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Karan and Arjun work for 12 days then Aman and Ankur replaced them and complete the remaining work in 5 days. The efficiency of Karan and Arjun is in the ratio 4 : 3. Aman alone can complete work in 10 days and Ankur alone completes the work in 20 days. Find the number of days in which Karan and Arjun both complete the work.

Karan and Arjun work for 12 days then Aman and Ankur replaced them and complete the remaining work in 5 days. The efficiency of Karan and Arjun is in the ratio 4 : 3. Aman alone can complete work in 10 days and Ankur alone completes the work in 20 days. Find the number of days in which Karan and Arjun both complete the work. Correct Answer 48 days

Given:

Efficiency of Karan and Arjun = 4 : 3

Karan and Arjun worked only for 12 days.

Calculation:

Let the efficiency of Karan and Arjun be 4x and 3x respectively.

⇒ Work done by Karan and Arjun in 12 days = 12 × (4x + 3x) = 84x

Let total work be 20 units (LCM of 10, 20)

⇒ Efficiency of Aman = 20/10 = 2 units/day

⇒ Efficiency of Ankur = 20/20 = 1 unit/day

According to the question,

84x + 5 × (2 + 1) = 20

⇒ 84x = 5

⇒ x = 5/84

∴ Required time = 20/(4x + 3x) = (20 × 84) / (7 × 5) = 48 days 

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