X, Y and Z complete a work in 6 days. X for Y alone can do the same work in 16 days. In how many days Z alone can finish the same work?
X, Y and Z complete a work in 6 days. X for Y alone can do the same work in 16 days. In how many days Z alone can finish the same work?
Aa) 12
Bb) 24
Cc) 16
Dd) 36
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Answer is 24
X and Y and Z complete a work in = 6 days;
One day's work of (X+Y+Z) = \(\frac{1}{6}\);
X complete the work in = 16 days;
One day's work of X = \(\frac{1}{16}\);
Y complete the work in = 16 days;
One day's work of Y = \(\frac{1}{16}\);
Then, Z's one day's work = TotalWork - X's Work -Y's Work
\(=>\frac{1}{6}-\frac{1}{16}-\frac{1}{16} \)\(=> \frac{1}{6}-\frac{2}{16} \)
\(=> \frac{(16-12)}{96} \)
\(=>\frac{4}{96}\)
\( =>\frac{1}{24}\)
Thus, Z can complete the work in = 24 days.
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