Shortcut Trick
Jack works for the entire 15 days, completing 15 ÷ 30 = 1/2 of the work.
The remaining 1/2 of the work must be completed by Ryan.
Time Ryan needs to do 1/2 of the work = 1/2 × 14 = 7 days.
Since the work lasts 15 days and Ryan works for 7 days, he joins after 15 − 7 = 8 days.
∴ The correct answer is 8 days.
Alternate Method
Given:
Time taken by Jack = 30 days
Time taken by Ryan = 14 days
Total time to finish work = 15 days
Formula Used:
Total Work = Efficiency × Time
| Person | Days | Total Work | Efficiency |
|---|
| Jack | 30 | 210 | 7 |
| Ryan | 14 | 15 | |
Calculations:
⇒ Total work (LCM of 30 and 14) = 210 units.
⇒ Jack started the work and stayed until the end (15 days).
⇒ Work done by Jack in 15 days = 15 × 7 = 105 units.
⇒ Remaining work to be done by Ryan = 210 − 105 = 105 units.
⇒ Days Ryan worked = 105 ÷ 15 = 7 days.
⇒ Ryan joined after = Total time − Ryan's working days
⇒ Joining day = 15 − 7 = 8 days.
∴ The correct answer is 8 days.
Additional Information
Efficiency and Time Relationship
Efficiency is inversely proportional to the time taken to complete the work (Efficiency ∝ 1/Time).
Combined Efficiency
When two or more people work together, their efficiencies are added: Total Efficiency = E1 + E2 + ... + En.
Work and Wages
Wages are always distributed in the ratio of the actual work done by each individual (Efficiency × Time worked).