Time and Work Questions for SSC CGL

Core Concept: Work as a Rate

Think of work as filling a bucket. If A can fill it in 10 days, every day A fills 1/10 of the bucket. Work done = Rate x Time. The trick is: instead of fractions, assign the total work a convenient number (usually LCM of all given days) and work with whole numbers. This LCM method kills fraction arithmetic and saves precious seconds.

• If A finishes work in N days, A's daily work = 1/N of total work.
• LCM method: Set total work = LCM of all days given. Each person's daily output becomes a whole number.
• Combined rate: Add individual daily outputs when people work together.
• Time taken together = Total Work divided by Combined daily output.
• Always check: Does the question ask for days, fraction of work, or wages?

Efficiency and Men-Days Concept

When the number of workers changes, use the Men-Days-Work formula. It treats total work as a product of manpower and time. If you double the workers, you halve the time. This concept also handles efficiency comparisons: if A is twice as efficient as B, A does in 1 day what B does in 2 days.

• M1 x D1 = M2 x D2 (when work is constant and equal efficiency).
• Extended: M1 x D1 x H1 = M2 x D2 x H2 (H = hours per day).
• If efficiency differs: M1 x D1 x E1 = M2 x D2 x E2.
• More men = less days (inverse relation). More work = more days (direct relation).
• When A is n times as efficient as B, A takes 1/n times the days B takes.

Pipes and Cisterns

Pipes and Cisterns is just Time and Work in disguise. An inlet pipe filling a tank = a worker doing work. A leak or outlet pipe = a worker undoing work. Subtract the outlet rate from the inlet rate to find net filling rate. The only new idea: outlet pipes have negative rates.

• Inlet pipe fills tank: rate is positive (+1/T).
• Outlet pipe/leak empties tank: rate is negative (-1/T).
• Net rate = sum of all inlet rates minus sum of all outlet rates.
• Time to fill = 1 / Net rate (using fraction method) or Total Work / Net rate (LCM method).
• If a pipe fills in X hours and a leak empties in Y hours, net fill time = XY/(Y-X) assuming Y > X.

Work and Wages

When a group earns a total wage for completing work, each person is paid proportional to the work they contributed. First find each person's share of work done (using their rate and the days they actually worked), then split the total wage in that ratio. Do not split wages equally unless rates are equal.

• Work done by each person = their rate x days they actually worked.
• Wage ratio = ratio of work done by each person.
• If all work for the same duration, wage ratio equals rate ratio (which is inversely proportional to their individual days).
• Always compute actual work contribution, not just their efficiency.

• Using T = A+B instead of T = AB/(A+B) for combined work. Remember: rates add, not days.
• In pipes problems, forgetting that an outlet pipe is negative. Adding all pipe times directly gives wrong answer.
• Splitting wages equally when workers have different efficiencies or worked different days.
• In the Men-Days formula, not accounting for hours per day when the question mentions shift duration changes.
• Forgetting to check what fraction of work is already done before computing remaining time when someone joins or leaves midway.

• RATE ADD, DAYS DON'T: You can never add days directly. Always convert to rates (1/day), add them, then take reciprocal for combined time.
• LCM = Magic Number: Whenever you see multiple people or pipes with different time values, immediately write LCM as your total work. It turns ugly fractions into clean whole numbers.
• INLET is a worker, OUTLET is a saboteur: For pipes, treat filling pipes as positive workers and leaks as workers who undo the job. Net work = sum with signs.
• Wages follow WORK, not TIME: Two people working the same hours but different rates earn differently. Mnemonic: Pay for OUTPUT not PRESENCE.

• SSC CGL typically places 2-3 Time and Work questions per shift. Expect one straightforward combined-work question, one pipes-cistern, and occasionally one wage-distribution or men-days problem.
• LCM method is fastest for combined work questions. Avoid fraction arithmetic on paper — it slows you down and invites errors.
• Pipe and cistern questions in recent CGL papers (2023-24 Tier 1) often add a twist: one pipe is closed after some hours. Set up partial work done, then change the rate.
• For 2-person combined work, the formula T = AB/(A+B) is a 10-second calculator move. Memorize it for speed but verify with LCM if unsure.
• If a question says A is twice as efficient as B and together they take N days, resist plugging in random numbers. Assign B's rate = 1x, A's rate = 2x, total rate = 3x, then solve. Takes under 40 seconds.