MCQ
Numerical: Time & Work MCQ - Practice Questions with Answers
Solve 28 Numerical: Time & Work questions for RAS/RPSC preparation.
Practice questions
Q1A can complete a piece of work in 12 days and B can complete the same work in 18 days. If they work together, in how many days will the work be completed?
Use work rates. A's one-day work is 1/12 and B's one-day work is 1/18. Together, their one-day work is 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the work. Therefore, the time needed for one complete work is the reciprocal of the combined rate: 36/5 days = 7 1/5 days. So the work will be completed in 7 1/5 days.
Q2A can complete a work in 20 days and B can complete it in 30 days. They work together for 6 days, and then A leaves. Assertion (A): The whole work will be completed in 21 days from the start. Reason (R): In 6 days, A and B together complete half of the work, and B alone takes 15 more days for the remaining half.
A's 1-day work = 1/20 and B's 1-day work = 1/30. Together, they do 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 of the work per day. In 6 days, completed work = 6 × 1/12 = 1/2. Remaining work = 1/2. B alone completes 1/30 of the work per day, so time for 1/2 work = (1/2) ÷ (1/30) = 15 days. Total time = 6 + 15 = 21 days. Thus both A and R are true, and R explains A.
Q3Pipe A can fill a tank in 12 hours, pipe B can fill it in 15 hours, and pipe C can empty it in 20 hours. If all three pipes are opened together, which statement is incorrect?
For filling pipes, add rates; for the emptying pipe, subtract its rate. A's rate is 1/12, B's rate is 1/15, and C's emptying rate is 1/20 of the tank per hour. Net rate = 1/12 + 1/15 − 1/20 = 5/60 + 4/60 − 3/60 = 6/60 = 1/10. Therefore, the tank fills in 10 hours. A, B, and C are correct statements, while D says 8 hours, so D is the incorrect statement.
Q4A can complete a piece of work in 12 days, while B can complete the same work in 18 days. If they work together, in how many days will the work be completed?
Use daily work rates. A completes 1/12 of the work in one day and B completes 1/18 of the work in one day. Together, their one-day work is 1/12 + 1/18. Taking LCM 36, this is 3/36 + 2/36 = 5/36 of the work per day. Therefore, the time required for the full work is 1 ÷ (5/36) = 36/5 = 7.2 days. This is the required time.
Q5A and B together can complete a work in 8 days. A alone can complete it in 12 days. In how many days can B alone complete the work?
Together A and B complete 1/8 of the work in one day. A alone completes 1/12 of the work in one day. So B's one-day work is the combined rate minus A's rate: 1/8 − 1/12. Taking LCM 24, we get 3/24 − 2/24 = 1/24. Thus B completes 1/24 of the work per day, so B alone will finish the whole work in 24 days.
You've seen 5 of 28 sample questions
Unlimited practice on Numerical: Time & Work comes with the RAS Test Series + Practice pack or Gate Pass.
More questions
6A tap can fill a tank in 8 hours, while a leak can empty the full tank in 12 hours. If both are open together, how long will it take to fill the empty tank?
7A can do a work in 15 days. B is twice as efficient as A. How many days will B take to complete the same work alone?
8A can complete a work in 8 days and B can complete it in 12 days. Match the work done in 3 days with the correct fraction of the total work.
9P can finish a work in 10 days, Q in 15 days and R in 30 days. Consider the statements: 1. P and Q together can finish it in 6 days. 2. Q and R together can finish it in 10 days. 3. P and R together can finish it in 8 days. Which statements are correct?
10Three machines P, Q and R can finish the same job alone in 6 hours, 8 hours and 12 hours respectively. Match each pair with the time needed when they work together: I. P + Q, II. P + R, III. Q + R. Which matching is correct?
11A is twice as efficient as B. If A and B together can complete a work in 12 days, how many days will B alone take to complete the same work?
12A can finish a piece of work in 12 days and B can finish the same work in 18 days. In how many days will they finish the work together?
13A can complete a piece of work in 12 days and B can complete the same work in 18 days. If both work together, in how many days will the work be completed?
14Mohan can complete a work in 16 days and Sohan can complete the same work in 24 days. They complete the work together and receive ₹5000 as wages. Assertion: Mohan should receive ₹3000 and Sohan should receive ₹2000. Reason: Wages are divided in the inverse ratio of their individual times, that is 24:16 = 3:2. Choose the correct option.
15A fills a tank in 10 hours and B fills the same tank in 15 hours. Which statement is correct?