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There are three galleries in a coal mine. On the first day, two galleries are operative and after some time, the third gallery is made operative. With this, the output of the mine became half as large again. What is the capacity of the second gallery as a percentage of the first, if it is given that a four-month output of the first and the third galleries was the same as the annual output of the second gallery?
- a)60%
- b)64%
- c)65%
- d)70%
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
There are three galleries in a coal mine. On the first day, two galler...
The third gallery making the capacity ‘half as large again’ means an increase of 50%.
Further, it is given that: 4(first + third) = 12 (second) In order to get to the correct answer, try to fit in the options into this situation.
(Note here that the question is asking you to find the capacity of the second gallery as a percentage of the first.)
If we assume option (a) as correct – 70% the following solution follows:
If the second is 70, then first is 100 and the first + second is 170. Then third will be 85 (50% of first + second).
If the second is 70, then first is 100 and the first + second is 170. Then third will be 85 (50% of first + second).
Then the equation:
4 X (100 + 85) should be equal to 12 X 70
But this is not true.
4 X (100 + 85) should be equal to 12 X 70
But this is not true.
Through trial and error, you can see that the third option fits correctly.
4 X (100 + 80) = 12 X 60.
Hence, it is the correct answer.
4 X (100 + 80) = 12 X 60.
Hence, it is the correct answer.
Most Upvoted Answer
There are three galleries in a coal mine. On the first day, two galler...
Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 * (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15
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Community Answer
There are three galleries in a coal mine. On the first day, two galler...
Let's assume the capacity of the first gallery is x units.
Capacity of the second gallery = y units
Capacity of the third gallery = z units
After the third gallery is made operative, the output becomes half as large again. This means the new output is 1.5 times the original output.
So, (2x + y + z) * 1.5 = 2x + 2y + 2z
3x + 1.5y + 1.5z = 2x + 2y + 2z
x = 0.5y + 0.5z
The four-month output of the first and third galleries is the same as the annual output of the second gallery.
So, 8x = 12y or x = 1.5y
Substituting x in terms of y in the first equation:
0.5y + 0.5z = 1.5y
z = y
This means the capacity of the third gallery is the same as the capacity of the second gallery.
Therefore, the capacity of the second gallery is 60% of the first gallery.
Answer: (a) 60%
Capacity of the second gallery = y units
Capacity of the third gallery = z units
After the third gallery is made operative, the output becomes half as large again. This means the new output is 1.5 times the original output.
So, (2x + y + z) * 1.5 = 2x + 2y + 2z
3x + 1.5y + 1.5z = 2x + 2y + 2z
x = 0.5y + 0.5z
The four-month output of the first and third galleries is the same as the annual output of the second gallery.
So, 8x = 12y or x = 1.5y
Substituting x in terms of y in the first equation:
0.5y + 0.5z = 1.5y
z = y
This means the capacity of the third gallery is the same as the capacity of the second gallery.
Therefore, the capacity of the second gallery is 60% of the first gallery.
Answer: (a) 60%
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There are three galleries in a coal mine. On the first day, two galleries are operative and after some time, the third gallery is made operative. With this, the output of the mine became half as large again. What is the capacity of the second gallery as a percentage of the first, if it is given that a four-month output of the first and the third galleries was the same as the annual output of the second gallery?a)60%b)64%c)65%d)70%Correct answer is option 'A'. Can you explain this answer?
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