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22 Jan 2021, 03:30
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Difficulty:
55%
(hard)
Question Stats:
72% (02:47) correct
28%
(02:46)
wrong
based on 311
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If 3 men or 6 boys can do a piece of work in 10 days, working 7 hours a day; how many days will it take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day?
(A) 6
(B) 7.5
(C) 8.5
(D) 9
(E) 9.5
(A) 6
(B) 7.5
(C) 8.5
(D) 9
(E) 9.5
22 Jan 2021, 18:49
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3 Men working 7 hours a day take 10 days
Therefore work done by 1 man working 1 hour a day in 1 day = \(\frac{1}{3 * 7 * 10}\)
Work done by 6 men working 8 hours a day in 1 day = \(\frac{6 * 8}{3 * 7 * 10} = \frac{8}{35}\)
Similarly, 6 Boys working 7 hours a day take 10 days
Therefore work done by 1 Boy working 1 hour a day in 1 day = \(\frac{1}{6 * 7 * 10}\)
Work done by 2 Boys working 8 hours a day in 1 day = \(\frac{2 * 8}{6 * 7 * 10} = \frac{8}{210}\)
Work done in 1 day when 6 Men and 2 boys work together = \(\frac{8}{35} + \frac{8}{210} = \frac{56}{210} = \frac{4}{15}\)
Time taken to do 1 work = \(\frac{15}{4}\) days
Time taken to do double the work = \(2 * \frac{15}{4} = \frac{15}{2} = 7.5\) days
Option B
Arun Kumar
Therefore work done by 1 man working 1 hour a day in 1 day = \(\frac{1}{3 * 7 * 10}\)
Work done by 6 men working 8 hours a day in 1 day = \(\frac{6 * 8}{3 * 7 * 10} = \frac{8}{35}\)
Similarly, 6 Boys working 7 hours a day take 10 days
Therefore work done by 1 Boy working 1 hour a day in 1 day = \(\frac{1}{6 * 7 * 10}\)
Work done by 2 Boys working 8 hours a day in 1 day = \(\frac{2 * 8}{6 * 7 * 10} = \frac{8}{210}\)
Work done in 1 day when 6 Men and 2 boys work together = \(\frac{8}{35} + \frac{8}{210} = \frac{56}{210} = \frac{4}{15}\)
Time taken to do 1 work = \(\frac{15}{4}\) days
Time taken to do double the work = \(2 * \frac{15}{4} = \frac{15}{2} = 7.5\) days
Option B
Arun Kumar
General Discussion
07 Feb 2022, 13:37
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Relation given:
3men = 6boys (M = 2B)
3 men or 6 boys can do a piece of work in 10 days, working 7 hours a day;
Total Work = 3M*10*7
Work with 6 men and 2 boys working together for 8 hours a day;
Total Work = (6M+2B)*8*days
**
Assume that the work done by both groups to be equal:
3M*10*7 = (6M+2B)*8*days
3M*10*7 = 7M*8*days
days = 3.75
Given that the work is twice as large: Days*2 = 3.75*2 = 7.5days
3men = 6boys (M = 2B)
3 men or 6 boys can do a piece of work in 10 days, working 7 hours a day;
Total Work = 3M*10*7
Work with 6 men and 2 boys working together for 8 hours a day;
Total Work = (6M+2B)*8*days
**
Assume that the work done by both groups to be equal:
3M*10*7 = (6M+2B)*8*days
3M*10*7 = 7M*8*days
days = 3.75
Given that the work is twice as large: Days*2 = 3.75*2 = 7.5days
