Average Question and Answers -3

Quantitative Aptitude (Averages - Part 3)

Below are questions 21 to 27 from the document, presented in the same format with accurate mathematical explanations.

21. The average height of 30 girls out of a class of 40 is 160 cm and that of the remaining girls is 156 cm. The average height of the whole class is

• (a) 158 cm
• (b) 158.5 cm
• (c) 159 cm
• (d) 157 cm

Correct Answer: (c) 159 cm

Explanation:
Step 1: Sum of heights of 30 girls = 30 × 160 = 4800 Step 2: Remaining girls = 40 - 30 = 10 Step 3: Sum of heights of remaining 10 girls = 10 × 156 = 1560 Step 4: Total Average =

4800 + 1560 40

Step 5: Average =

6360 40

= 159 cm

22. A batsman made an average of 40 runs in 4 innings, but in the fifth inning, he was out on zero. What is the average after fifth inning?

• (a) 32
• (b) 22
• (c) 38
• (d) 49

Correct Answer: (a) 32

Explanation:
Step 1: Total runs in 4 innings = 40 × 4 = 160 Step 2: Runs in 5th inning = 0 Step 3: Total runs in 5 innings = 160 + 0 = 160 Step 4: New Average =

160 5

= 32

23. A train travels with a speed of 20 m/s in the first 10 minutes, goes 8.5 km in the next 10 minutes, 11 km in the next 10, 8.5 km in the next 10 and 6 km in the next 10 minutes. What is the average speed of the train in kilometer per hour for the journey described?

• (a) 42 kmph
• (b) 35.8 kmph
• (c) 55.2 kmph
• (d) 46 kmph

Correct Answer: (c) 55.2 kmph

Explanation:
Step 1: Convert first segment to km: 20 m/s × 600s = 12,000 m = 12 km Step 2: Total Distance = 12 + 8.5 + 11 + 8.5 + 6 = 46 km Step 3: Total Time = 50 minutes =

50 60

hours Step 4: Average Speed =

46 50/60

=

46 × 60 50

Step 5: Average Speed = 55.2 kmph

24. The average income of a person for the first 6 days is 29, for the next 6 days it is 24, for the next 10 days it is 32 and for the remaining days of the month it is 30. Find the average income per day.

• (a) 31.64
• (b) 30.64
• (c) 29.26
• (d) Cannot be determined

Correct Answer: (d) Cannot be determined

Explanation:
Step 1: The phrase "remaining days of the month" is ambiguous as the specific month (28, 29, 30, or 31 days) is not stated. Step 2: Without the total number of days, the weighted average cannot be calculated accurately.

25. The average of 5 consecutive numbers starting with x is y, find the average of 6 consecutive numbers staring with x+2

• (a) (y+5)/2
• (b) (y+7)/2
• (c) (y+8)/2
• (d) (2y+5)/2

Correct Answer: (d) (2y+5)/2

Explanation:
Step 1: Average of 5 consecutive integers starting at x is x+2. Thus, y = x+2. Step 2: The average of 6 consecutive integers starting at x+2 is the value between the 3rd and 4th term. Step 3: Terms are: x+2, x+3, x+4, x+5, x+6, x+7. Median is x+4.5. Step 4: Substitute x = y - 2 into x + 4.5. Step 5: (y - 2) + 4.5 = y + 2.5 =

2y + 5 2

26. Find the average of 1000.0001, 100.001, 10.01 and 1.1 is:

• (a) 277.777
• (b) 322.222
• (c) 11.11
• (d) 233.333

Correct Answer: (a) 277.777

Explanation:
Step 1: Sum = 1000.0001 + 100.001 + 10.01 + 1.1 = 1111.1111 Step 2: Average =

1111.1111 4

Step 3: Average = 277.7777... ≈ 277.777

27. A man covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. Find his average speed during the entire journey?

• (a) 36 kmph
• (b) 30 kmph
• (c) 24 kmph
• (d) 18 kmph

Correct Answer: (c) 24 kmph

Explanation:
Step 1: Let Total Distance = 120 km. Step 2: Train (Half = 60km): Time = 60/60 = 1 hr. Step 3: Remaining = 60km. Bus (Half of remainder = 30km): Time = 30/30 = 1 hr. Step 4: Cycle (Rest = 30km): Time = 30/10 = 3 hrs. Step 5: Average Speed =

Total Distance Total Time

=

120 1 + 1 + 3

=

120 5

= 24 kmph