Aptitude · Lesson 4 of 9
Averages & mixtures
Average formula, effect of adding/removing items, and weighted averages.
- Average =
sum of values / number of values, so Sum = Average × Count. - Adding a value above the average raises it; the change in average =
(new value − old average) / new count. - Weighted average of groups:
(n₁a₁ + n₂a₂) / (n₁ + n₂). - Average of consecutive numbers = average of the first and last.
- Alligation (mixing two prices to get a mean): ratio =
(dearer − mean) : (mean − cheaper)for cheaper : dearer.
Example: The average age of 10 employees is 28. When the manager joins, the average becomes 29. Find the manager's age.
- Old sum = 10 × 28 = 280.
- New sum = 11 × 29 = 319.
- Manager = 319 − 280.
Answer: 39 years
Example: In what ratio must rice at ₹40/kg be mixed with rice at ₹60/kg to get a mixture worth ₹45/kg?
- Cheaper : dearer = (60 − 45) : (45 − 40) = 15 : 5.
Answer: 3 : 1
Key points
- Sum = Average × Count — work with sums.
- Weighted average for groups of different sizes.
- Alligation gives mixing ratios quickly.
Quick check
Average of 5 numbers is 20. If one number 30 is removed, the new average is…
Sum 100 − 30 = 70; 70 / 4 = 17.5.
Practice task
A batsman's average over 20 innings is 42. How many runs must he score in the 21st innings to raise his average to 44?
Show answer
Needed sum = 21 × 44 = 924; current = 20 × 42 = 840; runs = 84.
Interview corner
Class A (30 students) averages 60, class B (20) averages 70. Combined average?
(30×60 + 20×70) / 50 = 3200/50 = 64.
What is the average of the first 50 natural numbers?
(1 + 50) / 2 = 25.5.
Original lesson written by the InfoparkDaily team · © 2026 InfoparkDaily · Free to learn — no paid course or subscription.