# Short cut Technique For Time And Work :: Railway and SSC CHSL And All Competitive exams

**Time and work chapter is most important topic for railway and ssc all kind of competitive exams.**

Here we are providing the some short cut techniques from this chapter.

Under this chapter, we will study the following:

A. How to calculate the required number of persons to complete a particular work in a stipulated time period?

B. How to calculate the required time to complete a particular work by certain number of persons?

To find ‘A’ and ‘B’, the 1

^{st}and foremost task is to keep following basic point mind:

1. While
solving problems, the work done is always supposed to be equal to 1.

2. If a
person can do a piece of work in ‘n’ days, then that person’s 1 day work = 1/n.

3. If a
person 1 day’s work = 1/n, then the person will complete the work in ‘n’ days.

4. A person
works equally every day.

**Important Relations:**

1. Work
and persons directly proportional (more work, more men and conversely more men,
more work).

2. Time
and person inversely proportional (more men, less time and conversely more
time, less men).

3. Work
and time directly proportional (more work, more time and conversely more time,
more work).

**TECHNIQUE 1:**

If ‘M1’ persons can do ‘W1’ work in ‘D1’ days working T1 h in a day and
‘M2’ persons can do ‘W2’ work in ‘D2’ days working T2 h in a day, then we have
a very basic and all in one relationship as

**M1D1T1W2 = M2D2T2W1**

**Example:**16 men can do a piece of a work in 10 days. How many men are needed to complete the work in 20 days?

Solution: Here, M1=16, D1= 10, W1 = W2 = 1, D2 = 20, M2 =?

According to the formula, M1D1W2 = M2D2W1

16X10X1 = M2X20X1

M2 = 16X10/20 =
160/20

M2 = 8 men

**Alternate method:**

To do a work in 10 days, 16 men are needed.

To do the work in 1 day, 16X10 men are needed.

Here, to do the work in 20 days, = 1610/20 = 160/20

= 8 men are needed.

**TECHNIQUE 2:**

If A can do a piece of work in ‘x’ days and B can do the same work in ‘y’ days then

**(A+B)’s 1 day’s work = 1/x+1/y**

Inverse of
(A+B)’s 1 day’s work = time taken by (A+B) to complete the work

**Note: this formula is also applicable for 3 or more persons**

**Example:**A can do a piece of work in 4 days, B can do the same work in 8 days and C can do the same work in 12 days, then working together, how many days will they take to complete the work?

**Answer:**A’s 1 day’s work = 1/4

B’s
1 day’s work=1/8

C’s
1 day’s work=1/12

Therefore (A+B+C)’s 1 day’s work =1/4+1/8+1/12= 6+3+2/24

= 11/24

Therefore (A+B+C) complete the
whole work in 24/11 days

**TECHNIQUE 3:**

If A and B can do a piece of work in X days, B and C can do the same work in y days and A and C can do it in z days, then working together, A, B, and C can do that work in

**2xyz/ xy+ yz+zx days.**

**Example:**A and B can do a piece of work in 3 days. B and C can do the same work in 9 days while C and A can do it in 12 days. Find the time in which A, B, and C can finish the work, working together.

**Answer:**According to the formula

=
2x3x9x12/3x9+9x12+3x12

=
2x3x9x12/27+108+36

=
2x3x9x12/171

=
6x12/19

**= 72/19 days.**

**TECHNIQUE 4:**

If ‘x’ takes
‘a’ days more to complete a work than the time taken by (x+ y) to do same work
and ‘y’ takes ‘b’ days more than the time taken by (x+y) to do the same work,
then (x+y) do the work in

**Example:**when A alone does a piece of work, he takes 16 days more then the time taken by (A+B) to complete that work while B alone takes 9 days more than the time taken by (A+B) to finish the work. What time, A and B together will take to finish this work?

**Answer:**according to the formula, where A= 16 B= 9

Required answer: square root of 16x9 = 4x3 = 12 days.

**Answer = 12 days.**

**Technique 5:**

A and B, each alone can do a piece of work in ‘a’ and ‘b’
days, respectively. Both begin together and if

i. A leaves the
work ‘X’ days before its completion, then total time taken for completion of
work will be given as

**T = (a+x) b/ (a+b)**

ii. B leaves the work ‘x’ days before its completion,
then total time taken for completion of work will be given as

**T = (b+x)a/(a+b)**

**Example:**A can do a piece of work in 10 days while B can do it in 15 days. They begin together but 5 days before completion of the work, B leaves off. Find the total number ofdays for the work to be completed.

**Answer:**here, a=10 days, b= 15 days, x= 5, t=?

According to the formula,

Required
time T = (b+x)a/(a+b)

= (15+5)10/10+15

**= 4X2 = 8 days**

**Technique 6:**

A and B do a piece of work in ‘a’ and ‘b’ days,
respectively. Both begin together but after some days, A leaves off and the
remaining work is completed by B in ‘x’ days. Then, the time after which A
left, is given by

**Example:**A and B do a piece of work in 40 days and 50 days, respectively. Both begin together but after certain time, A leaves off. In this case B finishes the remaining work in 20 days.After how many days did a leave?

**Answer:**given that a= 40 days, b=50 days, X=20, t =?

Required time = (b-x) a/ a+b

= (50-20)
40 / 50+40

= 30X40 / 90

**= 40 / 3 days**

Short cut Technique For Time And Work :: Railway and SSC CHSL And All Competitive exams
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