Exercise : 5


1. X can do a piece of work in 15 days. If he is joined by Y who is 50% more efficient, in what time will X and Y together finish the work?
(a) 10 days
(b) 6 days
(c) 18 days
(d) Data insufficient
(e) None of these
Ans.b

X’s one day’s work = 115 th work.

Y’s one day’s work = 115 + 50% of 115 = 110 th work.

∴ (X + Y)’s one day’s work = 115 + 110 = 16 th work.

Hence, they together finish the work in 6 days.

2. A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of wall?
(a) 1313 days
(b) 713 days
(c) 613 days
(d) 7 days
(e) None of these
Ans.b

A’s one day’s work = 18th work.

B’s one day’s work = 13rd work.

∴ A’s 4 day’s work = 4 × 18 = 12nd work

∴ In next two days, total wall = 12 + 2(18) - 2(13) = 112th wall

Remaining wall = 1 - 112 = 1112th

Now, 18th wall is built up by A in one day.

1112th wall is built up by A in 8 × 1112 = 713 days.

3. Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is:
(a) 15
(b) 16
(c) 18
(d) 25
(e) None of these
Ans.b

Sakshi’s one day’s work = 120th work.

Tanya’s one day’s work

= 120 + 25% of 120 = 116th work

Hence, Tanya takes 16 days to complete the work.

4. Two taps can fill a tank in 12 and 18 minutes respectively. Both are kept open for 2 minutes and the first is turned off. In how many minutes more will the tank be filled ?
(a) 15 min.
(b) 20 min.
(c) 11 min.
(d) 13 min.
(e) None of these
Ans.d

Part filled by first tap in one min = 112th

Part filled by second tap in one min = 118th

Now, 2[112 + 118] + unfilled part = 1

⇒ unfilled part = 1318th

118th part of tank is filled by second tap in 1 min.

1318th part of tank is filled by second tap in 1 min.

= 18 × 1318 min = 13 min.

5. A cistern normally takes 6 hours to be filled by a tap but because of a leak, 2 hours more. In how many hours will the leak empty a full cistern ?
(a) 20 hours
(b) 24 hours
(c) 26 hours
(d) 18 hours
(e) None of these
Ans.b

∵ cistern fill in 6 hours.

∴ in 1 hour, filled part = 16th

Now, due to leakage, filled part in 1 hour = 18th

Part of the cistern emptied, due to leakage in 1 hour

= 16 - 18 = 124th

∴ The leakage will empty the full cistern in 24 hrs.

6. One fill pipe A is 3 times faster than second fill pipe B and takes 10 minutes less time to fill a cistern than B takes. Find when the cistern will be full if fill pipe B is only opened.
(a) 20 min
(b) 18 min
(c) 15 min
(d) 10 min
(e) None of these
Ans.c

Let B can fill the cistern in x min. Then,

then A can fill the cistern in x3 min

Given x - x3 = 10 ⇒ x = 15 min.

7. Two pipes can fill a cistern in 14 and 16 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom, 32 minutes extra are taken for the cistern to be filled up. If the cistern is full, in what time would the leak empty it ?
(a) 110 hours
(b) 112 hours
(c) 115 hours
(d) 100 hours
(e) None of these
Ans.b

Cistern filled by both pipes in one hour

= 114 + 116 = 15112th

∴ Both pipes filled the cistern in 11215 hrs.

Now, due to leakage both pipes filled the cistern in

11215 + 3260 = 8 hrs.

∴ due to leakage, filled part in one hour 18

∴ part of cistern emptied, due to leakage in one hour

= 15112 - 18 = 1112th

∴ in 112 hr, the leakage would empty the cistern.

8. Two pipes A and B can fill a cistern in 10 and 15 minutes respectively. Both fill pipes are opened together,but at the end of 3 minutes, ‘B’ is turned off. How much time will the cistern take to fill ?
(a) 6 min
(b) 8 min
(c) 10 min
(d) 12 min
(e) None of these
Ans.b

In one min, (A + B) fill the cistern = 110 + 115 = 16th

In 3 min, (A + B) fill the cistern = 36 = 12th

Remaining part = 1 - 12 = 12

110th part filled by A in one min.

12nd part filled by A in 10 × 12 = 5 min.

∴ Total time = 3 + 5 = 8 min.

9. A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the three are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty the full cistern ?
(a) 10 min
(b) 12 min
(c) 15 min
(d) 9 min
(e) None of these
Ans.a

Work done by the waste pipe in 1 minutes

= 120 - (112 + 115) = -110 [-ve sign means emptying]

∴ Waste pipe will empty the full cistern in 10 minutes.

10. Two taps A and B can fill a cistern in 12 minutes and 18 minutes respectively. They are turned on at the same time. If the tap A is turned off after 4 minutes, how long will tap B take to fill the rest of the cistern ?
(a) 8 min.
(b) 9 min.
(c) 10 min.
(d) 7 min.
(e) None of these
Ans.a

In one min, (A + B) fill the cistern = 112 + 118 = 536th

In 4 min, (A + B) fill the cistern = 536 × 4 = 59th

Rest part = 1 - 59 = 49th

118th part is filled by B in one min.

49th part is filled by B in 18 × 49 = 8 min.