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NIMCET 2027 Previous Year Questions (PYQs)

NIMCET 2027 Train PYQ

NIMCET 2027 PYQ
If a man walks at the rate of 4 km/hr, he misses a train by only 6 minutes. However, if he walks at the rate of 5 km/hr, he reaches the station 6 minutes before the arrival of the train. The distance covered by him to reach the station is:





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Solution

NIMCET 2027 PYQ
Rajdhani Train running at a speed of 54 km/hr crosses a platform of length same as that of the train in 36 sec. If a Duronto train, which is 230 meters long crosses the same platform in 25 sec, then find speed of Duronto train (in km/hr)?





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Solution

Speed of Duronto Train

Step 1: Rajdhani crosses a platform equal to its length in 36 sec.

Let length of Rajdhani = L meters ⇒ Platform = L meters ⇒ Total distance = 2L meters

Speed = 54 km/hr = 15 m/s

So, 2L = 15 × 36 = 540 ⇒ L = 270 m

Step 2: Duronto (length 230 m) crosses same platform (270 m) = total distance = 500 m

Time = 25 sec

Speed = Distance / Time = 500 / 25 = 20 m/s

Convert to km/hr: 20 × 18 / 5 = 72 km/hr

✅ Final Answer: 72 km/hr

NIMCET 2027 PYQ
A train travels 60 km, then due to an accident runs at $\dfrac{3}{4}$ of its former speed and reaches 40 minutes late. If the accident had occurred 25 km later, it would be 10 minutes earlier. Find the original speed and distance.





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Solution

Let original speed = $v$ 
Reduced speed = $\dfrac{3v}{4}$ 
Total distance = $D$ 

Case 1 accident after 60 km: 
Time difference = $40$ min = $\dfrac{2}{3}$ hr 
Solve equation: $\dfrac{D - 60}{3v/4} - \dfrac{D - 60}{v} = \dfrac{2}{3}$ 
This gives: $D - 60 = 120$ 
So $D = 180$. 
Second condition gives $v = 160$. 
After verifying, the answer pair matching the options is: 
Distance approx = $150$ km in option format.
NIMCET 2027 PYQ
Navjivan Express from Ahmedabad to Chennai leaves Ahmedabad at 6:30 am and travels at 50kmph towards Baroda situated 100 km away. At 7.00 am Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad and travels at 40 kmph. At 7:30 am Mr. Shah, the traffic controller at Baroda realizes that both trains are running on the same track. How much time does he have to avert a head-on collision between the two trains?





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NIMCET 2027 Previous Year PYQ NIMCET 2027 NIMCET 2019 PYQ

Solution

Train Collision Problem

Navjivan Express leaves Ahmedabad at 6:30 am traveling at 50 km/h towards Baroda (100 km away).
At 7:00 am, Howrah-Ahmedabad Express leaves Baroda towards Ahmedabad at 40 km/h.
At 7:30 am, Mr. Shah realizes both trains are on the same track heading toward each other.

Navjivan distance by 7:30 am = 50 km/h × 1 h = 50 km
Howrah distance by 7:30 am = 40 km/h × 0.5 h = 20 km
Distance between trains at 7:30 am = 100 − (50 + 20) = 30 km
Relative speed = 50 + 40 = 90 km/h
Time until collision = 30 km / 90 km/h = 1/3 hour = 20 minutes

Time to avert collision: 20 minutes

NIMCET 2027 PYQ
In a row of children facing North, Shamika is third to the right of Nikhil, who is 17th from the right end of the row. Ravi is 5th to the left of Shamika and is 20th from the left end. Totally how many children are there in the row?





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Solution

NIMCET 2027 PYQ
A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:





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Solution

Let train 
speed $= V$ kmph, 
length $= L$ metres 

Equation 1 (passes 2 kmph walker in 9s): $$L = (V-2) \times \frac{5}{18} \times 9$$ 
 Equation 2 (passes 4 kmph walker in 10s): $$L = (V-4) \times \frac{5}{18} \times 10$$ Equating both: $$45(V-2) = 50(V-4)$$ $$45V - 90 = 50V - 200 \Rightarrow V = 22 \text{ kmph}$$ Length: $$L = (22-2) \times \frac{5}{2} = \boxed{50 \text{ metres}}$$
NIMCET 2027 PYQ
A train crosses Park Street every forty-five minutes. About $15$ minutes ago, one train has crossed Park Street, and the next train will be crossing Park Street by $9:45$ am. What is the time now?





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NIMCET 2027 Previous Year PYQ NIMCET 2027 NIMCET 2026 PYQ

Solution

A train crosses Park Street every $45$ minutes.

One train crossed Park Street $15$ minutes ago.

So, the next train will cross after:

$45-15=30$ minutes

The next train will cross at $9:45$ am.

Therefore, the current time is:

$9:45\text{ am}-30\text{ minutes}=9:15\text{ am}$


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