EduGoog

Time & Work

A is thrice as good as B and can finish a work in 60 days less than that of B. If they work together, in how many days work will be completed ?

Option:
A. 45 days
B. 30 days
C. $22{1/2}$ days
D. $17{1/2}$ days
Answer: C . $22{1/2}$ days

Justification:

Suppose B takes $x$ days to finish a certain work.
B's day's work = $1/x$
A's day's work = $3/x$
By hypothesis,
$x - x/3 = 60$
or ${2/3}x = 60$
or $x$ = 90
Now, (A + B)'s 1 day's work
=$1/x + 3/x = 4/x = 4/90 = 2/45$
Hence, A and B can together finish the work in $45/2 = 22{1/2}$ days. 

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