Quantitative Aptitude practice

Time and Work Questions with Answers

Time and work asks how long a job takes when one or more people, machines or pipes work on it. Time and work questions in SSC CGL, CHSL and MTS, RRB NTPC and Group D, and bank prelims include working together, one worker leaving midway, efficiency comparisons and tanks with inlet and outlet pipes. Tip: take the whole job as the LCM of the given days. Then each person's work per day is a whole number and the arithmetic stays simple.

Formulas you need

Work per day of a person = 1 ÷ (days taken alone)
Working together: time = (a × b) ÷ (a + b) days for two workers taking a and b days
Total work = Efficiency × Time; efficiency is work done per day
Work done = (Number of workers) × (Days) × (Efficiency per worker)
Efficiency is inversely proportional to time taken for the same work
If A is k times as efficient as B, A takes 1/k of the time B takes
Men × Days × Hours ÷ Work is constant: M₁D₁H₁ ÷ W₁ = M₂D₂H₂ ÷ W₂
Inlet pipe fills (+), outlet pipe empties (−): net rate = sum of signed rates
Wages are shared in proportion to work done (efficiency × days)

Worked examples

Q1. A can finish a job in 10 days and B can finish it in 15 days. In how many days will they finish it working together?

Take total work = LCM(10, 15) = 30 units
A does 3 units a day; B does 2 units a day
Together = 5 units a day
Time = 30 ÷ 5 = 6 days

Answer: 6 days

Q2. A can do a piece of work in 20 days and B in 30 days. They work together for 6 days, then A leaves. How many more days does B need to finish the work?

Total work = LCM(20, 30) = 60 units; A = 3 units a day, B = 2 units a day
Work in 6 days together = 6 × 5 = 30 units
Remaining = 60 − 30 = 30 units
B alone: 30 ÷ 2 = 15 days

Answer: 15 days

Q3. Pipe A fills a tank in 12 hours and pipe B fills it in 15 hours. Pipe C empties the full tank in 20 hours. If all three are opened together, how long will the empty tank take to fill?

Capacity = LCM(12, 15, 20) = 60 units
A fills 5 units an hour; B fills 4 units an hour; C empties 3 units an hour
Net rate = 5 + 4 − 3 = 6 units an hour
Time = 60 ÷ 6 = 10 hours

Answer: 10 hours

Shortcuts that save time

Assume the total work equals the LCM of the days given. Every worker's daily output becomes a whole number, so you avoid fractions and the slips that follow.
For outlet pipes or workers who undo the work, subtract their rate. Writing the sign beside each rate before adding prevents the classic error of adding an outlet pipe.
For two workers taking a and b days, use a × b ÷ (a + b) directly. It saves a step when the numbers are given and is quick to check against the options.

Where this appears

SSC CGL Tier-1	Quantitative Aptitude section
SSC CHSL Tier-1	Quantitative Aptitude section
SSC MTS	Numerical and Mathematical Ability section
RRB NTPC CBT-1	Mathematics section
Bank PO/Clerk Prelims	Quantitative Aptitude section

Time and Work

Practice Set

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A can complete a piece of work in 11 days. Find the time A takes to complete 3/4 of the work.

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