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abhirup1711
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Time and rate are RECIPROCALS.abhirup1711 wrote:Randy can finish a job in a hrs and Alvin can finish the same in b hrs.If they both work together which of the following represents the portion of the job that Randy will not have to complete?
ab/(a+b)
(a-b)/(a+b)
b/(b-a)
a/(a+b)
b/(a+b)
Since the time ratio for Randy and Alvin = a:b, the rate ratio for Randy and Alvin = b:a.
Implication:
For every b units produced by Randy, a units are produced by Alvin.
Thus, of every a+b units, the fraction produced by Alvin = a/(a+b).
The correct answer is D.
Alternate approach:
Let the job = 10 units.
Let a = 5 hours.
Rate for Randy alone = w/t = 10/5 = 2 units per hour.
Let b = 2 hours.
Rate for Alvin alone = w/t = 10/2 = 5 units per hour.
The combined rate for Randy and Alvin = 2+5 = 7 units per hour.
Of the 7 units produced each hour, 2 will produced by Randy and 5 will be produced by Alvin.
Thus, the fraction of the job produced by Alvin = 5/7. This is our target.
Now we plug a=5 and b=2 into the answers to see which yields our target of 5/7.
A quick scan of the answers reveals that only D works:
a/(a+b) = 5/(5+2) = 5/7.
The correct answer is D.
