2 women and 5men can together finish an embroidery work in 4 days while 3 women and 6men can finish it 8n 3days .find the time taken by 1 women alone to finish the work and also that taken by 1 man alone
Answers
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 explaination:
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 = 1/4
∴5x+2y= 1/4
⟶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 = 1/3
∴6x+3y= 1/3
⟶eq ^n 2
Multiplying by 3 in eq ^n 1we get
⇒15x+6y= 3/4
⟶eq ^n 3
Multiplying by 2 in eq ^n 2 ,we get
⇒12x+6y= 2/3
⟶eq ^n4
On subtracting eq ^n 4 from eq ^n 3 , we get
⇒15x+6y−12x−6y= 3/4 - 2/3
⇒3x= 1/12
⇒x= 1/36
On substituting the value of x in eq ^n 2 , we get
⇒6× 1/36 +3y= 1/3
⇒3y= 1/3 - 1/6
⇒y= 1/18
Thus,
work done by 1 man in 1 day = 1/36 days
∴ Time taken by 1 man alone to finish the work =36 days
work done by 1 woman in 1 day = 1/18 days
∴ Time taken by 1 woman alone to finish the work =18 days