Average - Questions and Answers - Arithmetic Aptitude

11.

A car travels from A to B at 40 km/h and returns at 60 km/h. Find the average speed.

A
48 km/h
B
50 km/h
C
52 km/h
D
54 km/h

View Answer

Answer: Option A

Explanation:

Average speed for a round trip with speeds $x$ and $y$ is $\frac{2xy}{x+y}$. Average speed = $\frac{2 \times 40 \times 60}{40 + 60} = \frac{4800}{100} = 48$ km/h.

12.

The average temperature for M, T, and W was 40°C. The average for T, W, and Th was 41°C. If Thursday was 42°C, find Monday's temperature.

A
38°C
B
39°C
C
40°C
D
41°C

View Answer

Answer: Option B

Explanation:

$(T+W+Th) - (M+T+W) = 3(41) - 3(40) = 3$. This simplifies to $Th - M = 3$. Given $Th = 42$, then $42 - M = 3$, so $M = 39$°C.

13.

A cricketer with a bowling average of 12.4 takes 5 wickets for 26 runs, decreasing his average by 0.4. How many wickets did he have before this match?

A
80
B
85
C
90
D
95

View Answer

Answer: Option B

Explanation:

Let initial wickets be $x$. $\frac{12.4x + 26}{x + 5} = 12$. Solving for $x$: $12.4x + 26 = 12x + 60 \implies 0.4x = 34 \implies x = 85$.

14.

The average of 50 numbers is 38. If 45 and 55 are discarded, find the average of the remaining numbers.

A
36.5
B
37.0
C
37.5
D
38.0

View Answer

Answer: Option C

Explanation:

Original sum = $50 \times 38 = 1900$. New sum = $1900 - (45 + 55) = 1800$. New average = $1800 / 48 = 37.5$.

15.

In a group of 15 people, when one person weighing 50 kg is replaced by a new person, the average weight decreases by 1 kg. Find the weight of the new person.

A
30 kg
B
35 kg
C
40 kg
D
45 kg

View Answer

Answer: Option B

Explanation:

Total decrease = $15 \times 1 = 15$ kg. New person = $50 - 15 = 35$ kg.

16.

The average salary of all workers is $8,000. 7 technicians average $12,000 and the rest average $6,000. How many workers are there in total?

A
18
B
21
C
24
D
28

View Answer

Answer: Option B

Explanation:

Using alligation: Ratio of technicians to others = $(8000-6000) : (12000-8000) = 2000 : 4000 = 1 : 2$. Since 1 part = 7 technicians, 2 parts = 14 others. Total = $7 + 14 = 21$.

17.

The average of 'n' numbers is 'a'. If the 1st number is increased by 2, 2nd by 4, 3rd by 8, etc., what is the new average?

A
$a + \frac{2^{n}-1}{n}$
B
$a + \frac{2^{n+1}-2}{n}$
C
$a + \frac{2^{n+1}}{n}$
D
$a + \frac{2^{n}-2}{n}$

View Answer

Answer: Option B

Explanation:

The sum of increases is a geometric progression: $2 + 4 + 8 + ... + 2^n = 2(2^n - 1)$. The average increase is $\frac{2^{n+1}-2}{n}$. New average = $a + \frac{2^{n+1}-2}{n}$.

18.

The average weight of 40 students is 45 kg. Including the teacher makes the average 45.5 kg. Find the teacher's weight.

A
64.5 kg
B
65.0 kg
C
65.5 kg
D
66.0 kg

View Answer

Answer: Option C

Explanation:

Teacher's weight = Old average + (New count $\times$ Increase) = $45 + (41 \times 0.5) = 45 + 20.5 = 65.5$ kg.

19.

A library has 510 visitors on Sundays and 240 on other days. Find the average visitors per day in a 30-day month starting on Sunday.

A
275
B
280
C
285
D
290

View Answer

Answer: Option C

Explanation:

A 30-day month starting on Sunday has 5 Sundays and 25 other days. Total visitors = $(5 \times 510) + (25 \times 240) = 2550 + 6000 = 8550$. Average = $8550 / 30 = 285$.

20.

8 persons spent $30 each on meals. The 9th spent $20 more than the average of all 9. What was the total money spent?

A
$282.50
B
$290.00
C
$292.50
D
$300.00

View Answer

Answer: Option C

Explanation:

Let average = $x$. $9x = (8 \times 30) + (x + 20) \implies 8x = 260 \implies x = 32.5$. Total = $32.5 \times 9 = 292.5$.

Exercise : Average - General Questions