Akash is three times as efficient a workman as Baldev and therefore finishes a certain job in 40 days less than Baldev. If they work together on the same job, in how many days will they complete it?

Introduction / Context:
This question combines relative efficiency and time difference information. One worker is said to be three times as good, or three times as efficient, as another worker, and their individual completion times differ by a fixed number of days. The objective is to deduce their individual times and then find how long they would take if they worked together.

Given Data / Assumptions:

• Akash is three times as efficient as Baldev.
• Akash finishes the job 40 days earlier than Baldev.
• Both work at constant rates.
• We want the time required for Akash and Baldev working together to complete the job.

Concept / Approach:
If Akash is three times as efficient as Baldev, then Akash's daily work rate is three times Baldev's rate. Since time is inversely proportional to efficiency for the same job, the time taken by Akash will be one third of the time taken by Baldev. We set up an equation using the information that Akash's time is 40 days less than Baldev's time, solve for each time separately, and then compute their combined rate for the job.

Step-by-Step Solution:
Step 1: Let time taken by Baldev alone to finish the job be T days.Step 2: Since Akash is three times as efficient as Baldev, his time to finish the job is T / 3 days.Step 3: According to the question, Akash finishes the job 40 days earlier than Baldev, so T - T / 3 = 40.Step 4: Simplify the equation: T - T / 3 = (3T / 3 - T / 3) = 2T / 3.Step 5: So 2T / 3 = 40, which gives T = 40 * 3 / 2 = 60 days.Step 6: Therefore Baldev alone takes 60 days, and Akash alone takes T / 3 = 60 / 3 = 20 days.Step 7: Rate of Akash = 1 / 20 of the work per day, rate of Baldev = 1 / 60 of the work per day.Step 8: Combined rate of Akash and Baldev = 1 / 20 + 1 / 60.Step 9: Use common denominator 60: 1 / 20 = 3 / 60, so combined rate = 3 / 60 + 1 / 60 = 4 / 60 = 1 / 15.Step 10: Time taken together = 1 divided by (1 / 15) = 15 days.

Verification / Alternative check:
We can verify by imagining their joint work over 15 days. In 15 days Akash completes 15 * (1 / 20) = 3 / 4 of the job, and Baldev completes 15 * (1 / 60) = 1 / 4 of the job. Together this is 3 / 4 + 1 / 4 = 1 whole job, confirming that 15 days is correct.

Why Other Options Are Wrong:

• 60 days: This is the time taken by Baldev alone, not the joint time.
• 20 days: This is the time taken by Akash alone, not the time when both work together.
• 10 days: This would require a combined rate of 1 / 10, which is larger than 1 / 15 and not consistent with the given separate times.

Common Pitfalls:
One common error is to assume that if Akash is three times as efficient, his time is three times Baldev's time, which is the opposite of the truth. Another mistake is to mis-handle the time difference and set up the equation incorrectly, such as T / 3 - T = 40, which would produce a negative value. Always remember efficiency and time are inversely related for the same job.

Final Answer:
Akash and Baldev together can finish the work in 15 days.