Ahluwalia and Bimal together take 6 days to finish the work. Bimal and Jalan together take 10 days to finish the work. What is the difference between number of days taken by Ahluwalia and Jalan when they worked alone to complete the whole work?

Options

A. 12 days
B. 16 days
C. 15 days
D. can't be determined

Answer

To solve the problem, we need to determine the individual efficiencies of Ahluwalia, Bimal, and Jalan based on the information given. Let's break down the steps:

### Step 1: Understand the Work Done Together
Ahluwalia and Bimal together take 6 days to finish the work. We can denote the total work as W. The work done by Ahluwalia and Bimal in one day is:
\[ \text{Work per day (A + B)} = \frac{W}{6} \]

### Step 2: Work Done by Bimal and Jalan
Bimal and Jalan together take 10 days to finish the work. Therefore, the work done by Bimal and Jalan in one day is:
\[ \text{Work per day (B + J)} = \frac{W}{10} \]

### Step 3: Set Total Work
To simplify calculations, we can assume the total work W is the least common multiple (LCM) of 6 and 10, which is 30 units.

### Step 4: Calculate Daily Work
From our assumptions:
- For Ahluwalia and Bimal:
\[ A + B = \frac{30}{6} = 5 \text{ units/day} \]
- For Bimal and Jalan:
\[ B + J = \frac{30}{10} = 3 \text{ units/day} \]

### Step 5: Create Equations
Now we have two equations:
1. \( A + B = 5 \) (Equation 1)
2. \( B + J = 3 \) (Equation 2)

### Step 6: Solve for Individual Efficiencies
From Equation 1, we can express B in terms of A:
\[ B = 5 - A \]

Substituting this into Equation 2:
\[ (5 - A) + J = 3 \]
\[ J = 3 - (5 - A) \]
\[ J = A - 2 \]

### Step 7: Find Days Taken by Each Worker Alone
Now we have:
- \( B = 5 - A \)
- \( J = A - 2 \)

The number of days taken by each worker alone to complete the whole work can be calculated as follows:
- Days taken by Ahluwalia:
\[ \text{Days by A} = \frac{W}{A} = \frac{30}{A} \]
- Days taken by Jalan:
\[ \text{Days by J} = \frac{W}{J} = \frac{30}{A - 2} \]

### Step 8: Find the Difference
The difference in the number of days taken by Ahluwalia and Jalan is:
\[ \text{Difference} = \left| \frac{30}{A} - \frac{30}{A - 2} \right| \]

### Conclusion
However, since we have two variables (A and J) and only two equations, we cannot determine the exact values of A and J without additional information. Therefore, we cannot find the difference in days taken by Ahluwalia and Jalan.

### Final Answer
The difference in the number of days taken by Ahluwalia and Jalan cannot be determined with the given information.

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