akurathi12 wrote:
5 boys and 4 girls together can complete a job in 6 hours. If these 5 boys were to complete the work alone taking the same time, they would need to involve 3 men whereas 4 girls with the help of same number of men can complete the work taking just 4 hours. If 4 boys, 4 girls and 1 man together complete the work, how much time will it take?
A. 3 hours
B. 4 hours
C. 5 hours
D. 6 hours
E. 8 hours
Let b, g, and m be the respective rates of each boy girl and man
5b + 4g = (1/6) ..... Eqn 1 ( Since time = 6 hours)
5b + 3m = (1/6) ......Eqn 2 ( Since time = 6 hours)
4g + 3m = (1/4) ......Eqn 3 ( Since time = 4 hours )
4b + 4g + 1m = ? ... Reqd Case
5b + 4g = 5b + 3m From Eqn 1 and Eqn 2
4g = 3m
1.5 (5b + 4g )= 4g + 3m From Eqn 1 and Eqn 3
7.5b = 1.5m or 5b = m
In The required case compared to the case in equation 1, 1 boy has been replaced by 1 man ( who is faster than the boy)
So time ( t ) will be less than 6 hrs
Similarly comparing The required case with the case in Eqn 3
In Eqn 3 , 4 girls and 3 men take 4 hours
While in the required Case , there are 4 boys, 4 girls and 1 man
i.e 2 men have been replaced by 4 boys
Since 5b = m, Time ( t ) will be more than 4 hours ( Time taken in Eqn 3 )
So, 4 < t < 6
Only t = 5 satisfies
Choice C
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