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Anand and Ravi can complete a piece of work in 12 days. Ravi and Chinmay can complete the same work in 16 days while Chinmay and Anand can complete the same work in 48 days. In how many days can Ravi alone complete the work?

Anand and Ravi can complete a piece of work in 12 days. Ravi and Chinmay can complete the same work in 16 days while Chinmay and Anand can complete the same work in 48 days. In how many days can Ravi alone complete the work? Correct Answer 16 days

Given:

Anand and Ravi can complete a piece of work in 12 days

Ravi and Chinmay can complete the same work in 16 days

Chinmay and Anand can complete the same work in 48 days

Formula used:

One day work = Total work/Number of days

Calculation:

A + R →  12 days

R + C → 16 days

C + A → 48 days 

Total work = LCM (12, 16, 48) = 48 unit

(A + R)'s one day's work = 48/12 = 4 unit

(R + C)'s one day's work = 48/16 = 3 unit

(C + A)'s one day's work = 48/48 = 1 unit

Now,

(A + R) + (R + C) = (2R + A + C) = 4 + 3 = 7 unit

⇒ 2R = 7 - (A + C) = 7 - 1 = 6 unit

⇒ R = 6/2 = 3 unit

⇒ R's one day's work = 3 unit

∴ Number of days = Total work/One day's work

⇒ 48/3 = 16

 In 16 days Ravi alone can complete the work

 

 

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