Work is always considered as 1 unit (complete job). If A can complete work in 10 days, A's rate of work is 1/10 per day. This means A completes 1/10th of the total work each day
Work = Rate × Time. If multiple people work together, their rates add up. Total work is always 1 unit. Rate of work = 1/Time taken to complete the job
- If A completes work in 'a' days, A's one day work = 1/a - If A and B together complete work in 'd' days, (1/a + 1/b) = 1/d - Time taken by A and B together = (a × b)/(a + b) days - If A completes work in 'x' days and B in 'y' days, working together they complete in xy/(x+y) days
SSC CGL typically asks 2-3 questions from this topic. Common patterns include: two people working together, one person leaving midway, comparing efficiencies, and alternative work scenarios.
- LCM Method: Take LCM of all time periods given. This becomes total work. Then find individual rates by dividing LCM by individual time.
This eliminates fractions and makes calculations faster.
A's one day work = 1/12
B's one day work = 1/18
Combined one day work = 1/12 + 1/18 = (3+2)/36 = 5/36
Time taken together = 36/5 = 7.2 days Alternative (Shortcut): Time = (12 × 18)/(12 + 18) = 216/30 = 7.2 days Worked Example 2: A and B together can complete work in 6 days. A alone can complete it in 10 days. In how many days can B alone complete the work?
Combined one day work = 1/6
A's one day work = 1/10
B's one day work = 1/6 - 1/10 = (5-3)/30 = 2/30 = 1/15
B alone can complete work in 15 days Shortcut Formula: If A and B together complete work in T days and A alone in A days, then B alone takes: B = (A × T)/(A - T) days Applying: B = (10 × 6)/(10 - 6) = 60/4 = 15 days Most Common Trap: Students often add time instead of adding rates. Remember - when people work together, their RATES add up, not their TIME. If A takes 4 days and B takes 6 days, together they DON'T take 4+6=10 days. Instead, calculate 1/4 + 1/6 to find combined rate. Another Major Mistake: Forgetting that work is always 1 unit. Students sometimes assume work quantity changes, leading to wrong calculations. Always treat complete work as 1 unit regardless of the scenario. Efficiency Trick: If A is twice as efficient as B, then A takes half the time B takes. If A:B efficiency ratio is 2:3, then their time ratio is 3:2 (inverse relationship). Negative Work Concept: Sometimes one person does work while another undoes it (like filling and emptying a tank). In such cases, subtract the rates instead of adding them.
6graded MCQs · easy to hard · full solution & trap analysis