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Quality checking time

CMAT 2019 · Quantitative Techniques & Data Interpretation · Medium · Time and Work

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Rajesh can check the quality of 10001000 items in 55 hours and Rakesh can complete 75%75\% of the same job in 33 hours. How much time is required for both of them to check 13001300 items, if Rakesh stops checking after 22 hours?

  1. A.

    1 hour

  2. B.

    2 hours

  3. C.

    4 hours

  4. D.

    3 hours

Answer

C

Explanation

Efficiency of Rajesh =10005=200 items/hr= \frac{1000}{5} = 200\text{ items/hr}.

Rakesh completes 75%75\% in 3 hrs  ⟹  3\text{ hrs} \implies Rakesh takes 10075×3=4 hrs\frac{100}{75} \times 3 = 4\text{ hrs} to check 10001000 items.

Efficiency of Rakesh =10004=250 items/hr= \frac{1000}{4} = 250\text{ items/hr}.

Let the total time taken by Rajesh be tt hours. Rakesh works for 22 hours.

Total Work=250×2+200×t=1300\text{Total Work} = 250 \times 2 + 200 \times t = 1300 500+200t=1300  ⟹  200t=800  ⟹  t=4 hours500 + 200t = 1300 \implies 200t = 800 \implies t = 4\text{ hours}.

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