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Sunny and Paula can complete a piece of work together in 12 hours. Paula takes 18 hours to complete work alone, another individual, Jane, takes 45 hours to complete the same piece of work alone. How many hours would it take sunny and Jane to complete the same work together?

Sunny and Paula can complete a piece of work together in 12 hours. Paula takes 18 hours to complete work alone, another individual, Jane, takes 45 hours to complete the same piece of work alone. How many hours would it take sunny and Jane to complete the same work together? Correct Answer 20

Suppose, Sunny alone can complete the task in x hours

According to the question,

1/x + 1/18 = 1/12

⇒ 1/x = (3 – 2)/36

⇒ x = 36 hours

Sunny alone can complete the task in = 36 hours

Suppose, Sunny and Jane together can complete the task in k hours

According to the question,

1/k = 1/36 + 1/45

⇒ 1/k = (5 + 4)/180

⇒ 1/k = 9/180

⇒ k = 20

∴ Sunny and Jane together can complete the task in 20 hours

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