Question

4 Men and 6 Boys can finish a piece of work in 5 Days , While 3 Men and 4 Boys can Finish it in 7 days . Find the time taken by 1 man alone or that by 1 boy alone ?

Answer 1

Heya !!!


Let 1 man alone can finish the work in X days and 1 boy alone can finish it in Y .



Then,



1 man's 1 days work = 1/X




And,


1 boy's 1 day's work = 1/Y





(4 men's 1 day's work )+(6 boys 1 day's work )= 1/5




=> 4/X + 6/Y = 1/5




=> 4U + 6V = 1/5 [ Where 1/X = U and 1/Y =V]



=> 4U + 6V = 1/5 --------(1)




Again,





( 3 men's 1 day's work ) + ( 4 boys 1 day's work ) = 1/7





=> 3/X + 4/Y = 1/7




=> 3U + 4V = 1/7 -------(2)






On multiplying (1) by 3 and ,(2) by 4 we get,



12U + 18V = 3/5 --------(3)


And,



12U + 16 V = 4/7 --------(4)




Subtracting (3) and (4) we get,




2V = ( 3/5 - 4/7)





2V = 1/35



V = 1/35 ×2



V = 1/70




1/Y = V




1/Y = 1/70



Y = 70 days




Putting V = 1/70 in equation (1) we get,







4U + 6V = 1/5




4U = ( 1/5 - 6V )




4U = ( 1/5 - 6/70 )





4U = ( 14 - 6 /70)




4U = ( 8/70)



U = 8/70 × 1/4



U = 1/35





1/X = U



1/X = 1/35



X = 35 days




Therefore,



One man alone can finish the work in 70 days and One boy alone can finish the work in 35 days.





★ HOPE IT WILL HELP YOU ★

Answer 2

Answer:

1 boy can alone complete the work in 35 days while 1 man do the same work in 70 days.

Explanation:

4 men + 6 boys = 5 days

3 men + 4 boys = 7 days

total work = lcm of 5 and 7 = 35

let the number of men = x

let the number of boys = y

so the equation be like:

4x + 6y = 7

3x + 4y = 5

by using elimination method,

12x + 18y = 21

12x + 16y = 20

from this we get,

2y = 1

y = 1/2 this is the efficiency of y .

putting this value of y in above equation, we get

x = 1 this is the efficiency of x.

this means y do 1 part of work while x can do half of it in the same time.

so total work = 35

x takes 2× 35 = 70 days to complete the work while y takes half of it that is 35 days to complete total work.