The daily wagesof A and B respectively are Rs.3.50 and 2.50 . When A finishes a certain work, he gets a total wage of Rs. 63. When B does the same work, he gets a total wage Rs.75. If both of them do it together what is the cost of the work ?

daily wage of A = rs 3.50

total wage earned by A = rs 63

no of days A worked =  $$\frac{total wage earned}{daily wage}$$ =$$\frac{63}{3.50}$$ = 18 days

daily wage of B = rs 2.50

total wage earned by B = rs 75

no of days B worked =  $$\frac{total wage earned}{daily wage}$$ =$$\frac{75}{2.50}$$ = 30 days

no of days taken to complete the work when A and B do together = $$\frac{xy}{x+y}$$ { when A takes x days and b takes y days}

= $$\frac{18 \times 30}{18+30}$$ = $$\frac{90}{8}$$ days

Total amount paid to A and B per day = 3.50 + 2.50 = rs 6

Total amount to be paid = $$\frac{90}{8} \times$$6 = $$\frac{135}{2}$$ = Rs 67.50