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Arithmetic: Time and Work Test-7

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Question 1
A tap can fill a tank in 16 min and another can empty it in 8 min. If the tank is already 1/2 full and both the taps are opened together, will the tank be filled or emptied? How long will it take before the tank is either filled or emptied completely as the case may be?
Emptied, 16 min
Filled, 8 min
Emptied, 8 min
Filled, 12 min
Question 1 Explanation: 
Let the volume of tank be 16 l.
Rate of A = 1l/m.
Rate of B= 2 l/m.
The tank will be emptied as clearly the rate of B is more than that of A.
Rate of emptying is = 1 l/min.
½ of the tank can be emptied in 16/2 = 8 mins.
Question 2
Two men and 7 children complete a certain piece of work in 4 days while 4 men and 4 children complete the same work in only 3 days. The number of days required by 1 man to complete the work is
60 days
15 days
6 days
51 days
Question 2 Explanation: 
4 men and 4 children complete the work in 3 days .
Therefore, 1 man and 1 child completed the work in 12 days.
7 men and 7 children complete the work in 12/7 days.
Therefore the rate of work of 7 men and 7 children is 7/12 per day.
2 men and 7 children do ¼ of the work in 1 day.
5 men can do 7/12 -1/4 =4/12 = 1/3 of the work in 1 day.
1 man can do the work in 5 x 3= 15 days.
Question 3
8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work be completed?
5 days
8 days
6 days
4 days
Question 3 Explanation: 
Let a man do 2x units of work per day. Thus a woman does x units of work per day.
8 men can do 16x units of work, 4 women can do 4x units of work.
Total 16x+4x=20x units of work is done in 1 day.
Total amount of work in 6 days = 120x units.
In 2 days: 8 men + 4 women can do 40x units of work.
Amount of work left = 120x - 40x= 80x .
Now, 4 men + 8 women can do 8x+8x= 16 x units in 1 day.
Total number of days required – 80/16= 5 days.
Question 4
Mr. Ram is on tour and he has Rs.360 for his expenses. If he exceeds his tour by 4 days he must cut down daily expenses by Rs.3. The number of days of Mr. Ram's tour program is
20 days
24 days
40 days
42 days
Question 4 Explanation: 
Let the tour expense per day be Rs. T and number of days to be traveled is D.
(T-3)(D+4) = 360 => TD - 3D + 4T - 12 = 360
TD= 360 ----------------1
4T-3D=12 ---------------2
We can see from 1 and 2 that both have to be factors of 360 and are natural numbers.
Valid options (a) and (c).
If D=40 then T=9,
but this is not valid as 4X9-3X40$ \ne $12
Putting D=20 and T= 18.
4T-3D= 72-60 = 12.
Question 5
12 men can complete a piece of work in 36 days. 18 women can complete the same piece of work in 60 days. 8 men and 20 women work together for 20 days. If only women were to complete the remaining piece of work in 4 days, how many women would be required?
Question 5 Explanation: 
12 men can do a piece of work in 36 days.
Therefore, 1 man can do {1/(12 x 36)} units of work in 1 day.
8 men can do {1/(54)} units of work in 1 day.
18 women can do the piece of work in 60 days.
Therefore, 1 woman can do {1/ (18X60)} units of work.
20 women can do {(1/54)} units of work in 1 day.
Total work done be 8 men and20 women in one day is 2/54 = 1/27 units of work.
Total work done in 20 days is 20/27.
Left work = 1-20/27 = 7/27.
7 /27 units of work can be done in {(18 x 60 x 7)/27}= 280 days.
To finish the work in 4 days 280/4 = 70 women would be required.
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