RRB NTPC Mains or Stage 2 Model Paper 9 with solutions

Concept:Work rate is the fraction of total work completed in one hour.Explanation:Let total work be $1$ unit.P's rate $= \frac{1}{8}$ per hour.Q's rate $= \frac{1}{10}$ per hour.R's rate $= \frac{1}{12}$ per hour.All three machines work from 9 a.m. to 11 a.m., i.e. $2$ hours.Combined rate of P, Q, and R $= \frac{1}{8} + \frac{1}{10} + \frac{1}{12}$.LCM of $8,10,12$ is $120$.So combined rate $= \frac{15}{120} + \frac{12}{120} + \frac{10}{120} = \frac{37}{120}$.Work done in $2$ hours $= \frac{37}{120} \times 2 = \frac{37}{60}$.Remaining work $= 1 - \frac{37}{60} = \frac{23}{60}$.After 11 a.m., only Q and R work.Combined rate of Q and R $= \frac{1}{10} + \frac{1}{12} = \frac{6}{60} + \frac{5}{60} = \frac{11}{60}$.Time taken to finish remaining work $= \frac{23/60}{11/60} = \frac{23}{11}$ hours.$\frac{23}{11} \approx 2.09$ hours $\approx 2$ hours.So the work finishes about 2 hours after 11 a.m., i.e. around 1 p.m.Answer:The work will be finished approximately at 1 p.m.