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Ram, Shyam and Gopal can finish a work in 22, 33 and 44 days respectively. In how many days they can complete the work if they work together?
1. \(10\frac{2}{{13}}\) days
2. 12 days
3. 15 days
4. 14.5 days
5. 16 days

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Best answer
Correct Answer - Option 1 : \(10\frac{2}{{13}}\) days

Given:

Ram, Shyam and Gopal can finish a work in 22, 33 and 44 days respectively

Calculation:

Ram finish his work in 22 days

⇒ Ram’s work in one day = 1/22 units

Shyam finish his work in 33 days

⇒ Shyam’s work in one day = 1/33 units

Gopal finish his work in 33 days

⇒ Gopal’s work in one day = 1/44 units

In one day together they will work = 1/22 + 1/33 + 1/44

Let x be number of day they will complete work

⇒ 1/22 + 1/33 + 1/44 = 1/x

⇒ 1/x = 13/132

⇒ x = 132/13 = \(10\frac{2}{{13}}\) days

∴ Working together they will complete the work in \(10\frac{2}{{13}}\) days

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