Time & work and pipes & cisterns are one picture: a wall of blocks. Each worker lays a fixed number of blocks a day, and a leak takes blocks away. Press Play and watch each picture build, or step with the arrow keys. Turn on Voice to have it read aloud.
Everything from the player, compressed. Every row starts the same way: turn days into blocks per day.
| Situation | Turn it into | Example |
|---|---|---|
| Each person's days alone | Work = LCM of the days; rate = work ÷ days | 12 and 18 days → 36 blocks → 3 and 2 a day |
| Working together | Add rates, never days. Two people: ab/(a+b) | 12 and 18 → 36 ÷ 5 = 7.2 days |
| Fraction of work done | rate × days ÷ total = Σ days worked ÷ days alone | 4 days → 4/12 + 4/18 = 5/9 |
| Pairs given (A+B, B+C, C+A) | Sum of pair rates ÷ 2 = all three | 5 + 4 + 3 = 12 → 6 a day → 10 days |
| A is p/q more efficient than B | Rate (q+p) : q ⇒ time q : (q+p) | 25% more → rate 5 : 4 → time 4 : 5 |
| Men, days, hours, amount of work | M×D×H ÷ W is fixed. Chain fractions: “more or fewer days?” | 12 × 10/15 × 6/8 × 450/300 = 9 days |
| Different kinds of worker | Convert everyone to blocks a day | 2 men = 3 women → man 3, woman 2 |
| Equal members inside a team | Per member = team rate ÷ team size | X: 6 ÷ 6 = 1 · Y: 8 ÷ 4 = 2 |
| Leaves k days before the end | Add phantom k × rate, divide by the full rate | (60 + 15) ÷ 5 = 15 days |
| Alternate days / turns | Full cycles until less than one cycle is left, then walk day by day | 18 blocks, 3 + 2: A first 7, B first 7⅓ |
| Pipe plus leak | Leak = negative blocks; subtract rates. ab/(b−a) | 10 h fill, 15 h leak → 30 h |
| Fill / empty in turns | Stop at the climb that reaches the top | 4 h fill, 6 h drain, hourly → 19 h, not 24 |
| Wages | Share ∝ blocks laid = rate × days worked | 15 : 10 : 5 of ₹3,000 → 1500 / 1000 / 500 |
Two labs. Change the numbers and watch the picture answer the question.
Pick how many days each worker needs alone. The wall is the LCM of those days. Press “+1 day” to watch everyone lay their blocks.
One pipe fills, one drain empties. Run them together, or one hour each in turns, and see when the tank is first full.
Written for this page, easy at the top and CAT level at the bottom. Each one is tagged with the picture it needs. Draw the wall or timeline first, then open the method.
Ravi can paint a fence in 15 days and Meera in 10 days. Working together, how many days do they need? What fraction of the fence is painted after the first 2 days?
Pipes P and Q can fill a tank in 12 and 15 minutes. A drain R can empty the full tank in 20 minutes. All three are opened on an empty tank. When is it full?
A is 50% more efficient than B. B alone takes 30 days to finish a job. How long do A and B take together?
16 workers, working 9 hours a day, lay 6 km of road in 15 days. How many workers are needed to lay 8 km in 12 days, working 8 hours a day?
3 men can finish a job in 30 days. 5 women can also finish it in 30 days. How long will 2 men and 5 women take together?
Team P has 6 members and finishes a project in 10 days. Team Q has 5 members and finishes the same project in 8 days. Members within a team work at the same speed. How long will 3 members of P and 2 members of Q take together?
A alone takes 24 days and B alone 36 days. They start together, but A leaves 6 days before the work is finished. How many days does the work take in all?
A can finish a job in 9 days and B in 12 days. They work on alternate days, with B working on the first day. How many days does the job take?
A and B together finish a job in 10 days, B and C in 12 days, and C and A in 15 days. All three work together and are paid ₹9,000 for the job. How many days do they take, and what is B's share?
Pipe A fills a tank in 3 hours and pipe B in 6 hours. A drain C, which alone empties the full tank in 9 hours, stays open the whole time. A and B are opened alternately for an hour each, starting with A. When is the empty tank first full?