Question

Choose the correct answer from the alternatives given :
Working together A and B can finish a piece of work in 5 days. If working speed of A was doubled and working speed of B reduced to half the same work was done in 4 days. In how many days can A finish the work alone.

• A. $10$ days
• B. $12$ days
• C. $15$ days
• D. $8$ days

Answer 1

Answer: (A)

$10$ days

Let the efficiency of A and B be a and b respectively.
According to the question, 5(a + b) = 4 $(2a+\frac{2b}{2})$
5a + 3b = 8a + 2b $\Rightarrow$ 3a = 3b $\Rightarrow$ a = b
Total work = 5 (a + a) = 10a units
Required time for A = $\frac{10a}{1a}$ = 10 days