NIMCET Averages Previous Year Questions (PYQs)
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Showing 3 questions
A set of consecutive positive integers beginning with
1 is written on the blackboard. A student came along
and erased one number. The average of the remaining
numbers is $35\frac{7}{15}$. What was the number erased?
1
2
3
4
Solution
The mean of consecutive positive
integers from 2 to n is
1
2
3
4
Solution
Step-by-step:
- First term: 2
- Last term: n
- Total numbers: n − 2 + 1 = n − 1
- Sum: (n − 1)/2 × (2 + n)
- Mean: Sum ÷ (n − 1) = (n + 2)/2
✅ Final Answer: The mean of numbers from 2 to n is (n + 2) / 2.
Three cities A, B, C are equidistant from each other.
A motorist travels from A to B at 30km/hour, from B
to C at $40$ km/hour, and from C to A at 50km/hour.
Then the average speed is
1
2
3
4
Solution
Let the distance between each pair of cities = d km.
Step 1: Distances & Speeds
- A → B: distance = d, speed = 30 km/h
- B → C: distance = d, speed = 40 km/h
- C → A: distance = d, speed = 50 km/h
Step 2: Total Distance
Total distance = d + d + d = 3d
Step 3: Total Time
Time = (d/30) + (d/40) + (d/50)
= d × (1/30 + 1/40 + 1/50)
LCM of (30,40,50) = 600
⇒ (20 + 15 + 12)/600 = 47/600
Total time = d × (47/600) = (47d / 600)
Step 4: Average Speed
Average speed = Total distance / Total time
= (3d) ÷ (47d/600)
= (3d × 600) / 47d
= 1800 / 47
≈ 38.3 km/h
✅ Final Answer: Average speed ≈ 38.3 km/h
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