169+ Problems on Average With Explanation

Q:

The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is :

A) 25	B) 35
C) 45	D) 55

Answer & Explanation Answer: B) 35

Explanation:

Excluded number = (27 x 5) - (25 x 4) = 135 - 100 = 35.

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Q:

How many window coverings are necessary to span 50 windows, if each window covering is 15 windows long?

A) 4	B) 15
C) 3	D) 50

Answer & Explanation Answer: A) 4

Explanation:

Given that,

Number of windows = 50

Each window covering covers 15 windows

=> 50 windows requires 50/15 window coverings

= 50/15 = 3.333

Hence, more than 3 window coverings are required. In the options 4 is more than 3.

Hence, 4 window coverings are required to cover 50 windows of each covering covers 15 windows.

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Q:

If the average of 31, x, 42, 39, 56, 78, 83 and 91 is 58.5, then what is the value of x?

A) 26	B) 34
C) 58	D) 48

Answer & Explanation Answer: D) 48

Explanation:

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Q:

The average of two numbers is 10 and the product of two numbers is 96. Find the two numbers.

A) 3, 32	B) 12, 8
C) 1, 96	D) 24, 4

Answer & Explanation Answer: B) 12, 8

Explanation:

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Q:

Find the range of the data 9, 5, 9, 3, 4, 7, 8, 4, 8, 9, 5, 9.

A) 3	B) 5
C) 6	D) 4

Answer & Explanation Answer: C) 6

Explanation:

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Q:

Consider the following frequency distribution:

x f

8 6

5 4

6 5

10 8

9 9

4 6

7 4

What is the median for the distribution?

A) 6	B) 7
C) 8	D) 9

Answer & Explanation Answer: C) 8

Explanation:

Summation of frequencies = 6+4+5+8+9+6+4 = 42

Median = mid value = average of 21st and 22nd value

Arranging data in increasing order we get

x f

4 6

5 4

6 5

7 4

8 6

9 9

10 8

So mid value i.e 21st and 22nd value = 8

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Q:

In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is :

A) 21	B) 20
C) 22	D) None of these

Answer & Explanation Answer: B) 20

Explanation:

It is the same as a person with 20 years more age replaces an existing person of the group ( or village)

Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village.

Alternatively : ( n x 42 ) + 20 = ( n x 43 )

=> n=20

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Q:

The ratio of speeds of a car, a train and a bus is 5:9:4. The average speed of the car, the bus and the train is 72 km/hr together. What is the average speed of the car and the train together ?

A) 84 km/hr	B) 96 km/hr
C) 72 km/hr	D) 60 km/hr

Answer & Explanation Answer: A) 84 km/hr

Explanation:

Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively.
Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr.
Also, 6x = 72 => x = 12 km/hr
Therefore, the average speed of the car and train together is = $\frac{5 x + 9 x}{2}$ = 7x = 7 x 12 = 84 km/hr.

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