Question : The daily wages of A and B, respectively, are Rs. 3.50 and Rs. 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 of Rs. 75. If both of them do it together, what is the cost of the work?
Option 1: Rs. 67.50
Option 2: Rs. 27.50
Option 3: Rs. 60.50
Option 4: Rs. 70.50
Correct Answer: Rs. 67.50
Solution :
The daily wages of A and B are Rs. 3.50 and Rs. 2.50, respectively.
A gets a total wage of Rs. 63.
So, time taken by A = $\frac{63}{3.5}$ = 18 days
B gets a total wage of Rs. 75.
So, time taken by B = $\frac{75}{2.5}$ = 30 days
(A + B)’s 1 day’s work = $\frac{1}{18}+\frac{1}{30}=\frac{4}{45}$
⇒ Required time = $\frac{45}{4}$ days
So, the total wages = $\frac{45}{4}×(3.5+2.5)$ = $\frac{45}{4}×6$ = Rs. 67.50
Hence, the correct answer is Rs. 67.50.
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