Time and Work, Efficiency, Pipes and Cisterns | Banking Quant Mastery

Why This Chapter Matters

This chapter gets easier the moment you stop thinking in raw days and start thinking in rates. It covers worker efficiency, man-day-hour scaling, wages, inlet-outlet logic, and mid-process pipe changes that appear frequently in banking sets.

Core Ideas

If A finishes a job in $15$ days, A's one-day work is $\frac{1}{15}$ .
Combined work means adding filling or working rates.
Emptying pipes and inefficient workers contribute negative rates.
LCM-based total work can make comparison questions cleaner than fraction-heavy setups.
In manpower questions, men, days, hours, and work are linked proportionally only after the work type is kept constant.
Wage-sharing questions are just work-rate questions with money attached at the end.

High-Value Formulas

Concept	Formula / Rule
One-day work	$rate = \frac{1}{time}$
Combined rate	$net rate = sum of positive rates - sum of negative rates$
Time from rate	$time = \frac{1}{net rate}$
Men-days-hours relation	$M_{1} D_{1} H_{1} W_{2} = M_{2} D_{2} H_{2} W_{1}$
Wages ratio	$share ratio = \frac{1}{d _{1}} : \frac{1}{d _{2}} : \dots$

How To Approach Questions

Convert every time statement into a rate.
Choose a common total work when multiple workers are compared.
Use negative signs for leak, drain, or destruction rates.
If people, hours, or output quantity change together, set up the man-day-hour relation before solving.
When one worker leaves or one pipe is closed midway, split the timeline into two phases.

Worked Examples

Example 1

Prompt: A can complete a work in $15$ days and B in $10$ days. Find the joint time.

Approach: Combined rate $= \frac{1}{15} + \frac{1}{10} = \frac{1}{6}$ . Time $= 6$ days.

Example 2

Prompt: A pipe fills a tank in $12$ hours and a drain empties it in $18$ hours. Find the net filling time.

Approach: Net rate $= \frac{1}{12} - \frac{1}{18} = \frac{1}{36}$ . So the tank fills in $36$ hours.

Example 3

Prompt: If $24$ men working $8$ hours a day build a road in $15$ days, in how many days will $48$ men working $6$ hours a day build a road $3$ times as long?

Approach: Use the relation $M_{1} D_{1} H_{1} W_{2} = M_{2} D_{2} H_{2} W_{1}$ . So $24 \times 15 \times 8 \times 3 = 48 \times D \times 6$ , which gives $D = 30$ days.

Example 4

Prompt: Two pipes fill a tank in $12$ and $16$ minutes. If both run for $3$ minutes and then the second pipe is closed, how much extra time does the first pipe need?

Approach: Take total capacity $48$ units. In $3$ minutes, both fill $3 (4 + 3) = 21$ units. The remaining $27$ units are filled by the first pipe alone at $4$ units per minute, so the extra time is $\frac{27}{4} = 6.75$ minutes.

Common Mistakes

Adding times directly instead of adding rates.
Ignoring the negative sign for emptying pipes.
Forgetting that efficiency and time are inversely related.
Using the manpower relation without checking whether the work quantity also changed.
For wage-sharing, forgetting that pay follows contribution, not headcount.

Quick Revision

This chapter becomes mechanical once every statement is translated into a rate, a workload, or a two-phase timeline.

7. Time and Work, Efficiency, Pipes and Cisterns