Question

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 1 Man alone and that by one boy alone to finish the work.​

Answer 1

1. Question⇒  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 1 Man alone and that by one boy alone to finish the work.​

Step-by-step explanation:

• 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