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Time & Work

Some machines complete the work in 4 days. But if 4 other machines are included in this work, then the job shall be completed in 2 days. If capacities of all machines are same, then in how many days 2 machines can complete this work ?

Option:
A. 6 days
B. 8 days
C. 10 days
D. 12 days
Answer: B . 8 days

Justification:

Suppose, originally there are x machines.
 x machines 1 days work = $ 1/4 $ or 1 machine's 1 day's work  $1/{4x}$ .... (i) 
Also (x + 4) machines 1 days's work = $1/2$
1 machine's 1 day's work = $ 1/ {2(x + 4)} $... (ii)
Equating (i) and (ii),
$ 1/{4x} = 1/ {2(x + 4)} $ or 2x + 8 = 4x
or 2x = 8
or  x = 4
Now, 1 machine's 1 days work = $ 1/{4x4} = 1/16$
2 machine's 1 day's work = $2/16 = 1/8 $
Hence, 2 machines can finish the work in 8 days. 

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