Ratio, Time and Work
Overview
Ratio, Time and Work is one of the most frequently tested topics in Railway NTPC and Group D exams. It covers how workers complete jobs together or separately, pipe and cistern problems, and ratio-based work sharing. Mastering a few core formulas and shortcuts can solve 90% of exam questions in under 60 seconds. Expect 2–4 questions per paper directly from this chapter.
Typed Notes
Basic Time & Work Formula
If A alone finishes work in 'a' days and B alone in 'b' days, together they finish in ab/(a+b) days. Example: A=6 days, B=12 days → Together = (6×12)/(6+12) = 72/18 = 4 days. Exam Tip: Always check if the question asks 'together' or 'remaining work after one leaves.' For three workers A, B, C: Time = 1/(1/a+1/b+1/c). Memorise the two-person formula as 'product over sum' — it appears in almost every Railway paper.
Efficiency / LCM Method (Fastest Shortcut)
Assume Total Work = LCM of all given days. Then each person's daily work = Total Work ÷ their days. Example: A=4 days, B=6 days. LCM=12 (total work units). A does 3 units/day, B does 2 units/day. Together = 5 units/day. Days = 12/5 = 2.4 days. This method avoids fractions entirely and is the fastest approach for Railway exams. Always use LCM method when 3 or more workers are involved or when partial work questions appear.
Pipes and Cisterns
Inlet pipe fills a tank in 'p' hours (positive work), outlet pipe empties in 'q' hours (negative work). Net filling rate = 1/p − 1/q per hour. Time to fill = pq/(q−p), valid only when q > p. If both are opened simultaneously and q < p, tank fills. Example: Inlet fills in 8 hrs, outlet empties in 12 hrs. Net = 1/8−1/12 = 1/24. Tank fills in 24 hrs. Memory Hook: Inlet = Plus (+), Outlet = Minus (−). Pipe questions are just Time & Work in disguise.
MDH Formula and Ratio-Based Work
M1×D1×H1 = M2×D2×H2 is used when men, days, or hours change for the same work. Example: 10 men finish work in 8 days working 6 hrs/day. How many days for 16 men working 5 hrs/day? → 10×8×6 = 16×D2×5 → D2 = 480/80 = 6 days. Ratio-based: If A:B efficiency = 3:2, and total work = 5 units, A gets 3/5 of wages. Wages are always distributed in ratio of work done, not time spent.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01If A completes work in 'n' days, A's 1-day work = 1/n. Combined 1-day work of A and B = 1/a + 1/b; Total time = ab/(a+b).
- 02If A is twice as fast as B, and B takes 'n' days, then A takes n/2 days. Speed and time are inversely proportional for the same work.
- 03Pipe & Cistern: Inlet pipe fills, outlet pipe empties. Net 1-hour work = 1/inlet − 1/outlet. If outlet > inlet, tank never fills.
- 04Work equivalence: M1 × D1 × H1 = M2 × D2 × H2 (Men × Days × Hours = constant for same work). Crucial for scaling problems.
- 05Efficiency method: Assume total work = LCM of given days. Each worker's daily output = LCM ÷ their days. Faster than fraction method in exams.
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
A can do a piece of work in 15 days and B can do it in 10 days. How many days will they take to complete the work together?
A pipe can fill a tank in 20 hours and another pipe can empty it in 30 hours. If both are opened together, in how many hours will the tank be full?
12 men can complete a work in 8 days. How many men are needed to complete the same work in 6 days?
A is twice as efficient as B. B alone can finish a task in 18 days. In how many days can A and B together finish the task?
A and B together can do a work in 12 days. A alone can do it in 18 days. In how many days can B alone do the work?
For Railway NTPC/Group D: Use 'product/sum' for two workers, LCM method for three or more. Pipes follow the same logic with inlet positive and outlet negative. MDH formula handles scaling of men, days, hours. Wages split in ratio of work done. Practice converting word problems to 1-day work fractions instantly. These shortcuts ensure answers in under 60 seconds.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.A can finish work in 10 days, B in 15 days. Working together, they finish in how many days?
Q2.An inlet pipe fills a tank in 6 hours. An outlet pipe empties it in 9 hours. Net time to fill the tank when both are open?
Q3.If 8 workers complete a job in 12 days, how many workers are needed to finish it in 4 days?
Q4.A and B together complete work in 8 days. B alone takes 24 days. How many days does A alone take?
Mark karo — dashboard par progress dikhega.