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16 Dec 2015, 12:31
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Five men can move a weight of 125 kg through a distance of 5 meters in 10 minutes. how much time will be taken by 10 men to move a weight of 250 kg through a distance of 15 meters?
(A) 10 minutes
(B) 20 minutes
(C) 30 minutes
(D) 40 minutes
(A) 10 minutes
(B) 20 minutes
(C) 30 minutes
(D) 40 minutes
well, my answer came out to be 3.33 minutes.
my way of doing was:
(125)/(5*10*5) = (250)/(10*x*15)
so, x=3.33 minutes
I suppose it is wrong.
so, please help me quickly as my exam date is fast approaching.
my way of doing was:
(125)/(5*10*5) = (250)/(10*x*15)
so, x=3.33 minutes
I suppose it is wrong.
so, please help me quickly as my exam date is fast approaching.
Sujan Sareen
Using the multiple variables work-rate method discussed here ( https://anaprep.com/arithmetic-work-rat ... variation/ ), you get
5 men...........125 kg..............5 m...............10 min
10 men..........250 kg.............15 m...............??
Time taken = 10 * (5/10) * (250/125) * (15/5) = 30 mins
18 Dec 2015, 15:03
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If we look at one variable at a time we can break the question down in to simpler parts.
Five men can move a weight of 125 kg through a distance of 5 meters in 10 minutes.
3 factors are affecting the time: number of men, weight, distance.
How much time will be taken by 10 men to move a weight of 250 kg through a distance of 15 meters?
(1) An increase in number of men will decrease the time taken
- The number of men is doubled from 5 to 10. If that was the only change, then the time taken would be cut in half. 10/2 = 5 minutes.
(2) An increase in weight will increase the time taken
- The weight is doubled from 125 kg to 250 kg. This will cause the time to double as well. Working from the result of (1), the new time would now be 5*2 = 10 minutes
(3) An increase in distance will increase the time taken
- The distance is tripled from 5 m to 15 m. This will cause the time taken to triple as well. Working from our result in (2), the new time would be 10*3 = 30 minutes.
Answer C
Or if you prefer formulas:
Time is proportional to (weight*distance)/(# of men)
\(t=\frac{k(w*d)}{m}\), where k is a positive constant
So with the two scenarios:
\(t_1=\frac{k(w_1d_1)}{m_1}\) --> \(k=\frac{t_1m_1}{w_1d_1}\)
\(t_2=\frac{k(w_2d_2)}{m_2}\) --> \(k=\frac{t_2m_2}{w_2d_2}\)
\(\frac{t_1m_1}{w_1d_1}\) = \(\frac{t_2m_2}{w_2d_2}\)
\(t_2=t_1*\frac{m_1}{m_2}*\frac{w_2}{w_1}*\frac{d_2}{d_1}\) Notice that the factors for scenario 2 that decrease the time taken are in the denominator (\(m_2\)), and the factors for scenario 2 that increase the time are in the numerator (\(w_2\), \(d_2\))
\(t_2=10*\frac{5}{10}*\frac{250}{125}*\frac{15}{5}=10*\frac{1}{2}*2*3=30\)
Answer C
Five men can move a weight of 125 kg through a distance of 5 meters in 10 minutes.
3 factors are affecting the time: number of men, weight, distance.
How much time will be taken by 10 men to move a weight of 250 kg through a distance of 15 meters?
(1) An increase in number of men will decrease the time taken
- The number of men is doubled from 5 to 10. If that was the only change, then the time taken would be cut in half. 10/2 = 5 minutes.
(2) An increase in weight will increase the time taken
- The weight is doubled from 125 kg to 250 kg. This will cause the time to double as well. Working from the result of (1), the new time would now be 5*2 = 10 minutes
(3) An increase in distance will increase the time taken
- The distance is tripled from 5 m to 15 m. This will cause the time taken to triple as well. Working from our result in (2), the new time would be 10*3 = 30 minutes.
Answer C
Or if you prefer formulas:
Time is proportional to (weight*distance)/(# of men)
\(t=\frac{k(w*d)}{m}\), where k is a positive constant
So with the two scenarios:
\(t_1=\frac{k(w_1d_1)}{m_1}\) --> \(k=\frac{t_1m_1}{w_1d_1}\)
\(t_2=\frac{k(w_2d_2)}{m_2}\) --> \(k=\frac{t_2m_2}{w_2d_2}\)
\(\frac{t_1m_1}{w_1d_1}\) = \(\frac{t_2m_2}{w_2d_2}\)
\(t_2=t_1*\frac{m_1}{m_2}*\frac{w_2}{w_1}*\frac{d_2}{d_1}\) Notice that the factors for scenario 2 that decrease the time taken are in the denominator (\(m_2\)), and the factors for scenario 2 that increase the time are in the numerator (\(w_2\), \(d_2\))
\(t_2=10*\frac{5}{10}*\frac{250}{125}*\frac{15}{5}=10*\frac{1}{2}*2*3=30\)
Answer C
