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Note: In the complete Time and Work series, Efficiency would mean "Work Done in 1 day", and efficiency has been denoted by small letters, e.g. "a" means "Efficiency of A".
Let the total work be 8 units (because 8 is the LCM of 4 and 8)
Efficiency of x (Work done by x in 1 hour) = 8/4 = 2 units
Efficiency of y (Work done by y in 1 hour) = 8/8 = 1 unit
Work done by (x + y) in 1 hour = 3 units
3 units work in completed in 1 hour. Hence 8 units work will be completed in 8/3 hours or 160 minutes.
Answer: (A)
Let the total work = 60 units
Efficiency of A = 60/20 = +3 units
Efficiency of B = 60/30 = -2 units
Now total work to be performed is 60 units. When 57 units work is complete, A will take 1 more minute to add 3 units and hence will make it a total of 60 units.
Hence time taken to fill the tank = Time taken to perform 57 units of work + 1 minute
Now A and B are opened alternatively. That means for the first minute only A is opened, for the second minute A is closed and B is opened, then for third minute again B is closed and A is opened and so on.
So for each 2 minutes cycle, work done = Efficiency of A + Efficiency of B = +3 + (-2) = 1 unit
1 unit work is done in 2 minutes, so 57 units work is done in 114 minutes
Time taken to fill the tank = 114 + 1 = 115 minutes
Answer: (D)
Explanation : We have to perform a total of 60 units of work. For the 1st minute - A adds 3 units of work, but in the 2nd minute, B adds (-2) units of work and hence makes total work for 2 minutes = (+3) + (-2) = 1 unit. So effectively in 2 minutes, we are just adding 1 unit of work. Hence in 4 minutes, 2 units of work will be performed and in 6 minutes 3 units of work will be performed. Same sequence will continue till 57 units. As soon as 57 units of work is done (in 114 minutes), it will be A's turn to do the work. A will add 3 units of work(in 1 minute) and hence take the total work from 57 units to 60 units. B won't be needed any more.
Let the total work be 240 units.
40 men complete the work in 6 months. Hence 10 men can complete the work in 6*4 = 24 months. Hence, Efficiency of 10 men = 240/24 = 10 units
60 women complete the work in 6 months. Hence 10 women can complete the work in 6*6 = 36 months. Hence, Efficiency of 10 women = 240/36 = 20/3 units
80 boys complete the work in 6 months. Hence 10 boys can complete the work in 6*8 = 48 months. Hence, Efficiency of 10 boys = 240/48 = 5 units
Efficiency of 10 men + Efficiency of 10 women + Efficiency of 10 boys = 10 + 20/3 + 5 = 65/3 units
So, 10 men, 10 women and 10 boys complete 65/3 units of work in 1 month. To complete 120 units(half of the work), they will take = 120 * 3/65 = 72/13 months
Answer: (C)
Let the total work be 112 units and the efficiency of 1 man and 1 woman be m and w respectively
2m + w = 112/14 = 8
4w + 2m = 112/8 = 14
Solve the equations and you will get w = 2 and m = 3
Hence the wage of woman = 2/3 * 180 = Rs. 120
Answer: (A)
A and C complete 19/23 of the work. Hence B does 4/23 of the work
Amount paid to B = 4/23 * 575 = Rs. 100
Answer: (B)
Let A and B complete the work in x days
Then A will complete the work in (x + 8) days and B will complete the work in (x + 4.5) days. Now,
1/(x + 8) + 1/(x + 4.5) = 1/x
Solve the equation and you will get x = 6 hours
Answer: (D)
The question is same the previous one.
Let A, B and C take 'x' days to do the job. Then,
A takes (x + 6) days, B takes (x + 1) days and C taken 2x days
1/(x + 6) + 1/(x + 1) + 1/2x = 1/x
1/(x + 6) + 1/(x + 1) = 1/x – 1/2x
1/(x + 6) + 1/(x + 1) = 1/2x ... (1)
Solve it and you will get x = 2/3
From equation (1) you can see that A and B take 2x days to complete the work
Answer: (D)
If Pratibha finishes the work in X days, then Sonia will take 3X days to finish the same work
Given 3X – X = 60
Or X = 30
Pratibha takes 30 days and Sonia takes 90 days
Answer: (A)
Let the total work be 24 units.
Efficiency of Sunil = 24/4 = 6 units (Since Sunil takes 4 days to complete the work)
Efficiency of Ramesh = 6 * 1.5 = 9 units (Since Ramesh is 1.5 times efficient as Sunil)
Efficiency of Dinesh = 24/6 = 4 units ((Since Sunil takes 6 days to complete the work))
3/m + 7/w = 1/8 ... (ii)
Multiply equation (i) with 3 and equation (ii) with 4
12/m + 18/w = 3/10
12/m + 28/w = 1/2
Subtract the equations
10/w = 1/5
So 10 women will complete the work in 5 days
Answer: (5)
Q. 24) If 3 men or 4 women can reap a field in 43 days, how long will 7 men and 5 women take to
reap it?
There is a direct formula to solve such questions
Here W is the work. For e.g., if 5 men are cutting 10 trees in 2 days, working 4 hours per day. Then,
M = 5, D = 2, H = 4 and W = 10.
D1 = 18
D2 = 12
H2 = ?
We know, H1 * D1 = H2 * D2
6 * 18 = H2 * 12
H2 = 9 hours
Answer : (B)
M1 = 15
D1 = 20
H1 = 8
M2 = 20
D2 = 12
H2 = ?
We know, M1 * D1 * H1 = M2 * D2 * H2
15*20*8 = 20*12*H2
H2 = 10 hours
Answer : (B)
In this question, Taps = Men
Number of taps required = 20*9/15 = 12
Answer : (B)
Let there be X number of men.
X men can finish a piece of work in 100 days. Hence total work = 100X
If there were (X - 10) men, it would have taken 110 days to finish the work. Total work in this case = 110(X - 10)
Total work remains the same. Hence,
100X = 110(X - 10)
X = 110
Answer : (D)
Efficiency of Subhash = 50/10 = 5 per hour
Efficiency of Subhash and Prakash = 300/40 = 7.5 per hour
Efficiency of Prakash = (Efficiency of Subhash and Prakash) - (Efficiency of Subhash) = 7.5 - 5 = 2.5
So Prakash can copy 2.5 pages per hour. To copy 30 pages, he would require 30/2.5 or 12 hours.
Answer : (D)
This is a very famous question. A company employed 200 workers to complete a certain work in 150 days. Here the total work is not 200*150 because 200 workers and 150 days was only a plan. In reality, only 1/4th of the work has been done in 50 days. So if they go with the same pace, 200 workers will take 200 days to complete the work.
So total work = 200*200 units
200 workers have worked for 50 days. Hence they have finished 200*50 units of work.
Remaining work = 200*200 - 200*50 = 200*150
Let the number of additional workers required = X.
Now (200+X) workers will work for 100 days to finish the work as per the schedule.
Work they need to perform = (200 + X)*100
Now, (200 + X)*100 = 200*150
X = 100
Answer : (C)
Q. 34) A contractor undertook to finish a certain work in 124 days and employed 120 men.After 64 days,he found that he had already done 2/3 of work. How many men can be discharged now so that the work may finish in time?
A) 56 B) 44 C) 50 D) 60
120 workers finish 2/3 of the work in 64 days. So to complete the whole work, workers will take 64*3/2 or 96 days.
Total work to be performed = 120*96
Now the workers have already finished 2/3 of the work and only 1/3 work has to be performed.
Remaining work = 120*96/3 = 120*32
Let the contractor discharges X men. Remaining workers = 120-X. These workers will continue the work for (124-64) or 60 days. Hence,
120*32 = (120-X)*60
X = 56
Answer : (A)
M1 = 120, D1 = 64, W1 = 2/3
M2 = 120 – x, D2 = 60, W2 = 1/3
(M1*D1)/W1 = (M2*D2)/W2
120*64*3/2 = (120 - x)*60*3
x = 56
Let the total work = 60 units
Efficiency of B = 60/15 = 4
Work done by B in 5 days= 5*4 =20
Earning of B = (20/60) * 720 = Rs. 240
Let the capacity be X
In 1 minute, the first pipe adds X/24 litres
In 1 minute, the second pipe adds X/40 litres
In 1 minute, the third pipe drains off 30 litres
So in 1 minute, all the three pipes are adding (X/24 + X/40 - 30) litres.
In 60 minutes, all the three pipes will add 60*(X/24 + X/40 - 30) litres. Hence
X = 60*(X/24 + X/40 - 30)
X = 600 litres
Note: In the complete Time and Work series, Efficiency would mean "Work Done in 1 day", and efficiency has been denoted by small letters, e.g. "a" means "Efficiency of A".
Q. 1)
Let the total work be 8 units (because 8 is the LCM of 4 and 8)
Efficiency of x (Work done by x in 1 hour) = 8/4 = 2 units
Efficiency of y (Work done by y in 1 hour) = 8/8 = 1 unit
Work done by (x + y) in 1 hour = 3 units
3 units work in completed in 1 hour. Hence 8 units work will be completed in 8/3 hours or 160 minutes.
Answer: (A)
Q. 2)
Let total work be 60 units (LCM of 10 and 12)
Raj completes the work in 12 days. Hence efficiency or per day work of Raj = 60/12 = 5 units
Raj and Ram take 10 days to complete the work, hence their efficiency = 60/10 = 6 units
Now Efficiency of Ram = (Efficiency of Raj and Ram) – (Efficiency of Raj) = 6 – 5 = 1 unit
That means Raj completes 1 unit of work per day. So to perform 60 units of work, he will take 60 days.
Answer: (D)
Let total work = 120 units
Efficiency of A + B = 120/15 = 8 units
Efficiency of B + C = 120/12 = 10 units
Efficiency of C + A = 120/10 = 12 units
Adding all the above 3 equations –
2 * (A + B + C) = 30
Efficiency of (A + B + C) = 15 units
Efficiency of B + C = 120/12 = 10 units
Hence Efficiency of A = Efficiency of (A + B + C) - Efficiency of (B + C) = 15 – 10 = 5 units
Hence time taken by A to do 120 units of work = 120/5 = 24 days
Answer: (D)
Let the total work be 16 units.
Efficiency of first pipe = 16/4 = +4 units
Efficiency of second pipe = 16/16 = -1 units [negative sign because this pipe is emptying the tank]
When both the pipes are opened together, their efficiency = (+4) + (-1) = +3 units [The positive sign indicates that when both the pipes are opened together, their net result will fill the tank]
3 units of work is done in 1 hour
16 units of work is done in 16/3 hours
Answer: (B)
Raj completes the work in 12 days. Hence efficiency or per day work of Raj = 60/12 = 5 units
Raj and Ram take 10 days to complete the work, hence their efficiency = 60/10 = 6 units
Now Efficiency of Ram = (Efficiency of Raj and Ram) – (Efficiency of Raj) = 6 – 5 = 1 unit
That means Raj completes 1 unit of work per day. So to perform 60 units of work, he will take 60 days.
Answer: (D)
Q. 3)
Efficiency of A + B = 120/15 = 8 units
Efficiency of B + C = 120/12 = 10 units
Efficiency of C + A = 120/10 = 12 units
Adding all the above 3 equations –
2 * (A + B + C) = 30
Efficiency of (A + B + C) = 15 units
Efficiency of B + C = 120/12 = 10 units
Hence Efficiency of A = Efficiency of (A + B + C) - Efficiency of (B + C) = 15 – 10 = 5 units
Hence time taken by A to do 120 units of work = 120/5 = 24 days
Answer: (D)
Q. 4)
Efficiency of first pipe = 16/4 = +4 units
Efficiency of second pipe = 16/16 = -1 units [negative sign because this pipe is emptying the tank]
When both the pipes are opened together, their efficiency = (+4) + (-1) = +3 units [The positive sign indicates that when both the pipes are opened together, their net result will fill the tank]
3 units of work is done in 1 hour
16 units of work is done in 16/3 hours
Answer: (B)
Note : In questions where one pipe is emptying the cistern while
another is filling it, you must put a positive or negative sign before
the efficiency. But in questions where both the pipes are emptying the
cistern or both the pipes are filling the cistern, you can take the
efficiency of both the pipes as positive.
Let the total work be 15 units.
Efficiency of first pipe = 15/3 = +5 units
Efficiency of second pipe = 15/3.75 = +4 units
Efficiency of third pipe = 15/1 = -15 units
Efficiency of all the three pipes = 5 + 4 – 15 = -6 units
If all the pipes are opened, it will take 15/6 or 5/2 hours to empty the cistern, but the cistern is already half empty, hence only 5/4 hours are required to empty it.
Answer: (C)
Q. 5)
Efficiency of first pipe = 15/3 = +5 units
Efficiency of second pipe = 15/3.75 = +4 units
Efficiency of third pipe = 15/1 = -15 units
Efficiency of all the three pipes = 5 + 4 – 15 = -6 units
If all the pipes are opened, it will take 15/6 or 5/2 hours to empty the cistern, but the cistern is already half empty, hence only 5/4 hours are required to empty it.
Answer: (C)
Q. 6)
Efficiency of A = 60/20 = +3 units
Efficiency of B = 60/30 = -2 units
Now total work to be performed is 60 units. When 57 units work is complete, A will take 1 more minute to add 3 units and hence will make it a total of 60 units.
Hence time taken to fill the tank = Time taken to perform 57 units of work + 1 minute
Now A and B are opened alternatively. That means for the first minute only A is opened, for the second minute A is closed and B is opened, then for third minute again B is closed and A is opened and so on.
So for each 2 minutes cycle, work done = Efficiency of A + Efficiency of B = +3 + (-2) = 1 unit
1 unit work is done in 2 minutes, so 57 units work is done in 114 minutes
Time taken to fill the tank = 114 + 1 = 115 minutes
Answer: (D)
Explanation : We have to perform a total of 60 units of work. For the 1st minute - A adds 3 units of work, but in the 2nd minute, B adds (-2) units of work and hence makes total work for 2 minutes = (+3) + (-2) = 1 unit. So effectively in 2 minutes, we are just adding 1 unit of work. Hence in 4 minutes, 2 units of work will be performed and in 6 minutes 3 units of work will be performed. Same sequence will continue till 57 units. As soon as 57 units of work is done (in 114 minutes), it will be A's turn to do the work. A will add 3 units of work(in 1 minute) and hence take the total work from 57 units to 60 units. B won't be needed any more.
Q. 7)
40 men complete the work in 6 months. Hence 10 men can complete the work in 6*4 = 24 months. Hence, Efficiency of 10 men = 240/24 = 10 units
60 women complete the work in 6 months. Hence 10 women can complete the work in 6*6 = 36 months. Hence, Efficiency of 10 women = 240/36 = 20/3 units
80 boys complete the work in 6 months. Hence 10 boys can complete the work in 6*8 = 48 months. Hence, Efficiency of 10 boys = 240/48 = 5 units
Efficiency of 10 men + Efficiency of 10 women + Efficiency of 10 boys = 10 + 20/3 + 5 = 65/3 units
So, 10 men, 10 women and 10 boys complete 65/3 units of work in 1 month. To complete 120 units(half of the work), they will take = 120 * 3/65 = 72/13 months
Answer: (C)
Q. 8)
Let the total work be 112 units and the efficiency of 1 man and 1 woman be m and w respectively
2m + w = 112/14 = 8
4w + 2m = 112/8 = 14
Solve the equations and you will get w = 2 and m = 3
Hence the wage of woman = 2/3 * 180 = Rs. 120
Answer: (A)
Q. 9)
A and C complete 19/23 of the work. Hence B does 4/23 of the work
Amount paid to B = 4/23 * 575 = Rs. 100
Answer: (B)
Q. 10)
Then A will complete the work in (x + 8) days and B will complete the work in (x + 4.5) days. Now,
1/(x + 8) + 1/(x + 4.5) = 1/x
Solve the equation and you will get x = 6 hours
Answer: (D)
Q. 11)
The question is same the previous one.
Let A, B and C take 'x' days to do the job. Then,
A takes (x + 6) days, B takes (x + 1) days and C taken 2x days
1/(x + 6) + 1/(x + 1) + 1/2x = 1/x
1/(x + 6) + 1/(x + 1) = 1/x – 1/2x
1/(x + 6) + 1/(x + 1) = 1/2x ... (1)
Solve it and you will get x = 2/3
From equation (1) you can see that A and B take 2x days to complete the work
Answer: (D)
Q. 12)
If Pratibha finishes the work in X days, then Sonia will take 3X days to finish the same work
Given 3X – X = 60
Or X = 30
Pratibha takes 30 days and Sonia takes 90 days
Answer: (A)
Q. 13)
Let the total work be 24 units.
Efficiency of Sunil = 24/4 = 6 units (Since Sunil takes 4 days to complete the work)
Efficiency of Ramesh = 6 * 1.5 = 9 units (Since Ramesh is 1.5 times efficient as Sunil)
Efficiency of Dinesh = 24/6 = 4 units ((Since Sunil takes 6 days to complete the work))
Efficiency of (Sunil + Ramesh + Dinesh) = 6 + 9 + 4 = 19 units
Time required to finish the complete work = 24/19 days
Answer: (D)
Let the total work be 15 units. Efficiency of A = a and Efficiency of B = b
A and B complete the work in 5 days.
Hence efficiency of A and B = 15/5 = 3 units
So, a + b = 3 … (1)
New efficiency of A = 2a
New efficiency of B = b/3
With new efficiency the work was completed in 3 days.
So, 2a + b/3 = 15/3 = 5 … (2)
Solve (1) and (2), you will get a = 12/5 = 2.4 units
So A will complete 15 units work in 15/2.4 or 25/4 days
Answer: (B)
Let the total work be 24 units
Given, 3*Efficiency of A = Efficiency of B + Efficiency of C
3a = b + c
A, B and C compete the work in 24 days.
Hence, a + b + c = 24/24 = 1 or 4a = 1 [Put b + c = 3a]
a = 1/4 = 0.25 unit
A completes 0.25 unit work in 1 day. So to complete 24 units of work, he will take 24/0.25 = 96 days
Answer: (B)
Let the total work be 7 units. Since they all complete the work in 7 days, so their total efficiency = 7/7 = 1 unit
Let efficiency of boy = x
Then efficiency of women = 2x
Efficiency of man = 4x
x + 2x + 4x = 1
7x = 1 or x = 1/7
The boy completes 1/7 work in 1 day, so to complete 7 units of work, he will take 49 days
Answer: (A)
A does 1/2 as much work as B in 3/4 of the time. Hence A will do (1/2 +
1/2) or complete work in (3/4 + 3/4) or 1.5 times more time than B.
A = 1.5B (where A = no. of days taken by A to finish the work and B = no. of days taken by B to finish the work)
Also A*B/(A+B) = 18
Put A = 1.5B in the above equation and solve
B = 30 days
Time required to finish the complete work = 24/19 days
Answer: (D)
Q. 14)
A and B complete the work in 5 days.
Hence efficiency of A and B = 15/5 = 3 units
So, a + b = 3 … (1)
New efficiency of A = 2a
New efficiency of B = b/3
With new efficiency the work was completed in 3 days.
So, 2a + b/3 = 15/3 = 5 … (2)
Solve (1) and (2), you will get a = 12/5 = 2.4 units
So A will complete 15 units work in 15/2.4 or 25/4 days
Answer: (B)
Q. 15)
Given, 3*Efficiency of A = Efficiency of B + Efficiency of C
3a = b + c
A, B and C compete the work in 24 days.
Hence, a + b + c = 24/24 = 1 or 4a = 1 [Put b + c = 3a]
a = 1/4 = 0.25 unit
A completes 0.25 unit work in 1 day. So to complete 24 units of work, he will take 24/0.25 = 96 days
Answer: (B)
Q. 16)
Let the total work be 7 units. Since they all complete the work in 7 days, so their total efficiency = 7/7 = 1 unit
Let efficiency of boy = x
Then efficiency of women = 2x
Efficiency of man = 4x
x + 2x + 4x = 1
7x = 1 or x = 1/7
The boy completes 1/7 work in 1 day, so to complete 7 units of work, he will take 49 days
Answer: (A)
Q. 17)
A = 1.5B (where A = no. of days taken by A to finish the work and B = no. of days taken by B to finish the work)
Also A*B/(A+B) = 18
Put A = 1.5B in the above equation and solve
B = 30 days
Answer: (B)
Let the total work = 60 units
Efficiency of A = 60/20 = 3 units
Efficiency of B = 60/30 = 2 units
Efficiency of (A + B) = 5 units
Work done by A and B in 7 days = 5*7 = 35 units
Work left = 60 – 35 = 25 units
C completes 25 units of work in 10 days. Hence he will complete 60 units of work in 10* 60/25 = 24 days
Answer: (C)
Let total work be 120 units.
Efficiency of A = 120/6 = 20 units
Efficiency of B = 120/12 = 10 units
Efficiency of C = 120/15 = 8 units
Work left = 7/8 * 120 = 105 units
Efficiency of A + B = 30 units
Hence time taken by A and B to complete 105 units of work = 105/30 = 3.5
Answer: (C)
Let the total work = 80 units
Efficiency of (A + B + C) = 80/40 = 2 units
Work done by (A + B + C) in 16 days = 16 * 2 = 32 units
Remaining work = 80 – 32 = 48 units
B and C complete the remaining work (48 units) in 40 days.
Efficiency of B + C = 48/40 = 1.2 units
Efficiency of A = Efficiency of (A + B + C) - Efficiency of (B + C) = 2 – 1.2 = 0.8 unit
Time taken by A to complete the whole work = 80/0.8 = 100 days
Answer: (C)
Let the total work = 360 units
Efficiency of A = 360/45 = 8 units
Efficiency of B = 360/40 = 9 units
Efficiency of A + B = 17 units
Let A left after x days, that means A and B worked together for x days. Total work done by A and B together = 17x
Then the remaining work is finished by B in 23 days. Hence work done by B alone = 23 * 9 = 207 units
So, 17x + 207 = 360
Or x = 9 days
Answer: (D)
Q. 18)
Let the total work = 60 units
Efficiency of A = 60/20 = 3 units
Efficiency of B = 60/30 = 2 units
Efficiency of (A + B) = 5 units
Work done by A and B in 7 days = 5*7 = 35 units
Work left = 60 – 35 = 25 units
C completes 25 units of work in 10 days. Hence he will complete 60 units of work in 10* 60/25 = 24 days
Answer: (C)
Q. 19)
Let total work be 120 units.
Efficiency of A = 120/6 = 20 units
Efficiency of B = 120/12 = 10 units
Efficiency of C = 120/15 = 8 units
Work left = 7/8 * 120 = 105 units
Efficiency of A + B = 30 units
Hence time taken by A and B to complete 105 units of work = 105/30 = 3.5
Answer: (C)
Q. 20)
Let the total work = 80 units
Efficiency of (A + B + C) = 80/40 = 2 units
Work done by (A + B + C) in 16 days = 16 * 2 = 32 units
Remaining work = 80 – 32 = 48 units
B and C complete the remaining work (48 units) in 40 days.
Efficiency of B + C = 48/40 = 1.2 units
Efficiency of A = Efficiency of (A + B + C) - Efficiency of (B + C) = 2 – 1.2 = 0.8 unit
Time taken by A to complete the whole work = 80/0.8 = 100 days
Answer: (C)
Q. 21)
Let the total work = 360 units
Efficiency of A = 360/45 = 8 units
Efficiency of B = 360/40 = 9 units
Efficiency of A + B = 17 units
Let A left after x days, that means A and B worked together for x days. Total work done by A and B together = 17x
Then the remaining work is finished by B in 23 days. Hence work done by B alone = 23 * 9 = 207 units
So, 17x + 207 = 360
Or x = 9 days
Answer: (D)
Q. 22) 
This question appeared in SSC Tier-2 2015, and stumped many candidates. Although there is nothing tricky about it.
Let the total work be 60 units.
p + q = 60/6 = 10
q + r = 60*7/60 = 7
Given, Total work done = 3 days work of P + 6 days work of Q and R
60 = 3*p + 6*(7)
p = 6
Hence time taken by P to complete the work = 60/6 = 10 days
p + q = 10, hence q = 4
q + r = 7, hence r = 3
Hence time taken by R to complete the work = 60/3 = 20 days
Difference = 20 - 10 = 10 days
Answer : (C)
Q. 23) 4 Men and 6 Women working together can complete the work in 10 days. 3 men and 7 women working together will complete the same work in 8 days. In how many days 10 women will complete this work?
One day work for a man = 1/m
One day work for a woman = 1/w
Q. 23) 4 Men and 6 Women working together can complete the work in 10 days. 3 men and 7 women working together will complete the same work in 8 days. In how many days 10 women will complete this work?
One day work for a man = 1/m
One day work for a woman = 1/w
In one day, 4 men and 6 women will do 1/10 of the work. Hence,
4/m + 6/w = 1/10 ... (i)
Similarly,4/m + 6/w = 1/10 ... (i)
3/m + 7/w = 1/8 ... (ii)
Multiply equation (i) with 3 and equation (ii) with 4
12/m + 18/w = 3/10
12/m + 28/w = 1/2
Subtract the equations
10/w = 1/5
So 10 women will complete the work in 5 days
Answer: (5)
Q. 24) If 3 men or 4 women can reap a field in 43 days, how long will 7 men and 5 women take to
reap it?
There is a direct formula to solve such questions
-------------------------------------------------------------------------------------------------------------
Here W is the work. For e.g., if 5 men are cutting 10 trees in 2 days, working 4 hours per day. Then,
M = 5, D = 2, H = 4 and W = 10.
Q. 25)
H1 = 6
D1 = 18
D2 = 12
H2 = ?
We know, H1 * D1 = H2 * D2
6 * 18 = H2 * 12
H2 = 9 hours
Answer : (B)
Q. 26)
M1 = 15
D1 = 20
H1 = 8
M2 = 20
D2 = 12
H2 = ?
We know, M1 * D1 * H1 = M2 * D2 * H2
15*20*8 = 20*12*H2
H2 = 10 hours
Answer : (B)
Q. 27)
In this question, Taps = Men
Number of taps required = 20*9/15 = 12
Answer : (B)
Q. 28)
X men can finish a piece of work in 100 days. Hence total work = 100X
If there were (X - 10) men, it would have taken 110 days to finish the work. Total work in this case = 110(X - 10)
Total work remains the same. Hence,
100X = 110(X - 10)
X = 110
Answer : (D)
Q. 29)
Efficiency of Subhash = 50/10 = 5 per hour
Efficiency of Subhash and Prakash = 300/40 = 7.5 per hour
Efficiency of Prakash = (Efficiency of Subhash and Prakash) - (Efficiency of Subhash) = 7.5 - 5 = 2.5
So Prakash can copy 2.5 pages per hour. To copy 30 pages, he would require 30/2.5 or 12 hours.
Answer : (D)
Q. 30)
40 men can finish a work in 60 days. Hence, total work = 40*60 = 2400
Let the 10 men left after X days.
For X days, all the 40 men worked. Total work performed = 40X
Now when 10 men quit, only 30 men were left to do the work and they took (70 - X) more days to finish it.
Total work done by 30 men = 30*(70 - X)
Now, 40X + 30*(70 - X) = 2400
X = 30 days
Answer : (C)
Q. 31)
Let the total work = 360 units
Efficiency of A = 360/45 = 8 units
Efficiency of B = 360/40 = 9 units
Efficiency of A + B = 17 units
Let A left after X days.
For X days, both A and B worked. Hence work performed = 17X
B worked for 23 days. Hence work performed by B = 23*9 = 207 units
Now, 17X + 207 = 360
X = 9 days
Answer : (D)
Q. 32)
B and C together do 8/23 of the work, hence A does (1 - 8/23) or 15/23 of the work.
A should be paid = 15*5290/23 = Rs. 3450
Answer : (D)
Note : In this question, they have asked the wages of A. Had they
asked the wages of B, firstly you would have calculated the work
performed by B with the formula-
Work done by B = (Portion of work done by A and B) + (Portion of work done by B and C) - 1
Work done by B = 19/23 + 8/23 - 1 = 4/23
Wages of B = 4*5290/23 = Rs. 920
Q. 33)
This is a very famous question. A company employed 200 workers to complete a certain work in 150 days. Here the total work is not 200*150 because 200 workers and 150 days was only a plan. In reality, only 1/4th of the work has been done in 50 days. So if they go with the same pace, 200 workers will take 200 days to complete the work.
So total work = 200*200 units
200 workers have worked for 50 days. Hence they have finished 200*50 units of work.
Remaining work = 200*200 - 200*50 = 200*150
Let the number of additional workers required = X.
Now (200+X) workers will work for 100 days to finish the work as per the schedule.
Work they need to perform = (200 + X)*100
Now, (200 + X)*100 = 200*150
X = 100
Answer : (C)
Q. 34) A contractor undertook to finish a certain work in 124 days and employed 120 men.After 64 days,he found that he had already done 2/3 of work. How many men can be discharged now so that the work may finish in time?
A) 56 B) 44 C) 50 D) 60
120 workers finish 2/3 of the work in 64 days. So to complete the whole work, workers will take 64*3/2 or 96 days.
Total work to be performed = 120*96
Now the workers have already finished 2/3 of the work and only 1/3 work has to be performed.
Remaining work = 120*96/3 = 120*32
Let the contractor discharges X men. Remaining workers = 120-X. These workers will continue the work for (124-64) or 60 days. Hence,
120*32 = (120-X)*60
X = 56
Answer : (A)
Method 2
M1 = 120, D1 = 64, W1 = 2/3
M2 = 120 – x, D2 = 60, W2 = 1/3
(M1*D1)/W1 = (M2*D2)/W2
120*64*3/2 = (120 - x)*60*3
x = 56
Q. 35)
Let the second pipe fills the pool in X hours. Then first pipe takes
(X+5) hours and the third pipe takes (X-4) hours to fill the pool. Now,
1st and 2nd pipe together take the same time to the fill the pool as the
3rd pipe alone. Hence,
1/(X+5) + 1/(X) = 1/(X - 4)
Solve this quadratic equation and you will get X = 10 hours
That means second pipe takes 10 hours to fill the pool while the third
pipe takes 6 hours. Together they will take 10*6/(10 + 6) hours to fill
the pool.
Answer: (B
Q. 36) A can complete a job in 12 days, B in 15 days. Both of them worked for 5 days and
rest of work was finished by C. If total earning is Rs. 720. Find wages of B.
rest of work was finished by C. If total earning is Rs. 720. Find wages of B.
Let the total work = 60 units
Efficiency of B = 60/15 = 4
Work done by B in 5 days= 5*4 =20
Earning of B = (20/60) * 720 = Rs. 240
Q. 37) A, B and C undertake to complete a piece of work for Rs 2574. A works for 8 days, B
for 9 days and C for 12 days. If their daily wages are in the ratio of 3:4:5 what does C get?
for 9 days and C for 12 days. If their daily wages are in the ratio of 3:4:5 what does C get?
Let the daily wages of A, B and C be 3x, 4x and 5x
A works for 8 days, hence total wages of A = 8*3x = 24x
B works for 9 days, hence total wages of B = 9*4x = 36x
C works for 12 days, hence total wages of C = 12*5x = 60x
Ratio of wages of A, B and C = 24x : 36x : 60x = 2 : 3 : 5
C gets = 5*2574/10 = Rs. 1287
A works for 8 days, hence total wages of A = 8*3x = 24x
B works for 9 days, hence total wages of B = 9*4x = 36x
C works for 12 days, hence total wages of C = 12*5x = 60x
Ratio of wages of A, B and C = 24x : 36x : 60x = 2 : 3 : 5
C gets = 5*2574/10 = Rs. 1287
Q. 38) Two pipes can fill a cistern separately in 24 min and 40 min respectively. A waste
pipe can drain off 30 litres per minute. If all the three pipes are opened the cistern fills in
one hour. The capacity of Cistern is?
pipe can drain off 30 litres per minute. If all the three pipes are opened the cistern fills in
one hour. The capacity of Cistern is?
Let the capacity be X
In 1 minute, the first pipe adds X/24 litres
In 1 minute, the second pipe adds X/40 litres
In 1 minute, the third pipe drains off 30 litres
So in 1 minute, all the three pipes are adding (X/24 + X/40 - 30) litres.
In 60 minutes, all the three pipes will add 60*(X/24 + X/40 - 30) litres. Hence
X = 60*(X/24 + X/40 - 30)
X = 600 litres
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