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Step-by-step explanation:
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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 = 1/4
∴5x+2y= 1/4⟶eq 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 2
Multiplying by 3 in eq 1, we get
⇒15x+6y= 3/4⟶eq 3
Multiplying by 2 in eq
n
2, we get
⇒12x+6y= 2/3 ⟶eq 4
On subtracting eq 4 from eq 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 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 = 1/36days
∴ 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.
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