10. Time, work and efficiency
Free study material · concepts, shortcuts & solved questions
If A completes a job in x days, A’s one-day work is 1/x. Combined rates add. Efficiency is inversely proportional to time: if A is twice as efficient as B, A takes half the time for the same work. Use LCM units when times are integers.
Method before formula For work done in stages, calculate each stage’s rate and work. A worker’s absence changes the rate only during the relevant interval. Never add days; add work rates. |
Formula and decision table
Model | Method |
A 12 days, B 18 days | Rate=1/12+1/18=5/36; time=36/5 days |
Efficiency ratio | Efficiency 3:2 => time ratio 2:3 |
Wages | Wages follow work contribution if rates are given |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
A takes 12 days and B 18 days. Together: | Combined rate=5/36, so time=36/5=7.2 days. | B. 7.2 days |
If A is 3 times as efficient as B, time ratio A:B: | Time is inverse to efficiency. | B. 1:3 |
Two workers’ rates should be: | Combined work rates are added. | A. Added |
What an examiner is testing
The options around Time, work and efficiency usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: A takes 12 days and B 18 days. Together: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 7.2 days, because Combined rate=5/36, so time=36/5=7.2 days.
Example 2: If A is 3 times as efficient as B, time ratio A:B: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 1:3, because Time is inverse to efficiency.
Example 3: Two workers’ rates should be: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is Added, because Combined work rates are added.
Chapter practice
1. A takes 12 days and B 18 days. Together:
(A) 6 days (B) 7.2 days (C) 8 days (D) 9 days
Answer: B. 7.2 days | Explanation: Combined rate=5/36, so time=36/5=7.2 days.
2. If A is 3 times as efficient as B, time ratio A:B:
(A) 3:1 (B) 1:3 (C) 2:3 (D) 3:2
Answer: B. 1:3 | Explanation: Time is inverse to efficiency.
3. Two workers’ rates should be:
(A) Added (B) Multiplied (C) Subtracted always (D) Ignored
Answer: A. Added | Explanation: Combined work rates are added.
SSC CGL speed and trap clinic
For Time, work and efficiency, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Time, work and efficiency? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Time, work and efficiency question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |