Aditya and Bhaskar undertake to do a piece of work for 15,000. Aditya alone can do it in 15 days while Bhaskar alone can do it in 18 days. With the help of Chandra, they finish it in 6 days. What is Chandra's share?

Correct option is A

Given:

Aditya alone can do it in= 15 days

Bhaskar alone can do it in= 18 days.

Aditya, Bhaskar and Chandra together can do the work in = 6 days

Formula used:

Efficiency = $$\frac{Total\ Work}{Time\ taken}$$​​

Solution:

Total work: Assume the total work is the Least Common Multiple (LCM) of the time taken by Aditya and Bhaskar to complete the work individually.

​$$\text{Total work} = \text{LCM of 15 and 18} = 90 \, \text{units}$$ 

​$$\text{Aditya's efficiency} = \frac{\text{Total work}}{\text{Days taken by Aditya}} = \frac{90}{15} = 6 \, \text{units/day} \\$$ 

$$\text{Bhaskar's efficiency} = \frac{\text{Total work}}{\text{Days taken by Bhaskar}} = \frac{90}{18} = 5 \, \text{units/day} \\$$

$$\text{Combined efficiency} = \frac{\text{Total work}}{\text{Time taken}} = \frac{90}{6} = 15 \, \text{units/day} \\$$​​​

​​$$\text{Chandra's efficiency} = \text{Combined efficiency} - (\text{Aditya's efficiency} + \text{Bhaskar's efficiency}) \\= 15 - (6 + 5) = 4 \, \text{units/day} \\$$

Ratio of efficiency of Aditya, Bhaskar and Chandra is : 6 : 5 : 4

So the share of Chandra is = $$\frac{4}{15}\times15000=4000$$ 

Share of Chandra is = ₹4000

Thus the correct answer is (A)

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