Question

3 men and 6 women together can finish a piece of work in 3 days while 2 men and 5 women can

finish it in 4 days. Find the time taken by one man alone to finish the work and also that taken

by one woman alone to finish the work.​

Answer 1

Answer:

Time taken by 1 woman alone to finish the work: 18 days, and also that taken by 1 man alone: 36 days

Step-by-step explanation:

Let the work done by man and woman per day be x and y respectively.

When the work is completed in 4 days

Since 5 men and 2 women complete the work in 4 days

therefore work done by 5 men and 2 women in 1 day =

4

1

∴5x+2y=

4

1

⟶eq

n

1

When the work is completed in 3 days

Since 6 men and 3 women complete the work in 3 days

therefore work done by 6 men and 3 women in 1 day =

3

1

∴6x+3y=

3

1

⟶eq

n

2

Multiplying by 3 in eq

n

1, we get

⇒15x+6y=

4

3

⟶eq

n

3

Multiplying by 2 in eq

n

2, we get

⇒12x+6y=

3

2

⟶eq

n

4

On subtracting eq

n

4 from eq

n

3, we get

⇒15x+6y−12x−6y=

4

3

−

3

2

⇒3x=

12

1

⇒x=

36

1

On substituting the value of x in eq

n

2, we get

⇒6×

36

1

+3y=

3

1

⇒3y=

3

1

−

6

1

⇒y=

18

1

Thus,

work done by 1 man in 1 day =

36

1

days

∴ Time taken by 1 man alone to finish the work =36 days

work done by 1 woman in 1 day =

18

1

days

∴ Time taken by 1 woman alone to finish the work =18 days