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Karan is twice as efficient as Tarun. If Karan alone takes 45 days less than the time taken by Tarun to finish the work, then find the time in which they together can finish the work.

Karan is twice as efficient as Tarun. If Karan alone takes 45 days less than the time taken by Tarun to finish the work, then find the time in which they together can finish the work. Correct Answer 30 days

GIVEN:

Karan is twice as efficient as Tarun in doing a piece of work.

Karan alone takes 45 days less than the time taken by Tarun to finish the work.

CONCEPT:

Time is inversely proportional to efficiency.

FORMULA USED:

Work = Time × Efficiency

CALCULATION:

According to the question,

Ratio of efficiencies of Karan and Tarun = EK: ET = 2 : 1

Ratio of time taken by Karan and Tarun

⇒ TK : TT = 1 : 2

Suppose the time take byTarun alone to finish the work is x days

⇒ Time take by Karan alone to finish the work = (x – 45) days

⇒ (x – 45) : x = 1 : 2

⇒ 2x – 90 = x

⇒ x = 90

Tarun alone can finish the work in 90 days

Karan alone can finish the work in 45 days

TK : TT = 45 : 90

∴ Time taken by them to complete the work together = 90/(1 + 2) = 30 days

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