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Arjun, Bablu and Charan together make a total of 10 chairs in one day. Together, they were assigned the job of making a total of 100 chairs. Initially, Arjun started the work, without Bablu and Charan joining him. After a few days, Arjun quit, and immediately Bablu and Charan took over and together they completed the job after a few more days. If it took a total of 20 days to complete the entire work and Arjun makes at least 6 chairs per day, then, how many days did Arjun work on the job?

Arjun, Bablu and Charan together make a total of 10 chairs in one day. Together, they were assigned the job of making a total of 100 chairs. Initially, Arjun started the work, without Bablu and Charan joining him. After a few days, Arjun quit, and immediately Bablu and Charan took over and together they completed the job after a few more days. If it took a total of 20 days to complete the entire work and Arjun makes at least 6 chairs per day, then, how many days did Arjun work on the job? Correct Answer 10

Suppose the number of chairs which can be made by each of Arjun, Bablu and Charan in a day be x, y and z, respectively.

Let us say Arjun worked alone for d days.

According to question –

Case I:

⇒ (x + y + z) = 10

Case II:

⇒ xd + (20 – d)(y + z)= 100

⇒ xd + (20 – d)(10 – x) = 100

⇒ xd + 200 – 10d – 20x + dx = 100

⇒ 2xd – 10d + 100 – 20x = 0

⇒ 2d(x – 5)+ 20(5 – x) = 0

⇒ 2d(x – 5) – 20(x – 5)= 0

⇒ (x – 5)(2d – 20) = 0

⇒ x = 5 and d = 20/2 = 10

Given that x ≥ 6

∴ x ≠ 5

∴ d = 10 days

Therefore, Arjun worked for 10 days.

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