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John is twice as efficient as Johny and Johny can do a piece of work in 30 days. Johny started the work and after a few days, John joined him. They completed the work in 22 days. From the very beginning, for how many days did they work together?

John is twice as efficient as Johny and Johny can do a piece of work in 30 days. Johny started the work and after a few days, John joined him. They completed the work in 22 days. From the very beginning, for how many days did they work together? Correct Answer 4 days

Johny - John

Efficiency ratio = 1 : 2

Number of days worked - 30 and 15

Johny’s one day work = 1/30

John’s one day work = 1/15

(John + Johny) one day work = 1/30 + 1/15 = (1 + 2) /30 = 1/10

Now, let us assume John joined Johny after (22 – x) days

Then,

(22 – x) /30 + (x × 1) /10 = 1

⇒ (22 – x + 3x) /30 = 1

⇒ 22 + 2x = 30

⇒ x = 4

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