Time and Work Question 2 - CAT 2020

This project variation scenario can be solved cleanly using the standard work-equivalence Chain Rule fraction formula:

M₁ × D₁/W₁ = M₂ × D₂/W₂

• Identify the Parameters for the First Phase:

Initial workers (M₁) = 140 people

Days worked (D₁) = 60 days

Work completed (W₁) = 1.5 km of road

• Identify the Parameters for the Remaining Phase:

Total length target = 6 km

⟹ Remaining road work (W₂) = 6 − 1.5 = 4.5 km

Total timeline target = 200 days

⟹ Remaining days (D₂) = 200 − 60 = 140 days

Let the total headcount needed for this second stretch be M₂.

• Set Up and Solve the Proportion Balance:

140 × 60/1.5 = M₂ × 140/4.5

Notice that 140 appears on both sides of the numerator, allowing us to cancel it out immediately:

60/1.5 = M₂/4.5

M₂ = 60 × (4.5/1.5)

M₂ = 60 × 3

= 180 people

• Calculate the Count of Additional Workers Required:

Additional Workers = M₂ − M₁

= 180 − 140

= 40 people

Correct Answer: 40

💡 FundaMakers Tip:

When handling work updates with the chain rule, look for scaling shortcuts across the parameters. Here, the remaining distance (4.5 km) is exactly 3 times the initial distance (1.5 km). Since the remaining time (140 days) happens to be exactly equal to the number of original workers (140 people), the factors cancel out cleanly, reducing the problem to a quick mental calculation of 60 × 3 = 180.