2 women and 5 men can together finish an embroidery work in 4days,while 3women and 6men can finish it in 3days. Find the time taken by 1 women alone to finish the work,and also that taken by 1 man alone.
Answers
Answer:
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 = 41
∴5x+2y= 41
⟶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 = 31
∴6x+3y= 31
⟶eq n 2
Multiplying by 3 in eq n 1, we get
⇒15x+6y= 43
⟶eq n 3
Multiplying by 2 in eq n2, we get
⇒12x+6y= 32
⟶eq n 4
On subtracting eq n 4 from eq n 3, we get
⇒15x+6y−12x−6y= 43 − 32
⇒3x= 121⇒x= 361
On substituting the value of x in eq
n 2, we get
⇒6× 361 +3y= 31
⇒3y= 31 − 61⇒y= 181
Thus,
work done by 1 man in 1 day = 361 days
∴ Time taken by 1 man alone to finish the work =36 days
work done by 1 woman in 1 day = 181
days
∴ Time taken by 1 woman alone to finish the work =18 days
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