Averages — Practice

Question 1

The average of the first five multiples of 7 is:
(a) 20 (b) 21 (c) 24 (d) 25

Accepted Answer

(b) 21.

7, 14, 21, 28, 35 are evenly spaced, so the average equals the middle term, 21 (or 105 ÷ 5).

Question 2

The average age of 30 students is 12 years. When the teacher's age is included, the average becomes 13 years. The teacher's age is:
(a) 40 (b) 42 (c) 43 (d) 45

Accepted Answer

(c) 43 years.

Students' total = 360. New total = 31 × 13 = 403. Teacher = 403 − 360 = 43.

Question 3

The average of five consecutive even numbers is 40. The largest of these numbers is:
(a) 42 (b) 44 (c) 46 (d) 48

Accepted Answer

(b) 44.

The middle term equals the average, 40, so the numbers are 36, 38, 40, 42, 44 — largest 44.

Question 4

In a class of 40, the 25 boys average 60 marks and the 15 girls average 68 marks. The class average is:
(a) 62 (b) 63 (c) 64 (d) 66

Accepted Answer

(b) 63.

(25 × 60 + 15 × 68)/40 = (1500 + 1020)/40 = 2520/40 = 63 — between 60 and 68 as it must be.

Question 5

The average weight of 8 persons increases by 2.5 kg when a new person replaces one weighing 65 kg. The weight of the new person is:
(a) 76 kg (b) 85 kg (c) 76.5 kg (d) 90 kg

Accepted Answer

(b) 85 kg.

Total weight rose by 8 × 2.5 = 20 kg. New person = 65 + 20 = 85 kg.

Question 6

The average of 11 results is 50. The average of the first six is 49 and of the last six is 52. The sixth result is:
(a) 54 (b) 55 (c) 56 (d) 60

Accepted Answer

(c) 56.

First six = 294, last six = 312, all eleven = 550. The sixth is counted in both sixes: 294 + 312 − 550 = 56.

Question 7

The average of 10 numbers was calculated as 15. It was later found that a number 36 was read as 26. The correct average is:
(a) 15 (b) 15.5 (c) 16 (d) 16.5

Accepted Answer

(c) 16.

The total was short by 36 − 26 = 10, so the true average rises by 10/10 = 1 → 16.

Question 8

A man goes to a town at 40 km/h and returns along the same road at 60 km/h. His average speed for the whole journey is:
(a) 48 km/h (b) 50 km/h (c) 52 km/h (d) 45 km/h

Accepted Answer

(a) 48 km/h.

Equal distances → harmonic mean = 2 × 40 × 60 / (40 + 60) = 4800/100 = 48. The plain mean 50 ignores that more time is spent at the slower speed.

Question 9

A batsman in his 17th innings scores 85 and thereby raises his average by 3 runs. His average after the 17th innings is:
(a) 34 (b) 35 (c) 36 (d) 37

Accepted Answer

(d) 37.

Let the average after 16 innings be x. Then 16x + 85 = 17(x + 3) → x = 34, so the new average is 34 + 3 = 37.

Question 10

The average of 6 numbers is 8. If each number is multiplied by 3 and then 4 is added, the new average is:
(a) 24 (b) 26 (c) 28 (d) 12

Accepted Answer

(c) 28.

Multiplying every value by 3 scales the average to 24; adding 4 to every value adds 4 to the average → 28.

Practice — Averages

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