NIMCET Time And Work Previous Year Questions (PYQs) – Page 2 of 2
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Showing 16 questions
Running at the same constant rate, 6
identical machines can produce a total of
270 bottles per minute. At this rate, how
many bottles could 10 such machines
produce in 4 minutes?
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Solution
Let the required number of bottles be x.
More machines, More bottles (Direct Proportion)
More minutes, More bottles (Direct Proportion)
$\begin{matrix}{\begin{matrix}{Machines} & {6\colon10}\end{matrix}} \\ {\begin{matrix}{Time} & {\, \, \, \, \, \, \, \, \, \, 1\colon4}\end{matrix}}\end{matrix}\Bigr{\}}: : 270:x$
∴$6×1×x=10×4×270$
⇒$x= \frac{(10×4×270)}{6}$
⇒$x=1800$
Two pipes A and B can fill a cistern in 37.5 and 45 min, respectively. Both pipes are opened. The cistern will be filled in just half an hour, if pipe B is turned off after
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Solution
A caterpillar crawls up a pole of 75 inches high, starting from the ground. Each day, it crawls up 5 inches and each night it slides down 4 inches. When will it reach the top of the pole?
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Solution
A child can do a piece of work 15 hours slower than a woman. The child works for 18 hours on the job and then the woman takes charge for 6 hours. In this way, 3/5 of the work is completed. To complete the job now, how much time does the woman take?
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Solution
Let the woman finish the whole work in W hours.
Then the child finishes it in W + 15 hours.
Work done:
Child’s 18 hours work = 18 / (W + 15)
Woman’s 6 hours work = 6 / W
Total = 3/5
So,
18/(W+15) + 6/W = 3/5
Solve:
Multiply by 5W(W+15):
5W·18 + 5(W+15)·6 = 3W(W+15)
90W + 30W + 450 = 3W² + 45W
120W + 450 = 3W² + 45W
3W² - 75W - 450 = 0
Divide by 3:
W² - 25W - 150 = 0
Solve quadratic:
W = [25 ± √(625 + 600)] / 2
W = [25 ± √1225] / 2
W = (25 ± 35) / 2
Positive solution → W = (25 + 35)/2 = 30 hours
Two men and three boys can do a piece of work in ten days; while three men and two boys can do the same work in eight days. In how many days can two men and one boy do the work?
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Solution
If 1 man or 2 women can finish a job in 20 days, how may days will 3 men and women take to finish the same job?
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Solution
$1$ man or $2$ women can finish the work in $20$ days.
Work by $1$ man in $1$ day $= \dfrac{1}{20}$
Work by $1$ woman in $1$ day $= \dfrac{1}{40}$
For $3$ men and $1$ woman:
Total work per day $= 3 \times \dfrac{1}{20} + 1 \times \dfrac{1}{40}$
$= \dfrac{6}{40} + \dfrac{1}{40} = \dfrac{7}{40}$
Time to finish the job $= \dfrac{1}{(7/40)} = \dfrac{40}{7}$ days
$\approx 5.71$ days
✅ Final Answer: $ \dfrac{40}{7} $ days
Work by $1$ man in $1$ day $= \dfrac{1}{20}$
Work by $1$ woman in $1$ day $= \dfrac{1}{40}$
For $3$ men and $1$ woman:
Total work per day $= 3 \times \dfrac{1}{20} + 1 \times \dfrac{1}{40}$
$= \dfrac{6}{40} + \dfrac{1}{40} = \dfrac{7}{40}$
Time to finish the job $= \dfrac{1}{(7/40)} = \dfrac{40}{7}$ days
$\approx 5.71$ days
✅ Final Answer: $ \dfrac{40}{7} $ days
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