sponsored links

**Time and Work**' with shortcuts. The main advantage of

*is, you can easily solve them without even knowing the basic formulas or shortcuts. But the shortcut methods help us solving the problems in less time. Let's start today's lesson.*

__Time and Work problems__## Time and Work Shortcuts

**Time and Work Formulas :**

1st of all you need to remember the basic formula,

i.e.,

**Work = Strength x Time**
in Simple words, the Work done by you is depends upon the amount of Strength you put on that work and the amount of Time you spent to do that work.

Simple, isn't it ?

Now let's derive some shortcut formulas from this main formula.

Strength x Time = Work

If you send the work to right hand side, then it will become,

**(Strength x Time) / Work = 1**

This condition will be true for every case, No matter whatever the numbers are given.

So, (SxT)/W will be same for all the cases. Keep this point in your mind.

Now lets see some more important conditions :

**If they give you Days :**

- If A can do some work in n days, then he can do 1/n work in One Day.

**If they give you Work :**

- If A can do 1/n work in One Day, he can finish it in n days.

**If A is TWICE as good a workman as B**:

- This means, A can do 2 times work than B. SO,
- The ratio of work done by A and B is 2 : 1
- The ratio of time taken by A and B to finish the work is 1:2

Now let's work with some models so that you will understand better. As usual I am explaining one problem per model and giving 3 problems as homework for your practice. Solve them and share your answers at the comments section below.

### Time & Work : Examples and Practice Problems

__Model 1__:**36 men can do a piece of work in 25 days. In how many days can 30 men do it ?**- 28
- 30
- 32
- 36
- None of these

**Solution :**

In this problem the work is same for both groups of men.

So, let's equate it

(S X T) / W = (s X t) / w

= > (S X T) / W = (s X t) / w [ Cancel W for both sides]

Now, substitute the values...

= > 36 X 25 = 30 X t

= > (36 X 25) / 30 = t => t = 900/3 = 30

**Practice Problems on Model 1**

**63 Men can do a piece of work in 52 days. In how many days can 91 men do it ?**- 28
- 30
- 32
- 36
- None of these
**48 Men can do a piece of work in 36 days. In how many days can 54 men do it ?**- 28
- 30
- 32
- 33
- None of these
**36 Men can do a piece of work in 35 days. In how many days can 45 men do it ?**- 28
- 30
- 32
- 33
- None of these

**:**

__Model 2__**32 men can do a piece of work in 15 days working for 6 hours a day. In how many days will 40 men can finish it if they work for 8 hours a day?**- 8
- 9
- 10
- 12
- None of these

**Solution**:

32 x 15 x 6 = 40 x d x 8 = 9

**Practice Problems on Model 2****63 men can do a piece of work in 36 days working for 6 hours a day. In how many days will 27 men finish it if they work for 7 hours a day ?**- 25
- 66
- 72
- 92
- None of these
**36 Men can do a piece of work in 25 days working for 7 hours a day. In how many days will 42 men finish it if they work for 6 hours per day ?**- 25
- 66
- 72
- 92
- None of these
**55 Men can do a piece of work in 45 days working for 8 hours a day. In how many days will 40 men finish it if they work for 7.5 hours a day ?**- 25
- 66
- 72
- 92
- None of these

**:**

__Model 3__**If 16 men can build a wall of 52 m long in 25 days working for 8 hours a day, in how many days can 64 men build a similar wall of 260m long working for 10hrs a day ?**- 12
- 20
- 25
- 28
- None of these

**Solution :**

We already know that

**(Strength X Time) / Work = 1**

We can write =>

(16 * 200) / 52 = (64 * X * 10) / 260

=> X = 25

**Practice Problems on Model 3 :**

**If 60 men can build a wall of 52 m long in 42 days working for 8 hours a day, in how many days can 35 men build a similar wall of 26 m long working for 9 hours a day ?**- 32
- 20
- 25
- 28
- None of these
**If 36 men can build a wall of 51 m long in 45 days working for 8 hours a day, in how many days can 120 men build a similar wall of 85 m long working for 7.5 hours a day ?**- 12
- 20
- 25
- 24
- None of these
**If 96 men can build a wall of 76 m long in 44 days working for 6 hours a day, in how many days can 55 men build a similar wall of 260 m long working for 8 hours a day ?**- 50
- 60
- 72
- 90
- None of these

__Model 4__:**A man engaged 10 laborers to make 320 toys in 5 days. After 3 days he found that only 120 toys were made. How many additional men should he engage to finish the work in time ?**- 15
- 20
- 25
- 30
- None of these

**Solution :**

Here, equate the complete work with the remaining work

(10 x 3) / 120 = (10+

*x*) x 2 / 200

= > 10+

*x*= 25 =>

*x*= 15

**Practice Problems on Model 4 :**

**A man engaged 15 laborers to make 320 toys in 10 days. After 7 days he found that only 175 toys were made. How many additional men should he engage to finish the work in time ?**- 4
- 14
- 29
- 30
- None of these
**A man engaged 45 laborers to make 350 toys in 21 days. After 15 days he found that only 210 toys were made. How many additional men should he engage to finish the work in time ?**- 4
- 14
- 29
- 30
- None of these
**A man engaged 20 laborers to make 360 toys in 20 days. After 12 days he found that only 200 toys were made. How many additional men should he engage to finish the work in time ?**- 4
- 14
- 29
- 30
- None of these

**:**

__Model 5__**A can do a task in 20 days and B can do it in 30 days. In how many days can they finish it if they work together ?**- 10
- 12
- 15
- 16
- None of these

**Solution**:

A can do a task in 20 days. That means A's one day's work = 1/20

Similarly, B's one day's work = 1/30

=> Their one day's work = (1/20)+(1/30) = (3+2)/60 = 5/60 = 1/12

This is their one day's work TOGETHER.

So, obviously the number of days will be = 12

**One More Short Cut**: calculate Product/Sum = (20 X 30) / 50 = 12 That's it ;)

**Practice Problems on Model 5 :**

**A can do a job in 60 days and B in 40 days. In how many days can they finish it if they work together ?**- 10
- 12
- 15
- 24
- None of these
**A can do a job in 24 days and B in 40 days. In how many days can they finish it if they work together ?**- 10
- 12
- 15
- 24
- None of these
**A can do a job in 120 days and B in 180 days. In how many days can they finish it if they work together ?**- 60
- 72
- 90
- 96
- None of these

**:**

__Model 6__**A, B and C can do a job in 20 days, 30 days and 60 days respectively. If they work together, in how many days will the work be finished ?**- 9
- 10
- 12
- 15
- None of these

**Solution**:

(1/20)+(1/30)+(1/60) = (3+2+1)/60 = 6/60 = 1/10

So, the number of days is = 10

**Practice Problems on Model 6 :**

**A, B and C can do a job in 40 days, 30 days and 60 days respectively. If they work together, in how many days will three such jobs be finished ?**- 30
- 40
- 60
- 72
- None of these
**A, B and C can do a job in 20 days, 30 days and 36 days respectively. If they work together, in how many days will the work will be finished ?**- 9
- 10
- 12
- 15
- None of these
**A, B and C can do a job in 20 days, 30 days and 24 days respectively. If they work together, in how many days will the work be finished ?**- 9
- 10
- 12
- 15
- None of these

**:**

__Model 7__- Two taps A and B can fill a tank in 10 hours and 15 hours respectively. a third tap C can empty the full tank in 12 hours. How many hours will be required if all of them are opened simultaneously to fill in an empty tank completely ?
- 9
- 10
- 12
- 15
- None of these

**Solution :**

Here, first two are

**Inlets**(

*which can fill the tank*) and the last one is

**Outlet**(

*which can empty the tank*),

If there is

**Inlet**use '

**+**', if there is

**Outlet**use '

**-**'

So, (1/10)+(1/15)-(1/12) = (6+4-5)/60 = 5/60 = 1/12

So, the answer is 12

**Practice Problems on Model 7 :**

**Two taps A and B can fill a tank in 20 hours and 15 hours respectively. A third tap C can empty the full tank in 12 hours. How many hours will be required if all of them are opened simultaneously to fill an empty tank completely ?**- 9
- 10
- 30
- 15
- None of these
**Two taps A and B can fill a tank in 25 min and 15 min respectively. A third tap C can empty the full tank in 10 min. How many hours will be required if all of them are opened simultaneously to fill in an empty tank completely ?**- 2
- 2.5
- 3
- 3.5
- None of these
**Two taps A and B can fill a tank in 24 min and 36 min respectively. A third tap C can empty the full tank in 15 mins. How many minutes will be required if all of them are opened simultaneously to fill in an empty tank completely ?**- 6
- 8
- 12
- 15
- None of these

**:**

__Model 8__- A and B can do a job in 12 days. B and C in 15 days and C and A in 20 days. In how many days can they finish it if they work TOGETHER ?
- 9
- 10
- 12
- 15
- None of these

**Solution :**

A+B = 12

B+C = 15

C+A = 20

So here,

A+B's One day's work = > 1/ (A+B) = 1/12

B+C's one day's work => 1/ (B+C) = 1/15

C+A's one day's work = > 1/(C+A) = 1/20

Just Add them => 1/( 2A+2B+2C) = 12/60 = 1/5

=> 1/2(A+B+C) = 1/5

=>1/(A+B+C) = 1/10 [this is their one day's work TOGETHER]

So, they can finish it in 10 days :)

**Practice Problems on Model 8 :**

**A and B can do one third of a job in 20 days, B and C in 15 days and C and A in 30 days. In how many days can they finish full job if they work together ?**- 36
- 40
- 48
- 60
- None of these
**A and B can do a job in 27 days, B and C in 45 days and C and A in 36 days. In how many days can they finish 47 such jobs if they work together ?**- 450
- 480
- 540
- 600
- None of these
**A and B can do a job in 60 days, B and C in 90 days and C and A in 100 days. In how many days can they finish 17 such jobs if they work together ?**- 450
- 480
- 540
- 600
- None of these

**:**

__Model 9__

**A and B can do a job in 12 days. B and C can do the same job in 15 days. C and A in 20 days. In how many days can A alone finish the whole task ?**

- 24
- 28
- 30
- 32
- None of these

**Solution :**

A+B = 1/12

B+C = 1/15

C+A = 1/20

Here we need A, so take a pair which is NOT HAVING A and subtract it from the others,

so, A+B-(B+C)+C+A = A+B-B-C+C+A = 2A

But according to our Problem, 2A = (1/12)-(1/15)+(1/20)

=>A = 1/30 (this is A's one day work but we need A's total work)

=> A = 30 Days

**Practice Problems on Model 9 :**

**A and B can do a job in 20 days. B and C in 15 days and C and A in 30 days. In how many days can B alone finish the whole work in the above problem ?**- 24
- 28
- 30
- 32
- None of these
**A and B can do a job in 27 min. B and C in 45 min and C and A in 36 min. In how many hours can C alone finish 7 such jobs ?**- 24
- 28
- 30
- 18
- None of these
**A and B can do a job in 60 days, B and C in 90 days and C and A in 100 days. In how many days can C alone finish the whole work ?**- 450
- 480
- 540
- 600
- None of these

**:**

__Model 10__

**A and B can do a piece of work in 20 days. A alone can do it in 30 days. In how many days can B alone do it ?**- 40
- 45
- 50
- 60
- None of these

**Solution :**

Per day work of A and B = 1/20

Work done by A= 1/30

So, B's one day work = 1/20 - 1/30 = (3-2)/60 = 1/60

=> B's work is 60 Days

**Short Cut**: Product/diff = 600/10 = 60

**Practice Problems on Model 10 :**

**A and B can do a piece of work in 20 days. A alone can do it in 24 days. In how many days can B alone do it ?**- 100
- 108
- 120
- 150
- None of these
**A and B can do a piece of work in 20 days. A alone can do it in 25 days. In how many days can B alone do it ?**- 100
- 108
- 120
- 150
- None of these
**A and B can do a piece of work in 40 days. A alone can do it in 30 days. In how many days can B alone do it ?**- 96
- 120
- 150
- 180
- None of these

**:**

__Model 11__**10 men can do a job in 15 days. 15 boys can do it in 16 days. IN how many days can 5 men and 8 boys do the same job ?**- 10
- 12
- 15
- 20
- None of these

**Solution :**

Men = (10m x 15d) / 5 m = 30 d

Boys = (15b x 16) / 8 = 30 d

Shortcut to Find the Ans =

**Product / Sum****=**(Men Days x Boy Days) / (Men Days + Boy Days)

= 900 / 60 = 15 Days

To avoid confusion, let's practice another problem of same type.

**20 men can do a job in 15 days. 15 boys can do it in 25 days. In how many days can 12 men and 5 boys do the same job ?**- 18 3/4
- 24
- 27 5/6
- 30
- None of these

**Solution :**

(20 x 15) / 12 = 25

(15 x 25) / 5 = 75

ans = 1875 / 100 = 18 3/4

**Practice Problems on Model 11 :**

**20 men can do a job in 30 days. 45 boys can do it in 48 days. In how many days can 25 men and 60 boys do the same job ?**- 36.
- 5.4
- 6.8
- 7.2
- None of these
**40 men can do a job in 60 days. 50 boys can do it in 75 days. In how many days can 100 men and 125 boys do the same job ?**- 12 1/2
- 13 1/3
- 15 3/4
- 18 2/3
- None of these

**:**

__Model 12__**8 men or 12 women can do a job in 30 days. In how many days can 20 men and 15 women do it ?**- 8
- 9
- 10
- 12
- None of these

**Solution :**

(8 M x 30 D) / 20 = 12 D

(12W x 30D) / 15 = 24 D

=> 288 / 36 = 8

**Practice Problems on Model 12**:

**18 men or 30 boys can do a job in 30 days. In how many days can 24 men and 40 boys do it ?**- 10
- 11 1/4
- 12 1/2
- 15 3/4
- None of these
**28 men or 32 women can do a job in 45 days. In how many days can 20 men and 20 women do it ?**- 23.2
- 24.8
- 28.4
- 33.6
- None of these
**50 men or 60 women can do a job in 30 days. In how many days can 45 men and 36 women do it ?**- 15
- 18
- 20
- 24
- None of these

__:__

**Model 13****A can do a job in 12 days and B in 15 days. A works for 4 days and then B works to finish it. For how many days does B work ?**- 8
- 9
- 10
- 12
- None of these

**Solution**:

A's per day work = 1/12

He worked in 4 days = 4/12 = 1/3

So B's remaining work = 2/3 x 15 = 10

**2nd Shortcut Method**:

Attendance of A / Full work time = 4/12 =1/3 +

*x*/15 = 1
=>

*x*/15 = 1 - 1/3 = 2/3
=>

*x*= 10

**Practice Problems on Model 13**:

**A can do a job in 30 days and B in 40 days. A works for 6 days and then B works to finish it. For how many days does B work ?**- 24
- 28
- 32
- 36
- None of these
**A can do a job in 25 days and B in 30 days. A works for 10 days and then B works to finish it. For how many days does B work ?**- 12
- 18
- 20
- 21
- None of these
**A can do a job in 70 days and B in 50 days. A works for 21 days and then B works to finish it. For how many days does B work ?**- 32
- 42
- 28
- 35
- None of these

__:__

**Model 14****A can do a job in 24 days. He worked for 6 days and then B completed it in 27 days. In how many days can B alone finish the whole job ?**- 32
- 36
- 40
- 42
- None of these

**Solution :**

Attendance / Full work = 6/24 = 1/4

6/24 + 27/

*x*= 1

27/

*x*= 3/4 = 36

**Practice Problems on Model 14**:

**A can do a job in 30 days. He worked for 8 days and then B completed it in 33 days. In how many days can B alone finish the whole job ?**- 32
- 36
- 40
- 45
- None of these
**A can do a job in 60 days. He worked for 24 days and then B completed it in 45 days. In how many days can B alone finish the whole job ?**- 60
- 75
- 80
- 90
- None of these
**A can do a job in 60 days. He worked for 22 days and then B completed it in 57 days. In how many days can B alone finish the whole job ?**- 60
- 75
- 80
- 90
- None of these

__:__

**Model 15****A and B can do a job in 10 days and 12 days respectively. They work together for 3 days and then B leaves. In how many days will the rest of the work be finished ?**- 4
- 5
- 6
- 7.5
- None of these

**Solution**:

A's attendance = 3+

*x*/ 10
B's attendance = 3/12

=> 3+

*x*/10 + 3/12 = 1
=>

*x =*4 1/2**Practice Problems on Model 15**:

**A and B can do a job in 30 days and 45 days respectively. They work together for 8 days and then A leaves. In how many days will the rest of the work be finished ?**- 33
- 30
- 25
- 24
- None of these
**A and B can do a job in 45 days and 40 days respectively. They work together for 16 days and then B leaves. In how many days will the rest of the work be finished ?**- 11
- 12
- 15
- 17
- None of these
**A and B can do a job in 90 days and 108 days respectively. They work together for 20 days and then B leaves. In how many days will the rest of the work be finished ?**- 50
- 56
- 60
- 64
- None of these

__:__

**Model 16****A and B can do a job in 15 days and 20 days respectively. They start the work together and 6 days before the completion of the work A leaves. In how many days is the total work finished ?**- 6
- 9
- 12
- 15
- None of these

**Solution :**

*x-*6/15

*+ x*/20 = 1

= (4

*x*- 24 + 3*x*) / 60 = 1
=> 7

*x*- 24 = 60
7

*x = 84**=> x*= 12

**Practice Problems on Model 16 :**

**A and B can do a job in 25 days and 15 days respectively. They start the work together and 1 day before the completion of the work B leaves. In how many days is the total work finished ?**- 6
- 9
- 10
- 15
- None of these
**A and B can do a job in 36 days and 45 days respectively. They start the work together and 9 days before the completion of the work A leaves. IN how many days is the total work finished ?**- 16
- 20
- 24
- 25
- None of these
**A and B can do a job in 28 days and 42 days respectively. They start the work together and 8 days before the completion of the work B leaves. In how many days is the total work finished ?**- 16
- 20
- 24
- 25
- None of these

__:__

**Model 17**- 15 men can do a job in 12 days and 20 women can do it in 10 days. What is the ratio between the capacities of a man and a woman ?
- 9 : 8
- 11 : 10
- 10 : 9
- 7 : 5
- None of these

**Solution :**

Work = Strength x Time

=> 180 M~~D~~ = 200 W~~D~~

=> 180 M = 200 W

=> 9M = 10W [This means, 10 Women can do 9 Men's work]

So,

*M : W = 10 : 9*[**Shortcut**: Just interchange the numbers to represent the ratios]**Practice Problems on Model 17 :**

**20 men can do a job in 12 days and 30 women can do it in 9 daus. What is the ratio between the capacities of a man and a woman ?**- 9 : 8
- 11 : 10
- 10 : 9
- 7 : 5
- None of these
**50 men can do a job in 10 days and 20 women can do it in 35 days. What is the ratio between the capacities of a man and a woman ?**- 9 : 8
- 11 : 10
- 10 : 9
- 7 : 5
- None of these
**15 men can do a job in 40 days and 20 women can do it in 33 days. What is the ratio between the capacities of a man and a woman ?**- 9 : 8
- 11 : 10
- 10 : 9
- 7 : 5
- None of these

**:**

__Model 18__**18 men can do a job in 30 days. After 6 days, 6 men left. In how many days will the remaining work be completed ?**- 32
- 44
- 33 3/4
- 40
- None of these

**Solution :**

Shortcut :

**Time = Remaining Work / Remaining strength**
= 18m x 24d / 12 mm

= 36d

**Practice Problems on Model 18 :**

**18 men can do a job in 30 days. After 8 days, 9 men left . In how many days will the remaining work be completed ?**- 32
- 44
- 33 3/4
- 40
- None of these
**28 men can do a job in 30 days. After 6 days, 7 men left. In how many days will the remaining work be completed ?**- 32
- 44
- 33 3/4
- 40
- None of these
**45 men can do a job in 40 days. After 10 days, 5 men joined. In how many days will the rest of the work be finished ?**- 32
- 44
- 33 3/4
- 40
- None of these

__:__

**Model 19**- A is twice as good a workman as B and together they finish a work in 12 days. In how many days can A alone do it ?
- 30
- 36
- 20
- 18
- None of these

**Solution :**

Given that, A is twice as good a workman as B.

Together they finish the work in 12 days.

=> A+B = 2+1 = 3 -> 12

=> A's work will be = 3/2 x 12 = 18 days

**Practice Problems of Model 19 :**

**A is half good a workman as B and together they finish a work in 12 days. In how many days can a A alone do it ?**- 30
- 36
- 20
- 18
- None of these
**A is 1 1/2 times as good a workman as B and together they finish a work in 12 days. In how many days can B alone do it ?**- 30
- 36
- 20
- 18
- None of these
**A is 4/5th as good a workman as B and B alone can finish a work in 36 days. In how many days can A and B both can do it ?**- 30
- 36
- 20
- 18
- None of these

**Work with these models and solve the given practice problems. Share your solutions in the comments section below**.

**Will post more shortcuts and Practice problems tomorrow. All the Best :)**

sponsored links