Question

8 men and 12 boys can finish a work in 10 days while 6men and8 boys can finish it in 14 days find the time taken by 1 man and1 boy alone to finish work

Answer 1

(8 men + 12 boys ) complete a work in 10 days . again, ( 6men + 8boys ) can finish same work in 14days .

we know,
N1 × D1 = N2 × D2
where N1 and N2 are no of people In first and 2nd cases respectively . and D1 and D2 is no of days respectively.

(8 men + 12 boys ) × 10 = (6 men + 8 boys) × 14
80men + 120boys = 84men + 112 boys
8 boys = 4 men
2 boys = 1 men

hence capacity of 1 men = capacity of 2 boys for doing work .
hence, (8men + 12boys ) = 28 boys.
28 boys doing work in 10 days
so, 1 boy doing same work in 28× 10 days

A/C to question,
1 man + 1 boy = 2boys + 1 boy = 3boys

hence, (1 man + 1 boys ) doing work = 28×10/3 days = 280/3 days

Answer 2

Let the time taken by man be x days

time taken by boys be y days

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

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

8/x+12/y = 1/10............eq 1

6/x+ 8/y = 1/14..........eq2

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

8u+ 12y=1/10.........eq3

6u+8v= 1/14...........eq4

Multiplying eq3 by 2 & eq4 by 3

16u+ 24y=2/10.........eq5
18u+24v= 3/14.........eq6

subtract eq 5 & 6
-2u= -3/14+2/10
-2u = (-3×10 +2×14)/140

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

-2u=-2/140

u=1/140

put this value in eq 5

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 can complete the work in 280 days