Study Notes & Questions for SSC Exams: Time & Work
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.
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.
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
⇒ 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
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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
⇒ 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
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
⇒ Let A + B takes x days
A → x + a days
B → x + b days
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?