Step 1: Analyse Question StemLet time taken by Yves to paint the fence = Y and time taken by Marcel to paint the same fence = M.
Then, as per the question data, Y = ½ M.
Let,
Rate at which Yves paints the fence = p
Rate at which Marcel paints the fence = q
Since time taken by Yves is half the time taken by Marcel, Rate of Yves = 2 * Rate of Marcel
Therefore, p = 2q
When both of them work together, their combined rate = p + q = 2q + q = 3q.
Time taken by them to paint the fence, working together = \(\frac{Total work }{ 3q}\).
Step 2: Analyse Statements Independently (And eliminate options) – AD / BCEStatement 1: Yves can paint the fence by himself in 3 hours.
Therefore, Y = 3.
Let total work done = 1 unit; then, rate at which Yves works = p = \(\frac{1}{3}\) units per hour.
We know that p = 2q; therefore, 2q = \(\frac{1 }{ 3}\) or q = \(\frac{1}{6}\) units per hour.
Since we know the value of q and the total work, the time taken can be calculated.
The data in statement 1 is sufficient to find out a unique value for the time taken.
Statement 1 alone is sufficient. Answer options B, C and E can be eliminated.
Statement 2: Working together, each at his own constant rate, they can paint the fence in \(\frac{1}{3}\) the time it would take Marcel, working alone, to paint the fence.
Working together, combined rate of Yves and Marcel = 3q.
Time taken by them, working together = \(\frac{1 }{ 3q}\) (assuming total work = 1 unit)
Rate of Marcel = q and hence, time taken by Marcel, working alone = \(\frac{1 }{ q}\).
The information given in statement 2 says that,
\(\frac{1 }{ 3q}\) = \(\frac{1 }{ 3}\) * \(\frac{1}{q}\)
Clearly, that is not sufficient to find out the value of q. If we cannot find the value of q, the question cannot be answered.
The data in statement 2 is insufficient to find out a unique value for the time taken.
Statement 2 alone is insufficient. Answer option D can be eliminated.
The correct answer option is A. _________________