Practice Mode•Instant Explanations & 50:50 Enabled
Time Work MCQs
High-yield multiple choice questions asked in previous years (UPSC, SSC CGL, JKSSB, RRB & State PSCs).
High-Yield Concept Capsule & Key Facts
📌 High-weightage arithmetic section across IBPS PO/Clerk, SSC CGL/CHSL, RRB NTPC, and State PSCs.
Reciprocal Work Rates & LCM Unitary Method
- • Foundational Principle: If person A can complete a work in 'n' days, then in 1 day A completes (1/n)th of the work.
- • LCM Method (Efficiency Shortcut): Assume Total Work = LCM of individual day values. Efficiency of A = Total Work / Days taken by A. Total Days together = Total Work / Combined Efficiency.
- • Efficiency-Time Inversion: Efficiency is inversely proportional to time taken (Efficiency = Work / Time). If A is twice as efficient as B, Ratio of Time = 1:2.
- • M1 × D1 × H1 / W1 = M2 × D2 × H2 / W2 (Chain Rule formula for manpower, days, hours per day, and work done).
Alternate Day Work & Pipes and Cisterns
- • Alternate Day Cycles: Calculate work completed in 1 full multi-day cycle. Divide total work by cycle work to find completed cycles and remaining balance units.
- • Pipes & Cisterns: Inlet pipes perform positive work (+ efficiency); Outlet/leak pipes perform negative work (- efficiency).
- • Wages Distribution: Money/wages are distributed strictly in proportion to the total work done by each individual (or in proportion to their daily efficiencies when working together for equal duration).
| Problem Type | Standard Formula / Method | Speed Calculation Shortcut |
|---|---|---|
| Two people together | Time = (A × B) / (A + B) | Direct product-over-sum formula |
| Three people together | Time = Total LCM / (e1 + e2 + e3) | Assign LCM as total work units |
| Chain Rule | M1 D1 H1 / W1 = M2 D2 H2 / W2 | Equalize man-hours per unit work |
| Pipes & Leaks | Net Rate = 1/Inlet - 1/Leak | Treat empty pipe as negative efficiency |
| Wages Distribution | Wages split by Work Done | Ratio of (Efficiency × Days worked) |
Showing 15 Practice Questions
Q1SSC CGL 2023Easy
A can complete a piece of work in 12 days and B can do the same work in 18 days. If they work together, how many days will they take to complete the work?
Q2IBPS PO 2022Easy
A is twice as efficient as B and together they can finish a piece of work in 16 days. In how many days can A alone finish the work?
Q3JKSSB FAA 2022Easy
If 15 men can build a wall in 20 days working 8 hours a day, how many days will 12 men take to build the same wall working 10 hours a day?
Sponsored Advertisement
Ad Space • Google AdSense Partner Network
Q4CDS 2022Medium
Pipe A can fill a tank in 10 hours and Pipe B can fill it in 15 hours. Pipe C can empty the full tank in 20 hours. If all three pipes are opened simultaneously, in how many hours will the empty tank be filled?
Q5JKSSB VLW 2023Medium
A and B undertake to do a piece of work for Rs. 4,500. A alone can do it in 8 days and B alone in 12 days. With the help of C, they finish it in 4 days. What is C's share of the money?
Q6SSC CGL Tier-1Easy
A can do a piece of work in 20 days and B in 30 days. They work together for 5 days and then A leaves. How many days will B take to finish the remaining work?
Q7JKPSC KAS PrelimsHard
A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 liters per minute. When the tank is full, the inlet is opened and due to the leak, the tank is emptied in 12 hours. What is the capacity of the tank?
Q8NDA 2022Easy
A can do a work in 10 days and B in 15 days. If they work on alternate days beginning with A, in how many days will the entire work be completed?
Q9SSC CHSLMedium
4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete the work?
Q10JKSSB Sub-InspectorMedium
Pipe A can fill a cistern in 24 minutes and pipe B in 32 minutes. If both pipes are opened together, after how many minutes should pipe B be closed so that the tank is full in 18 minutes?
Q11UPSC CSATEasy
A is 30% more efficient than B. How much time will they together take to complete a job which A alone could have done in 23 days?
Q12JKSSB Patwari 2024Medium
A, B, and C can do a piece of work in 24, 30, and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
Q13CDS 2021Hard
Two pipes A and B can fill a cistern in 12 hours and 15 hours respectively. A third pipe C can empty it in 20 hours. If A is open all the time and B and C are opened for one hour each alternately, the tank will be full in:
Q14SSC CGLEasy
12 men can complete a work in 16 days. 8 days after they started work, 8 more men joined them. How many more days will they now take to complete the remaining work?
Q15JKSSB Junior AssistantEasy
If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same work?
Frequently Asked Questions (Time Work)
Q: What is the fastest way to solve Time and Work problems in exam conditions?
The LCM method: Find the LCM of the days given for all participants and set that number as the 'Total Work Units'. Divide total units by each person's individual days to get their individual 'Units per Day' (efficiency). Add the efficiencies together and divide the total units by the combined efficiency to find the total time.
Q: How are wages divided when individuals work together on a contract?
Wages must always be distributed in the exact ratio of the work done by each person. If all workers work for the same total number of days, the wages can be split directly according to their individual daily efficiencies.
Q: How do you handle a leaking pipe in Pipes and Cisterns?
A leak is treated as an emptying pipe with negative efficiency. If filling pipe A takes 6 hours (+4 units/hr) and leak B empties in 8 hours (-3 units/hr for 24 unit tank), the net filling rate is 4 - 3 = +1 unit/hr, meaning the tank will fill in 24 / 1 = 24 hours.
Explore More Quantitative Aptitude Topics
Ready to test your speed under real exam conditions?
Attempt timed full-length CBT tests with negative marking and percentile analysis.