8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and one boy alone to finish the piece of work.
Answers
ǫᴜᴇsᴛɪᴏɴ :-
8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man alone and one boy alone to finish the piece of work.
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
ᴀɴsᴡᴇʀ :-
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