Time & Work — RRB NTPC Mathematics
This topic carries roughly 9% of Mathematics's 30 questions. The single most common error across every government exam's quant section is averaging individual times instead of adding work rates — this chapter exists to make rate-based thinking automatic.
1. What RRB NTPC actually asks
Expect combined-work problems (A and B working together), efficiency-ratio problems, partial-work problems where someone leaves or joins midway, and problems mixing men/women or machines with different individual rates.
2. The core idea: convert time to rate
If A completes a task in n days, A's work rate is 1/n of the task per day. Rates add directly; times never do. If A takes 10 days and B takes 15 days, their combined rate is 1/10 + 1/15 = 1/6, so together they take 6 days — not the average of 10 and 15.
3. Efficiency problems
"B is twice as efficient as A" means B's work rate is twice A's rate, so B takes half the time A would take for the same task. Efficiency and time are inversely related — a more efficient worker takes less time, not more.
4. Partial work and someone leaving midway
For a worker who leaves after some days: compute the fraction of work completed in that period (combined rate × days worked together), subtract from 1 to find the remaining fraction, then divide the remaining fraction by the remaining worker's individual rate to find the extra days needed.
Worked examples
Q1. A can complete a task in 20 days, and B can complete the same task in 25 days. They work together for 5 days, after which B leaves. How many more days will A alone take to finish the remaining work?
Pick an option to check your answer.
Show explanation
Solution. Combined rate = 1/20 + 1/25 = 5/100 + 4/100 = 9/100 per day. Work done in 5 days together = 5 × 9/100 = 45/100 = 9/20.
Remaining work = 1 − 9/20 = 11/20. A's individual rate is 1/20, so days needed = (11/20) ÷ (1/20) = 11 days. Answer: (c).
Q2. 6 men or 8 women can complete a job in 10 days. How many days will 3 men and 4 women together take to complete the same job?
Pick an option to check your answer.
Show explanation
Solution. Since 6 men take 10 days, one man's rate = 1/(6×10) = 1/60 per day. Since 8 women take 10 days, one woman's rate = 1/(8×10) = 1/80 per day.
3 men and 4 women's combined rate = 3×(1/60) + 4×(1/80) = 1/20 + 1/20 = 2/20 = 1/10 per day. So the job takes 10 days — exactly the same as the original groups, since 3 men + 4 women together happen to match the original combined effort proportionally. Answer: (b).
6. Common traps
- Averaging individual times instead of adding work rates. Two workers taking 10 and 15 days do NOT take 12.5 days together — always convert to rates first.
- Confusing "twice as efficient" with "takes twice as long." More efficient means a HIGHER rate and therefore LESS time, not more.
- Forgetting to convert back from rate to time at the final step. The answer to "how many days" is 1/(combined rate), not the rate itself.
- Mixing up men-rate and women-rate variables in combined-group problems — always compute each individual's rate separately before combining.
7. Guessing strategy
The combined time for two or more workers must always be LESS than the fastest individual worker's own time — this single sanity check eliminates any option that's too large, often clearing the guessing threshold immediately.
Summary
- Time & Work is roughly 9% of Mathematics's 30 CBT 1 questions.
- Convert every "days to finish" statement into a rate (1/days); rates add, times never do.
- Higher efficiency means a higher rate and therefore LESS time — not more.
- For partial-work problems, compute work done in the shared period, subtract from 1, then divide the remainder by the remaining worker's rate.
- The combined time for multiple workers is always less than the fastest individual worker's own time — a fast sanity check for eliminating wrong options.
