Question

2 men and 5 boys can finish a piece of work in 4days . find the time taken by one man alone to finish the work and that taken by one boy alone to finish the work​

Answer 1

Answer:

let the time taken by 1 men alone to finish the work be x days

let the time taken by 1 men alone to finish the work be x daysand the time taken by 1 boy alone to finish the work be y days then

let the time taken by 1 men alone to finish the work be x daysand the time taken by 1 boy alone to finish the work be y days then1 men's 1 day's work= 1/x

let the time taken by 1 men alone to finish the work be x daysand the time taken by 1 boy alone to finish the work be y days then1 men's 1 day's work= 1/x1 boy's 1 day's work=1/y

let the time taken by 1 men alone to finish the work be x daysand the time taken by 1 boy alone to finish the work be y days then1 men's 1 day's work= 1/x1 boy's 1 day's work=1/ytherefore 2men's 1 days work=2/x

let the time taken by 1 men alone to finish the work be x daysand the time taken by 1 boy alone to finish the work be y days then1 men's 1 day's work= 1/x1 boy's 1 day's work=1/ytherefore 2men's 1 days work=2/xand 5 boys 1 days work= 5/y

let the time taken by 1 men alone to finish the work be x daysand the time taken by 1 boy alone to finish the work be y days then1 men's 1 day's work= 1/x1 boy's 1 day's work=1/ytherefore 2men's 1 days work=2/xand 5 boys 1 days work= 5/ysince 2 men and 5 boys can together finish one work in 4 days

therefore

4(2/x+5/y)=1

2/x+5/y=1/4

again,3 men's 1 days work=3/x

and

6 boys's 1 day's work=6/y

since

3 men's and 6 boys can together finish one work in 3 days

therefore

3(3/x+6/y)=1

3/x+6/y=1/3....(1)

put 1/x=u.....(2)

and 1/y=v....(3)

then equation (1) and (2) can be rewritten as

2u+5v=1/4...(5)

3u+6v=1/3...(6)

multiplying equation (5) by 3 and equation (6) by 2 we get

6u+15v=3/4...(7)

6u+12v=2/3...(8)

subtracting, equation (8) from equation (7) we get

3v=1/12

v=1/36...(9)

substituting this value of v in equation (5) we get

u=1/18

from equation (3) and equation (10) we get

x=18

and y=36

hence the time taken by 1 men alone to finish the work is 18days and the time taken by 1 boy alone to finish the work is 36 days