Numerical: Time & Work MCQ — 15 Practice Questions with Answers

Explanation

Wages are shared according to work done, so they are proportional to daily work rates. Mohan's rate is 1/16 and Sohan's rate is 1/24. Their rate ratio is 1/16 : 1/24 = 24:16 = 3:2. Total wages are ₹5000, and the total ratio parts are 3 + 2 = 5. Mohan's share = 3/5 × 5000 = ₹3000. Sohan's share = 2/5 × 5000 = ₹2000. Thus, the assertion is true, and the reason correctly explains it.

Explanation

Check each statement by adding daily work rates. P + Q = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6, so they finish in 6 days; statement 1 is correct. Q + R = 1/15 + 1/30 = 2/30 + 1/30 = 3/30 = 1/10, so statement 2 is correct. P + R = 1/10 + 1/30 = 4/30 = 2/15, so time = 15/2 = 7.5 days, not 8 days. Thus only 1 and 2 are correct.

Explanation

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.

Explanation

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.

Explanation

For time and work, add daily 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 together is the reciprocal of the combined rate: 36/5 = 7.2 days. Hence, both will complete the work in 7.2 days.