Let the time taken by one man alone and one women alone to do the work be a and b respectively.
Amount of work done by one man in a day = 1/a
Amount o work done by 5 men in a day = 5/a
Amount of work done by one lady in a day = 1/b
Amount of work done by 2 ladies in a day = 2/b
According to the question
2/b + 5/a = 1/4. -(1)
Simialrily in case 2
3/b + 6/a = 1/3. -(2).
In eq 1 and 2
Let 1/b be x and 1/a be y.
Therefore the new equations are
2x + 5y = 1/4
= 8x + 20y = 1. -(3)
3x + 6y = 1/3
= 9x + 18y = 1. -(4)
On using elimination method for equations 3 and 4
x = 1/18 = 1/b
= b =18
And y = 1/36 = 1/a
= a = 36
Therefore the time taken by one man and one woman alone to do the work is 36 days and 18 days respectively.
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