8 people and 10 boys can do any work in 36 days. With the help of how many boys 4 people can do the job in 51 days while 2 people can do the work with 6 boys?
Answers
Answer:
12 boys be required
Step-by-step explanation:
2 people can do the work of 6 people I e
2 P = 6 B
I .e 1 P = 3B
According to condition (1) ,
8 people and 10 boys do a work in 36 days.
8 P + 10 B = 36 days
24 B + 10 B = 36 days [ 1 P = 3B ]
34 B = 36 days
This means 34 boys complete the work in 36 days.
In condition (2),
Let the no. of boys required = x
4 P + x B = 51 days
12 B + x B = 51 days
B ( 12 + x ) = 51 days
This means 12 + x boys will complete the work in 51 days.
In first condition 36 days were required and in second condition 51 days are required. As the no of days required have gone up, it means no of people have been reduced. So., this is a case of inverse variation.
34 / 36 = ( 12 + x ) / 51
51 ( 12 + x ) = 34 × 36
51 ( 12 + x ) = 1224
12 + x = 1224 ÷ 51
12 + x = 24
x = 24 - 12
x = 12
So , 12 boys will require with 4 people to finish the work in 51 days.