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03 Feb 2021, 03:00
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A
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Difficulty:
65%
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Question Stats:
68% (03:04) correct
32%
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wrong
based on 179
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The time taken by 4 women to complete a job is double the time taken by 6 men to complete the same job. Each woman is twice as fast as a Child. How long will 12 women, 12 men and 8 children take to complete a job, given that a man would finish the job in 24days?
(A) 1 days
(B) 1.5 days
(C) 2 days
(D) 2.125 days
(E) 4 days
(A) 1 days
(B) 1.5 days
(C) 2 days
(D) 2.125 days
(E) 4 days
03 Feb 2021, 12:23
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The time taken by 4 women to complete a job is double the time taken by 6 men to complete the same job
Let rate of 1 man is m and 1 women is w
=> Rate of 4 women = 4w and rate of 6 men is 6m.
Let work done is 1
Time taken by 4 women to finish a job = \(\frac{Work}{Rate}\) = \(\frac{1}{4w}\)
Time taken by 6 men to finish a job = \(\frac{Work}{Rate}\) = \(\frac{1}{6m}\)
Given that, Time taken by 4 women to finish a job = 2* Time taken by 6 men to finish a job
=> \(\frac{1}{4w}\) = 2 * \(\frac{1}{6m}\)
=> 6m = 8w => m = \(\frac{4}{3}\) * w = \(\frac{4w}{3}\) =\(\frac{1}{24}\) (men taken 24 days to finish the work)
=> w = \(\frac{3}{(24*4)}\) = \(\frac{1}{32}\)
Each woman is twice as fast as a Child
=> Rate of Child (c) = \(\frac{1}{2}\) * Rate of woman = \(\frac{1}{2}\) * w = \(\frac{w}{2}\)
12 women, 12 men and 8 children work together
=> Total rate = 12w + 12m + 8c = 12w + 12* \(\frac{4w}{3}\) + 8* \(\frac{w}{2}\)
= 12w + 16w + 4w = 32w = 32* \(\frac{1}{32}\) = 1
Work done is 1
=> Rate * Time = 1
=> 1 * Time = 1 => Time = 1
So, answer will be A
Hope it helps!
Let rate of 1 man is m and 1 women is w
=> Rate of 4 women = 4w and rate of 6 men is 6m.
Let work done is 1
Time taken by 4 women to finish a job = \(\frac{Work}{Rate}\) = \(\frac{1}{4w}\)
Time taken by 6 men to finish a job = \(\frac{Work}{Rate}\) = \(\frac{1}{6m}\)
Given that, Time taken by 4 women to finish a job = 2* Time taken by 6 men to finish a job
=> \(\frac{1}{4w}\) = 2 * \(\frac{1}{6m}\)
=> 6m = 8w => m = \(\frac{4}{3}\) * w = \(\frac{4w}{3}\) =\(\frac{1}{24}\) (men taken 24 days to finish the work)
=> w = \(\frac{3}{(24*4)}\) = \(\frac{1}{32}\)
Each woman is twice as fast as a Child
=> Rate of Child (c) = \(\frac{1}{2}\) * Rate of woman = \(\frac{1}{2}\) * w = \(\frac{w}{2}\)
12 women, 12 men and 8 children work together
=> Total rate = 12w + 12m + 8c = 12w + 12* \(\frac{4w}{3}\) + 8* \(\frac{w}{2}\)
= 12w + 16w + 4w = 32w = 32* \(\frac{1}{32}\) = 1
Work done is 1
=> Rate * Time = 1
=> 1 * Time = 1 => Time = 1
So, answer will be A
Hope it helps!
