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Gopi and Rashi working in the kitchen can together finish cooking in 22.5 minutes. Gopi is thrice as efficient as Rashi. Calculate the time in which they can finish the cooking if Gopi increased her efficiency by two times and Rashi increased her efficiency by three times.

Gopi and Rashi working in the kitchen can together finish cooking in 22.5 minutes. Gopi is thrice as efficient as Rashi. Calculate the time in which they can finish the cooking if Gopi increased her efficiency by two times and Rashi increased her efficiency by three times. Correct Answer 10

Given:

Time taken by Gopi and Rashi to do the work together = 22.5 minutes

Calculation:

Gopi is thrice as efficient as Rashi

Let the time taken by Gopi to finish the work alone be x

⇒ Gopi’s 1 minute work = 1/x

Then, time taken by Rashi to finish the work alone is 3x

⇒ Rashi’s 1 minute work = 1/3x

Time taken by Gopi and Rashi to do the work together = 22.5 minutes

⇒ (1/x) + (1/3x) = 1/22.5

⇒ (1/x) + (1/3x) = 2/45

⇒ 4/3x = 2/45

⇒ x = 30

Time taken by Gopi to finish the work alone = 30 minutes

Time taken by Rashi to finish the work alone = 3x = 3 × 30 = 90 minutes

Gopi increased her efficiency by two times and Rashi increased her efficiency by three times

Time taken by Gopi to finish the work alone = 30/2 = 15 minutes

Time taken by Rashi to finish the work alone = 90/3 = 30 minutes

∴ Working together they can finish the work in

⇒ (1/15) + (1/30) = 3/30 = 1/10

∴ Time taken by Gopi and Rashi to do the work together is 10 minutes

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