- LPU MCA Semester 1
- PEA515
- Unit 1
PEA515 · Unit 1: Number system and averages
Weighted average
30 practice questions · in the MTE and ETE syllabus
Key points
- Weight each group by its size
- Cross rule gives the ratio of group sizes
- Equal distances need the harmonic mean for speed
- Equal times allow a simple average of speeds
When groups have different sizes, the weighted average is (n1 x a1 + n2 x a2 + ...)/(n1 + n2 + ...). Larger groups pull the result closer to their own average.
Mixture shortcut (rule of the cross): if two groups with averages a1 < a2 combine to an average A, then n1 : n2 = (a2 - A) : (A - a1). Example: averages 40 and 70 mix to 52, so the ratio is (70 - 52) : (52 - 40) = 18 : 12 = 3 : 2.
Average speed over equal distances at speeds x and y is the harmonic mean, 2xy/(x + y), not (x + y)/2. For equal times it is the simple average. Example: 30 km/h up and 60 km/h back gives 2 x 30 x 60 / 90 = 40 km/h.
Exam trap: averaging two speeds directly when the distances, not the times, are equal.
Try two questions
A shopkeeper buys 40 kg of sugar at 21 rupees per kg and 5 kg at 57 rupees per kg. What is the average cost per kg in rupees?
- 39
- 53
- 1125
- 25
Show the answer
D. Total cost 1125 over 45 kg = 25.
Why not A: Averages the two rates without weighting by quantity.
Why not B: Swaps the quantities.
Why not C: Reports the total cost instead of the average per kg.
In a selection test the sections carry 40%, 30% and 30% weight. With 78 and 73 already scored, what mark in the third section gives a weighted score of 75?
- 74
- 73
- 21.9
- 75
Show the answer
B. Total needed = 7500; already earned 5310; divide the rest by 30: 73.
Why not A: Treats the three components as equally weighted.
Why not C: Divides by 100 instead of the final component's weight.
Why not D: Assumes the final score must simply equal the target.