MCQ
Time and Work MCQ - Practice Questions with Answers
Solve 12 Time and Work questions for RAS/RPSC preparation.
Practice questions
Q1Forty-five carpenters can assemble a batch of desks in 28 days. They work for 8 days, after which nine carpenters leave. How many days will the remaining carpenters need to finish the batch?
Total work is 45 × 28 = 1260 carpenter-days. In 8 days they complete 360, leaving 900. After nine leave, 36 carpenters remain, so they need 900/36 = 25 days.
Q2Printing presses X and Y have efficiencies in the ratio 5 : 3. Working together they can complete a catalogue order in 15 days. They work together for 6 days, after which X is taken offline. How many days will Y need to finish the remaining order alone?
Take efficiencies of X and Y as 5 and 3 units per day, so their combined rate is 8 units per day. The full order is 8 × 15 = 120 units. In 6 days they finish 8 × 6 = 48 units, leaving 72 units. Y alone works at 3 units per day, so the remaining order takes 72 ÷ 3 = 24 days.
Q3The efficiencies of two excavators are in the ratio 4 : 7. The slower excavator alone clears a spoil heap in 35 days. After it has worked alone for 14 days, the faster one joins. What is the ratio of work done by the faster excavator to that done by the slower over the entire job?
Slower rate = 1/35, so faster rate = (7/4) × (1/35) = 1/20. The slower alone does 14/35 = 2/5; remaining 3/5 is shared in the rate ratio 7 : 4. Faster therefore does (7/11) × (3/5) = 21/55 of the heap, and the slower’s total is 2/5 + (4/11) × (3/5) = 34/55. The required ratio is 21 : 34.
Q4Ravi paints a hall in 20 days and Meera in 30 days. They begin together; after 5 days Ravi leaves and Suresh, who alone needs 60 days, joins Meera. How many more days are needed to finish the painting?
In 5 days Ravi and Meera complete 5(1/20 + 1/30) = 5/12 of the hall. The remaining 7/12 is done by Meera and Suresh at 1/30 + 1/60 = 1/20 per day, which takes (7/12) ÷ (1/20) = 35/3 = 11⅔ days.
Q5Working together, Kamal and Neha pack a warehouse order in 10 days. After they pack for 5 days, Kamal leaves. Neha needs 15 more days to finish. Alone, Kamal would finish the same order in
Together they do 1/10 of the order per day, so in 5 days they complete 1/2. Neha finishes the remaining 1/2 in 15 days, so her rate is 1/30 per day. Kamal’s rate is 1/10 − 1/30 = 1/15 per day, so alone he needs 15 days.
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More questions
6Two labourers A and B dig at rates in the ratio 2 : 1 and together can finish a trench in 9 days. A works alone for the first 3 days, after which B joins A. From the moment B joins, how many days do they take working together to complete the trench?
7A sealing machine runs three times as fast as a labelling machine. Working together they process a consignment in 6 hours. How long would the labelling machine alone need for that consignment?
8Twelve gardeners can landscape a park in 18 days. After working for 6 days, four additional gardeners join them. By how many days is the project shortened compared with the original 18-day plan?
9P alone can weave a carpet in 18 days and Q alone in 24 days. They start together; P leaves after 6 days. How many additional days does Q need to finish the carpet?
10Anita is twice as efficient as Bharat. If they paint a fence together for the entire job, what percentage of the work does Anita complete?
11Two photocopiers have efficiencies in the ratio 5 : 3. The faster one alone copies a report stack in 12 hours. Both run for 4 hours, after which the faster stops. How long does the slower then take to finish the stack?
12Three inlet taps fill a cistern in 10, 15 and 30 minutes respectively. All three are opened together; after 2 minutes the 10-minute tap is shut. How many more minutes are required to fill the cistern?