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Two friends Raj and Rohit work in a factory. If Rohit worked alone, he would need 8 hours more to complete the work than if they both worked together. now If Raj worked alone, it would need 4.5 hours more to complete the work than they both working together. what time would it take Raj alone to complete the work?

Two friends Raj and Rohit work in a factory. If Rohit worked alone, he would need 8 hours more to complete the work than if they both worked together. now If Raj worked alone, it would need 4.5 hours more to complete the work than they both working together. what time would it take Raj alone to complete the work? Correct Answer 10.5

Given:

If Rohit worked alone = 8 + (Raj + Rohit)

If Raj worked alone = 4.5 + (Raj + Rohit)

Calculations:

Let the both will complete work in x hours.

There combined efficiency is = 1/x

⇒ Rohit’s work = x + 8

⇒ Rohit’s efficiency = 1/ (x + 8)

⇒ Raj’s work = x + 4.5

⇒ Raj’s efficiency = 1/ (x + 4.8\5)

Total efficiency

⇒ 1/ (x + 8) + 1/ (x + 4.5) = 1/x

⇒ 1/ (x + 4.5) = –

⇒ 1/ (x + 4.5) = (x + 8 – x)/x (x + 8)

⇒ x (x + 8) = 8(x + 4.5)

⇒ x2 = 40

⇒ x = √ 40 = 6.5

⇒ Raj alone can complete the work = 6.5 + 4.5 = 10 days

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