**Time & Work Concepts for SSC And Railway Exam:**

Quantitative Aptitude is an equally important section for

**SSC CGL****, SSC****CHSL****,****SSC MTS**exams and has even more abundant importance in some other exams conducted by**SSC**. Generally, there are questions asked related to basic concepts and formulas of Time & Work.To let you make the most of QUANT section, **we are providing important facts related to Time and Work.**** Also, RRB NTPC 2019 Exam is nearby with bunches of posts for the interested candidates in which quantitative aptitude is a major part. We have covered important notes and questions focusing on these prestigious exams. **We wish you all the best of luck to come over the fear of Mathematics section.

__Time And Work__

**Time= Work done/Efficiency**

**When work is same.**

**Time∝1/Efficiency**

**If A can do a piece of work in n days.**

**Then, per day working efficiency of A = 1/n**

**If working efficiency of A & B is → x : y.**

**Then, the time taken by A & B to finish the work is in the ratio → y : x**

e.g. If A does three times faster work than ‘B’, then ratio of work done by A and B is 3 : 1.

Then

Ratio of time taken by A & B = 1 : 3

**If A can do a piece of work is x days and B can do a piece of work in y days, then both of them working together will do the same work in**

**xy/(x+y) days**

__Explanation__⇒ A’s 1 day’s work = 1/x

B’s 1 day’s work = 1/y

(A + B)’s 1 day work = 1/x+1/y =(x + y)/xy

A + B will complete the work in = xy/(x + y)

**Q. A can finish a piece of work by working alone in 6 days and B, while working alone, can finish the same work in 12 days. If both of them work together, then in how many days, the work will be finished?**

**Sol.**x = 6, y = 12

Working together A + B will complete the work in = xy/(x + y)=(6 × 8)/18

= 4 days

**Click On The Links Below to Attempt More Questions From Time And Work**

Time & Work Quiz For SSC CGL – 1 | Time & Work Quiz For SSC CGL – 2 | Time & Work Quiz For SSC CGL – 3 |
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Time & Work Quiz For SSC CGL – 4 |
Time & Work Quiz For SSC CGL – 5 |
Time & Work Quiz For SSC CGL – 6 |

**If A, B & C will working alone, can complete a work in x, y and z days, respectively, then they will together complete the work in**

**xyz/(xy+yz+zx)**

__Explanation__⇒ A’s 1 day work = 1/x

B’s 1 day work = 1/y

C’s 1 day work = 1/z

(A + B + C)’s 1 day work = 1/x+1/y+1/z =(yz+xz+xy)/xyz

(A + B + C) will complete the work in

=xyz/(yz+xz+xy)

**Q. A, B, and C can complete a piece of work in 10, 15 and 18 days, respectively. In how many days would all of them complete the same work working together?**

**Sol.**x = 10 days, y = 15 days & z = 18 days

The work will be completed in

=(10×15×18)/(10×15+15×18+18×10)

=2700/600=4½ days

**Two persons A & B, working together, can complete a piece of work in x days. If A, working alone, can complete the work in y days, then B, working alone, will complete the work in**

**⇒xy/(y-x)**

__Explanation__⇒ A + B’s 1 day work = 1/x

A’s 1-day work = 1/y

B’s 1 day work = 1/x-1/y

=(y-x)/yx

B will complete the work = yx/(y – x)

**Q. A and B working together take 15 days to complete a piece of work. If A alone can do this work in 20 days, how long would B take to complete the same work?**

**Sol.**x = 15, y = 20

B will complete the work in = (15 × 20)/5

= 60 days

**Click Here to Attempt More Questions From Quantitative Aptitude For SSC CGL **

**If A & B working together, can finish a piece of work is x days, B & C in y days, C & A in z days. Then, A + B + C working together will finish the job is**

**⇒2xyz/(xy+yz+zx)**

__Explanation__⇒ A + B’s 1 day work = 1/x

B + C’s 1 day work = 1/y

C + A’s 1 day work = 1/z

[(A + B) + (B + C) + (C + A)]’s 1 day’s work

=1/x+1/y+1/z

=(yz+xz+xy)/xyz

2 (A + B + C)’s 1 day work = (xy + yz + xz)/xyz

A + B + C’s 1 day work = (xy + yz + xz)/2xyz

A + B + C working together will complete the work in

=2xyz/(xy+yz+xz)

**Q. A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. How long would they take to complete the full work together?**

**Sol.**x = 12 days, y = 15 days, z = 20 days

A+B+C=(2×12×15×20)/(180+300+240)

=7200/720=10 days

**If A can finish a work in x days and B is k times efficient than A, then the time taken by both A and B, working together to complete the work is**

**x/(1+k)**

__Explanation__⇒ Ratio of working efficiency, A & B = 1 : k

Ratio of Time taken = k : 1

k → x days

1r → x/k days

A → x days

B → x/k days

1 day work of A = 1/x

1 day work of B = k/x days

(A + B)’s 1 day work = 1/x+k/x=(k + 1)/x

(A + B) will complete the work is = x/(k+1)

**Q. Harbans Lal can do a piece of work in 24 days. If Bansi Lal works twice as fast as Harbans Lal, how long would they take to finish the work working together?**

**Sol.**x = 24, k = 2

Working together they will complete the work in = 24/(1 + 2)

=24/3=8 days

**If A & B working together can finish a work in x days & B is k times efficient than A, then the time taken by,**

**A working Alone will take ⇒ (k + 1) x**

**B working Alone will take ⇒ ((k+1)/k)x**

__Explanation__⇒ Efficiency Ratio → 1 : k

Time Ratio → k : 1

A’s 1 day work = 1/k

B’s 1 day work = 1

(A + B)’s 1 day work = 1/x

1/k+1=1/x

(k+1)/k=1/x

k = (k + 1) x

A alone working together will take ⇒ (k + 1) x days

1 ratio = ((k + 1) x)/k

B Alone working Alone will take

⇒((k + 1) x)/k

**Q. A and B together can do a piece of work in 3 days. If A does thrice as much work as B in a given time, find how long A alone would take to do the work?**

**Sol**. x = 3, k = 3

Time taken by A, working Alone to complete the work = ((3 + 1)/3) × 3 = 4 days

**If A working Alone takes a days more than A & B, & B working Alone takes b days more than A & B. Then ,**

**Number of days, taken by A & B working together to finish a job is = √ab**

__Explanation :__⇒ Let A + B takes x days

A → x + a days

B → x + b days

1/(x+a)+1/(x+b)=1/x

(2x+a+b)/(x²+xa+xb+ab)=1/x

2x² + xa + xb = x² + xa + xb + ab

x² = ab

x = √ab days

**Q. A alone would take 8 hrs more to complete the job than if both A and B worked together. If B worked alone, he took 41/2 hrs more to complete the job than A and B worked together. What time would they take if both A and B worked together?**

**Sol.**a = 8, b = 9/2

A + B will take = √(8×9/2)

=√36

= 6 days

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