Question

8 men 12 boys can finish a piece of work in 10 days and while 6 men and 8 boys can finish it in 14 days find the value check and buy one man alone and that by one man alone to finish the work​

Answer 1

Answer:

Let

the time taken by man be= x days

time taken by boys be= y days

work done by one man in one day=1/x

work done by one boy in one day=1/y

8/x+12/y = 1/10............ (1)

6/x+ 8/y = 1/14..........(2)

Let u=1/x & v=1/y

8u+ 12y=1/10.........(3)

6u+8v= 1/14...........(4)

Multiplying eq3 by a pair of & eq4 by three  

16u+ 24y=2/10.........(5)

18u+24v= 3/14.........(6)

subtract combining weight five -2u= -3/14+2/10

-2u = (-3×10 +2×14)/140

-2u=( -30+28)/140

-2u=-2/140

u=1/140

put this price in combining weight five

16u+ 24y=2/10

16×1/140 +24y =1/5

4/35+24y= 1/5

24y= 1/5-4/35

24y= (1×7 -4)/35

24y = (7-4)/35

24y= 3/35

y= 3/35×24

y= 1/280

u=1/x

1/140 = 1/x

x=140

v=1/y

1/280 = 1/y

y=280

A man complete the work in 140 days

A boy will complete the add 280 days

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@GauravSaxena01