8 men and 12 boys can finish a work in 5 days while 6 men and 8 boys can finish it in 7 days . find the time taken by 1 man alone and that by 1 boy alone to finish the work.
Answers
Answer:
1 man = 140 days
1 boy = 280 days
Step-by-step explanation:
Let the time taken by man be 'm' days.
And, the time taken by boys be 'b' days
Therefore, we get,
=> Work done by 1 man in one day = 1/m
And
=> Work done by 1 boy in one day = 1/b
Therefore, we will get,
=> 8/m+12/b = 1/10 ........(1)
And
=> 6/m+ 8/b = 1/14 ........(2)
Now, let u = 1/m and v =1/b
Therefore, we will get,
=> 8u+ 12y=1/10 .......(3)
And
=> 6u+8v= 1/14 ........(4)
Now, Multiplying eq (3) by 2 & eqn (4) by 3,
=> 16u+ 24y=2/10 .......(5)
And
=> 18u+24v= 3/14 ....... (6)
Now, subtract eqn (6) from eqn (5)
=> -2u = -3/14+2/10
=> -2u = (-3×10 +2×14)/140
=> -2u = ( -30+28)/140
=> -2u = -2/140
=> u = 1/140
Now, put this value in eqn (5),
=> 16u+ 24y = 2/10
=> 16×1/140 +24y =1/5
=> 4/35+24y= 1/5
=> 24b = 1/5-4/35
=> 24b = (1×7 -4)/35
=> 24b = (7-4)/35
=> 24b = 3/35
=> b = 3/35×24
=> b = 1/280
Now, we have,
=> u =1/x
=> 1/140 = 1/m
=> m = 140
And, also, we have,
=> v=1/b
=> 1/280 = 1/b
=> b = 280
Hence, a man can completes the work in 140 days and a boy can completes the work in 280 days.