NIMCET Time And Work Previous Year Questions (PYQs) – Page 1 of 2
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Showing 16 questions
Two pipes A and B can fill the cistern in 37.5
minutes and 45 minutes respectively. Both pipes are
opened. The cistern will be filled in just half an hour,
if the B is turned off after
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Solution
A can do a work in 10 days, B can do the same work in 20 days. After working for 4 days B left the job & C started working at the place of B, the remaining work was done by both A & C in 2 days. In how many days C alone can do the work?
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Solution
Work and Time – Find Days for C
A's 1 day work: \( \frac{1}{10} \)
B's 1 day work: \( \frac{1}{20} \)
Step 1: A and B work for 4 days:
Work done = \( 4 \times \left( \frac{1}{10} + \frac{1}{20} \right) = 4 \times \frac{3}{20} = \frac{3}{5} \)
Remaining work: \( 1 - \frac{3}{5} = \frac{2}{5} \)
Step 2: A and C do remaining work in 2 days:
\( 2 \times \left( \frac{1}{10} + \frac{1}{C} \right) = \frac{2}{5} \)
Dividing both sides by 2:
\( \frac{1}{10} + \frac{1}{C} = \frac{1}{5} \)
\( \frac{1}{C} = \frac{1}{5} - \frac{1}{10} = \frac{1}{10} \)
\( \Rightarrow C = 10 \)
✅ Final Answer: 10 days
Computer A takes 3 minutes per input.
Computer B takes 5 minutes per input.
Let C take x minutes per input.
Together A + B + C process:
14 inputs per hour = $\dfrac{14}{60}$ inputs per minute.
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Solution
Rates:
A: $\dfrac{1}{3}$ per minute
B: $\dfrac{1}{5}$ per minute
C: $\dfrac{1}{x}$ per minute
Total rate:
$\dfrac{1}{3} + \dfrac{1}{5} + \dfrac{1}{x} = \dfrac{14}{60} = \dfrac{7}{30}$
Compute:
$\dfrac{8}{15} + \dfrac{1}{x} = \dfrac{7}{30}$
$\dfrac{1}{x} = \dfrac{7}{30} - \dfrac{16}{30} = -\dfrac{9}{30}$
Rate cannot be negative → No such x exists.
So:
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both statements and
- Give the answer (U) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- Give the answer (V) if the data in statement I| alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- Give the answer (W) if the data either in Statement I or in Statement II alone are sufficient to the answer of the question.
- Give the answer (X) if the data in both statements I and II together are not sufficient to answer the question.
- Give the answer (Y) if the data in both statements I and II together are are necessary to answer the question.
How much time will the leak take to empty the full cistern?
- The cistern is normally filled in 9 hours.
- It takes one hour more than the usual time to fill the cistern because of a leak in the bottom.
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Solution
Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both statements and
- Give the answer (U) if the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
- Give the answer (V) if the data in statement I| alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
- Give the answer (W) if the data either in Statement I or in Statement II alone are sufficient to the answer of the question.
- Give the answer (X) if the data in both statements I and II together are not sufficient to answer the question.
- Give the answer (Y) if the data in both statements I and II together are are necessary to answer the question.
How will long it take to empty the tank if both the inlet pipe P1 and the outlet pipe P2 are opened simultaneously?
- P1 can fill the tank in 16 minutes.
- P2 can empty the full tank in 8 minutes.
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Solution
How long would it take you to count 1 billion orally if you could count 200 every minute and were given a day off every four years? Assume that you start counting on 1 January 2001.
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Solution
Numbers counted per minute = 200
Time needed for 1,000,000,000 numbers:
Minutes required = 1,000,000,000 / 200
= 5,000,000 minutes
Convert minutes:
5,000,000 minutes = 5,000,000 / 60 = 83,333.33 hours
= 3,472.22 days
Now include days off:
From 1 Jan 2001 to finish time → during this period, leap years add 1 day off every 4 years.
Total days ≈ 3472 + 1 leap day = 3473 days
Convert 3473 days to years:
3473 days = 9 years + remaining days
9 years = 3287 days
Remaining = 3473 – 3287 = 186 days
Now convert the decimal part of hours:
0.22×24 ≈ 5.20 hours
0.20×60 ≈ 20 minutes
Final answer = 9 years, 187 days, 5 hours, 20 minutes
A man walks down an escalator.
If he walks down 26 steps, he takes 30 seconds.
If he walks down 34 steps, he takes 18 seconds.
Time is measured from when the top step begins to descend until he steps off at the bottom.
What is the height of the stairway in steps?
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Solution
Let escalator speed = x steps/sec
Walking speed = y steps/sec
26 = (x + y) × 30
34 = (x + y) × 18
Solving gives x = 0.4, y = 0.47
Total steps = escalator speed × total time
= (x × time when he stands still)
Height = 52 steps
Directions for questions 83–85:
Mrs. Thomes received a large order for stitching school uniforms from Mayflower school and Little flower school. She has two cutters who will cut the fabric, five tailors who will do the stitching and two assistants to stitch the buttons and button holes. Each of these nine persons will work for exactly 10 hours a day. Each of the Mayflower uniforms requires 20 min for cutting the fabric, one hour for stitching, and 15 min for stitching buttons and button holes, whereas the Little flower uniform requires 30 min, 1 hour and 30 min respectively for these activities.
What is the number of Little flower uniforms that Mrs. Thomes can complete in a day?
What is the number of Little flower uniforms that Mrs. Thomes can complete in a day?
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Solution
Little flower uniform requires:
• Cutting = 30 min
• Stitching = 60 min
• Buttons = 30 min
Available daily working time:
• 2 cutters → 2 × 600 min = 1200 min
• 5 tailors → 5 × 600 min = 3000 min
• 2 assistants → 2 × 600 min = 1200 min
Calculate max number by each stage:
Cutting capacity = 1200 / 30 = 40
Stitching capacity = 3000 / 60 = 50
Button work capacity = 1200 / 30 = 40
Minimum of these = 40 uniforms
On a particular day, Mrs. Thomes decided to complete 20 Little flower uniforms. How many Mayflower uniforms can she complete on that day?
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Solution
Little flower uniform uses per piece:
Cutting 30 min → 20 uniforms = 600 min
Stitching 60 min → 20 uniforms = 1200 min
Buttons 30 min → 20 uniforms = 600 min
Remaining capacity:
Cutters: 1200 – 600 = 600 min
Tailors: 3000 – 1200 = 1800 min
Assistants: 1200 – 600 = 600 min
Mayflower uniform time:
Cutting = 20 min → capacity = 600 / 20 = 30
Stitching = 60 min → capacity = 1800 / 60 = 30
Buttons = 15 min → capacity = 600 / 15 = 40
Minimum = 30 uniforms
If she hires one more assistant, what is the maximum number of Mayflower uniforms that she can complete in a day?
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Solution
Mayflower uniform requires:
Cutting = 20 min
Stitching = 60 min
Buttons = 15 min
Daily capacity:
Cutters: 1200 min → 1200 / 20 = 60
Tailors: 3000 min → 3000 / 60 = 50
Assistants: previously 2 (1200 min), now 3 assistants → 3 × 600 = 1800 min
Buttons capacity = 1800 / 15 = 120
Minimum of 60, 50, 120 = 50 uniforms
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