Question

2 men and 5 boys can do a piece of work in 4 days while 4 men and 4 boys can do it in 3 days. how long would it take 1 man alone to do it and how many days would it take for 1 boy alone to do it it take

Answer 1

Answer:

$\bigstar{\bold{Time\:taken\:by\:1\:boy=36\:days}}$

$\bigstar{\bold{Time\:taken\:by\:1\:man=18\:days}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• 2 men and 5 boys finishes the work in 4 days
• 4 men and 4 boys finishes the work in 3 days

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Days taken by 1 boy to complete the work
• Days taken by  1 man to complete the work

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let days taken by 1 man to do the work be 1/x

→ Let days taken by 1 boy to do the work be 1/y

→ By first condition,

  2x + 5y = 1/4 -------equation 1

→ By the second condition,

   4x + 4y = 1/3---------equation 2

→ Multiplying equation 1 by 2,

   4x + 10y = 1/2--------equation 3

→ Solving equation 2 and 3 by elimination method,

   4x + 10y = 1/2

   4x + 4y = 1/3

           6y = 1/2 - 1/3

→ 6y = 3/6 - 2/6

   6y = 1/6

     y = 1/36

→ Time taken by one boy to complete the work = 1/y days = 1/1/36 = 36 days

$\boxed{\bold{Time\:taken\:by\:1\:boy=36\:days}}$

→ Substitute value of y in equation 2

   4x + 4 × 1/36 = 1/3

   4x + 1/9 = 1/3

   4x = 1/3 - 1/9

   4x = 3/9 - 1/9

   4x = 2/9

     x = 1/18

→ Time taken by one man to complete the work = 1/x days = 1/1/18 = 18 days.

$\boxed{\bold{Time\:taken\:by\:1\:man=18\:days}}$

Answer 2

Step-by-step explanation:

Answer:

$\bigstar{\bold{Time\:taken\:by\:1\:boy=36\:days}}$

★Timetakenby1boy=36days

$\bigstar{\bold{Time\:taken\:by\:1\:man=18\:days}}$★Timetakenby1man=18days

Step-by-step explanation:

Given:

2 men and 5 boys finishes the work in 4 days

4 men and 4 boys finishes the work in 3 days

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

Days taken by 1 boy to complete the work

Days taken by 1 man to complete the work

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Let days taken by 1 man to do the work be 1/x

→ Let days taken by 1 boy to do the work be 1/y

→ By first condition,

2x + 5y = 1/4 -------equation 1

→ By the second condition,

4x + 4y = 1/3---------equation 2

→ Multiplying equation 1 by 2,

4x + 10y = 1/2--------equation 3

→ Solving equation 2 and 3 by elimination method,

4x + 10y = 1/2

4x + 4y = 1/3

6y = 1/2 - 1/3

→ 6y = 3/6 - 2/6

6y = 1/6

y = 1/36

→ Time taken by one boy to complete the work = 1/y days = 1/1/36 = 36 days

$\boxed{\bold{Time\:taken\:by\:1\:boy=36\:days}}$

Timetakenby1boy=36days

→ Substitute value of y in equation 2

4x + 4 × 1/36 = 1/3

4x + 1/9 = 1/3

4x = 1/3 - 1/9

4x = 3/9 - 1/9

4x = 2/9

x = 1/18

→ Time taken by one man to complete the work = 1/x days = 1/1/18 = 18 days.

$\boxed{\bold{Time\:taken\:by\:1\:man=18\:days}}$

Timetakenby1man=18days