Question

3 men and 4 boys can do a piece of work in 14 days while 4 men and 6 boys can do the same work in 10 days how long will it take one man to finish the same work

Answer 1

Answer:

20 days

Step-by-step explanation: I hope you understood please mark me brainliest

Answer 2

Let the man finishes the work alone in x hours.

and boy finishes the work alone in y hours.

Case I :-

3/x +4/y=1/14 --(1)

Case II:-

4/x +6/y =1/10--(2)

Let 1/x =m and 1/y =n

(1)=>3m+4n=1/14--(3)

(2)=>4m+6n=1/10--(4)

eqn 3 divide by 2 and eqn 4 divide by 3.

(3)=>3/2m+2n=1/28-(5)

(4)=>4/3m+2n=1/30-(6)

Now subracting eqn 5 from 6.

=>m(4/3-3/2)+2n-2n=1/30 -1/28

-m/6= -3/840

m= 3x6/840

m=3/140

Putting value of m in eqn 6

=>1/35+2n=1/30

2n=1/30-1/35

2n=5/1050

2n=1/210

=>n=1/420

Therefore 1/x=m=3/140

=> x=140/3=46.67hrs

and 1/y=n=1/420

=>y=420

Therefore the man finishes the work separtely in 46.67 hours and boy finish work separately in 420 hours.

Hope it is helpful