CaptainLevi wrote:
P, V and G had to paint three identical fences. On the first day, only P turned up for work and he completed the work only on the first fence, taking m hours. On the second day, all three of them turned up for work and they completed the work only on the second fence, taking (m –4) hours. On the third day, V and G turned up and they completed the work on the third fence, taking (m+ 5) hours. What is the value of m?
a) 6
b) 8
c) 9
d) 10
e) 12
Since P takes m hrs to complete one fence, his rate of work = 1/m fence/hr = p
P, V and G take (m - 4) hrs to complete one fence so their rate of work = 1/(m - 4) fence/hr = p + v + g
V and G take (m + 5) hrs to complete one fence so their rate of work = 1/(m + 5) = v + g
1/m + 1/(m+5) = 1/(m - 4)
Now just try to plug in the options to see which value of m works.
Note that m = 6 gives 11 in the second denominator on left hand side. It is a big prime number and seeing that on right hand side, we will have 1/2, m = 6 will not work. Same logic works for 8 and 9 too.
The first option you should actually try is m = 10 which works.
Answer (D)
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Karishma
Veritas Prep GMAT Instructor
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