistern will be emptied by C Now, $$frac{6}{x}$$ part of the cistern would be filled by A and B in 2 min. Hence, cistern will be filled in $$frac{3}{x}$$ min. And $$frac{x}{3}$$ = 6 x = 18 min.
[#103] There is a group of 5 boys and 2 girls. The two groups working together can do four times as much work as a boy and a girl. Ratio of working capacities of a boy and a girl is:
Correct Answer
(A) 2 : 1
Explanation
Solution: Let 1 boy's 1 day's work = x And 1 girl's 1 day's work = y Now, (5 boys + 2 girls)'s work = 5x + 2y Given , 5x + 2y is equal to 4 times work done by a boy and a girl Thus, 5x + 2y = 4(x + y) 5x + 2y = 4x + 4y x = 2y $$frac{{ ext{x}}}{{ ext{y}}} = frac{2}{1}$$ Hence, the required ratio is 2 : 1
[#104] A group of 12 men can do a piece of work in 14 days and other group of 12 women can do the same work in 21 days. They begin together but 3 days before the completion of work, man's group leaves off. The total number of days to complete the work is:
Correct Answer
(C) $$frac{{51}}{5}$$
Explanation
Solution: Let x be the required number of days Given, 12 men and 12 women can complete a work separately in 14 days and 21 days respectively Then, 12 men's 1 day work = $$frac{1}{{14}}$$ And, 12 women's 1 day work = $$frac{1}{{21}}$$ Then , 12 women's 3 days work = $$frac{3}{{21}}$$ = $$frac{1}{7}$$ The remaining work = $$1 - frac{1}{7}$$xa0 = $$frac{6}{7}$$ Man's group leaves 3 days before the completion of work That is, they were working together for x - 3 days Thus, we have $$frac{1}{7}$$ work left to be done in last 3 days by the women's group. This also means $$frac{6}{7}$$ th of work has been done by both the groups (before men left) Now, (12 men + 12 women)'s 1 day work = $$frac{1}{{14}} + frac{1}{{21}}$$ xa0 = $$frac{5}{{42}}$$ i.e., $$frac{5}{{42}}$$ work is done by 2 groups in 1 day. So, $$frac{6}{7}$$ of work is done by 2 groups together in $$frac{{42}}{5} imes frac{6}{7}$$ xa0 = $$frac{{36}}{5}$$ days Total time take to complete the work will be = $$frac{{36}}{5}$$ + 3 = $$frac{{51}}{5}$$
[#105] Vimal can do a piece of work in 20 days, Vimal and Kamal together can do in 12 days. If Kamal does the work only for half a day daily then in how many days the work will be completed ?
Correct Answer
(D) 15
Explanation
Solution: Vimal's 1 day work = $$frac{1}{{20}}$$
Since, Vimal and Kamal can together complete in 12 days i.e. (Vimal + Kamal)'s 1 day work = $$frac{1}{{12}}$$ Then, Kamal's 1 day work, $$ = frac{1}{{12}} - frac{1}{{20}} Rightarrow frac{2}{{60}} Rightarrow frac{1}{{30}}$$ If Kamal Works only for half a day daily, then his 1 day work becomes $$frac{1}{2} imes frac{1}{{30}}$$xa0 = $$frac{1}{{60}}$$ Therefore, 1 day work of both Vimal and Kamal, $$ = frac{1}{{20}} + frac{1}{{60}} Rightarrow frac{4}{{60}} Rightarrow frac{1}{{15}}$$ Hence, the work will be completed in 15 days.