Pariksha SaathiTime and Work Questions with Solutions
Time and Work questions all rest on one idea: convert everyone’s time into a daily work-rate, combine the rates, then convert back to time. Here’s the concept, four fully worked examples, and a few to try yourself.
The concept, quickly
- If a person finishes a piece of work in n days, their work rate is 1/n of the work per day. Converting everyone to a rate like this is the key move in almost every question here.
- When people work together, ADD their individual daily rates to get the combined rate. Time to finish together = 1 ÷ (combined rate).
- Shortcut for two people, A in x days and B in y days, working together from the start: combined time = xy / (x + y). (This is just the rate-addition rule worked out algebraically — useful to recall directly.)
- "X% more efficient" means X% more work done per day, i.e., the rate is multiplied by (1 + X/100) — and since rate and time are inverses, the time is divided by the same factor, not multiplied.
Worked examples
1. A can complete a piece of work in 12 days. What fraction of the work does he complete in 4 days?
Solution
- A’s rate = 1/12 of the work per day.
- Work done in 4 days = 4 × (1/12) = 4/12
- = 1/3
Answer: 1/3 of the work
2. A can complete a work in 10 days and B can complete the same work in 15 days. If they work together, in how many days will they finish it?
Solution
- A’s rate = 1/10, B’s rate = 1/15 per day.
- Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6 of the work per day.
- Time to finish together = 1 ÷ (1/6) = 6 days.
Answer: 6 days
3. A can do a piece of work in 20 days. B is 25% more efficient than A. Find the number of days B alone takes to complete the same work.
Solution
- "25% more efficient" means B’s work rate is 1.25 times A’s rate.
- Since time is inversely proportional to rate, B’s time = A’s time ÷ 1.25 = 20 ÷ 1.25
- = 16 days
Answer: 16 days
4. A and B together can complete a work in 12 days. A alone can complete it in 20 days. In how many days can B alone complete the work?
Solution
- Combined rate (A + B) = 1/12. A’s rate = 1/20.
- B’s rate = 1/12 − 1/20 = 5/60 − 3/60 = 2/60 = 1/30 of the work per day.
- B’s time alone = 1 ÷ (1/30) = 30 days.
Answer: 30 days
Try these yourself
Work through these the same way, then check against the answer.
1. A can complete a work in 8 days. What fraction of the work does he complete in 3 days?
Answer: 3/8 of the work
2. A can complete a work in 6 days and B can complete the same work in 12 days. Working together, how many days will they take?
Answer: 4 days
3. A and B together can complete a work in 15 days. B alone can complete it in 25 days. In how many days can A alone complete the work?
Answer: 37.5 days
Where this comes up
Time and Work is tested directly in the Quantitative/Numerical Aptitude section of every exam Pariksha Saathi covers — SSC CGL, SSC MTS, SSC CHSL, IBPS PO, IBPS Clerk, SBI PO and SBI Clerk — and the same rate-based thinking carries over into Pipes and Cisterns questions.
Practice more Time and Work questions
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