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Adil and Biren together can complete a task in 20 days. Biren and Chirag together can complete the same task in 50 days. Adil and Chirag together can complete the same task in 40 days. If the same task was to be done by them alone, what would be the ratio of time taken by Adil alone to Biren alone? A. 11: 9 B. 11 : 3 C. 7 : 9 D. 9 : 11

Adil and Biren together can complete a task in 20 days. Biren and Chirag together can complete the same task in 50 days. Adil and Chirag together can complete the same task in 40 days. If the same task was to be done by them alone, what would be the ratio of time taken by Adil alone to Biren alone? A. 11: 9 B. 11 : 3 C. 7 : 9 D. 9 : 11 Correct Answer D

Given:

Adil and Biren together can complete a task in = 20 days

Bire and Chirag together can complete the same task in = 50 days

Adil and Chirag together can complete the same task in = 40 days

Formula:

Total work = Efficiency × Time

Calculation:

Total work = 200 unit (LCM of 20, 40, and 50)

Efficiency of Adil and Biren = 200/20 = 10 units/day

Efficiency of Biren and Chirag = 200/50 = 4 units/day

Efficiency of Adil and Chirag = 200/4 = 5 units/day

⇒ Efficiency of Adil, Biren and Chirag = (10 + 4 + 5)/2 = 9.5 units/day

Efficiency of Adil = 9.5 – 4 = 5.5 units/day

Efficiency of Biren = 9.5 – 5 = 4.5 units/day

⇒ Time taken by Adil to complete the whole work = 200/5.5 = 400/11

⇒ Time taken by Biren to complete the whole work = 200/4.5 = 400/9

∴ Required ratio = (400/11) : (400/9)

⇒ 9 : 11

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