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02 Dec 2021, 09:15
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Difficulty:
45%
(medium)
Question Stats:
73% (03:06) correct
27%
(03:20)
wrong
based on 181
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George takes 4 days to build one-third of a house, Michael takes 3 days to build one-sixth of the same house and Jose takes 5 days to build half of the same house. If all three men work together for 3 days and then George and Jose quit, how long will Michael take to build the remaining portion of the house alone?
A. 2 days
B. 5.1 days
C. 8 days
D. 7.5 days
E. 12 days
A. 2 days
B. 5.1 days
C. 8 days
D. 7.5 days
E. 12 days
02 Dec 2021, 11:11
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Bunuel
George takes 4 days to build one-third of a house, Michael takes 3 days to build one-sixth of the same house and Jose takes 5 days to build half of the same house. If all three men work together for 3 days and then George and Jose quit, how long will Michael take to build the remaining portion of the house alone?
A. 2 days
B. 5.1 days
C. 8 days
D. 7.5 days
E. 12 days
A. 2 days
B. 5.1 days
C. 8 days
D. 7.5 days
E. 12 days
We can solve this question quite easily by assigning a "nice" value the job of building a house.
We want a value that works with all of the given numbers 4, 1/3, 3, 1/6, 5 and 1/2
Pro tip: 360 is often a good number to work with because it's divisible by so many other numbers
So let's say the job of building a house = hammering 360 nails
Let's first calculated each person's RATE
George takes 4 days to build one-third of a house
1/3 of a house = 1/3 of 360 = 120 nails.
If it takes George 4 days to hammer 120 nails, then George's rate = 30 nails per day
Michael takes 3 days to build one-sixth of the same house
1/6 of a house = 1/6 of 360 = 60 nails.
If it takes Michael 3 days to hammer 60 nails, Michael's rate = 20 nails per day
Jose takes 5 days to build half of the same house
1/2 of a house = 1/2 of 360 = 180 nails.
If it takes Jose 5 days to hammer 180 nails, Jose's rate = 36 nails per day
All three men work together for 3 days and . . .
The combined rate of all three men = 30 + 20 + 36 = 86 nails per day
So, in three days, the total number of nails hammered = (3)(86) = 258
The number of nails remaining to complete the job = 360 - 258 = 102
. . . then George and Jose quit, how long will Michael take to build the remaining portion of the house alone?
Michael (at his rate of 20 nails per day) must hammer the remaining 102 nails to complete the job.
Time = output/rate
So the time it takes Michael to complete the job = 102/20 = 5.1 days.
Answer: B
05 Dec 2021, 15:05
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G, M & J take 12, 18 & 10 days respectively to complete the house.
G, M & J completes 1/12, 1/18 & 1/10 work in 1 day.
In 3 days, work done= 3*(1/12 + 1/8 + 1/10)*100= 71.5%
work left for M=28.5%
M takes (18*28.5)/100=5.1 days
(B)
G, M & J completes 1/12, 1/18 & 1/10 work in 1 day.
In 3 days, work done= 3*(1/12 + 1/8 + 1/10)*100= 71.5%
work left for M=28.5%
M takes (18*28.5)/100=5.1 days
(B)
