Q187
ArithmeticTime & Work, Pipes & Cisterns
Mohan takes 6 hours to do a job. Laltu takes 10 hours to do the same job. How long should it take if Mohan and Laltu work together the same job?
- a.$1\frac{1}{2}$ hrs.
- b.$3\frac{3}{4}$ hrs.
- c.$2\frac{1}{3}$ hrs.
- d.$3\frac{1}{4}$ hrs.
Answer: (B) $3\frac{3}{4}$ hrs.
Mohan does $\frac{1}{6}$ of the job per hour and Laltu $\frac{1}{10}$. Together: $\frac{1}{6}+\frac{1}{10}=\frac{5+3}{30}=\frac{4}{15}$ of the job per hour, so the time taken is $\frac{15}{4}=3\frac{3}{4}$ hours (3 hours 45 minutes). Shortcut for two workers: $\frac{ab}{a+b}=\frac{6\times10}{16}=3.75$. The answer must be less than the faster worker's time (6 h) and more than half of it (3 h), which rules out $1\frac{1}{2}$ and $2\frac{1}{3}$.