A Constructor wants some men and boys to build the temple as it has to be completed in one month. 2 men and 7 boys can do a peice of work in 4 days.It ia done by 4 men and 4 boys in 3 days.How long would it take for one man or one boy to do it?
Answers
One man and one boy can complete the work in 12 days
Step-by-step explanation:
The time taken by 1 man to do the work is x days, while the no. of days taken by a boy to do the work is y days.
Thus, amount of work done by the main in 1 day = 1/x, while the amount of work done by the boy in 1 day is 1/y
Similarly, 2 men complete 2/x amount of work in a day, while 7 boys complete 7/x work in one day
Based on the first condition;
2/x + 7/y = ¼ ………………. (1)
Based on condition 2;
4/x + 4/y = 1/3 ……………….(2)
Multiply Eq 2 by 2, i.e.,
4/x + 14/y = ½ ………………(3)
Subtracting Eq. 2 from Eq. 3
4/x + 14/x = ½
_
4/x + 4/y = 1/3
10/ y = 1/6
Y = 60
Thus, a boy completes the job in 60 days.
Substituting the value of y in Eq. 1
2/x + 7/60 = ¼
2/x = 8/60
X = 120/8 = 15
The man completes the work in 15 days.
However, one man and one boy will complete the job in 1/15 + 1/60 days
= 5/60 = 1/12 days
Thus, one man and one boy complete the job in 12 days.
Answer:
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