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Phrases PYQ
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?





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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

Solution

Phrases PYQ
The mean of consecutive positive integers from 2 to n is





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Phrases Previous Year PYQPhrases NIMCET 2024 PYQ

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.

Phrases PYQ
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 40km/hour, and from C to A at 50km/hour. Then the average speed is





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Phrases Previous Year PYQPhrases NIMCET 2020 PYQ

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

 Solution Contribution by Priyanka Soni

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