169+ Problems on Average With Explanation

Q:

The average age of 36 students in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years ?

A) 35 years	B) 45 years
C) 51 years	D) 54 years

Answer & Explanation Answer: C) 51 years

Explanation:

Age of the teacher = (37 * 15 - 36 * 14) years = 51 years.

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Q:

In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ?

A) 8	B) 9
C) 10	D) 11

Answer & Explanation Answer: D) 11

Explanation:

Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11.

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Q:

Ian has 14 boxes of paper and divides them evenly between 4 coworkers. How many whole boxes did each coworker get?

A) 2	B) 2.5
C) 3	D) 3.5

Answer & Explanation Answer: C) 3

Explanation:

Given number of boxes = 14

Number of workers = 4

Now, number of whole boxes per worker = 14/4 = 3.5

Hence, number of whole boxes per each coworker = 3

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28 29138

Q:

The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ?

A) 16,12	B) 10,16
C) 23,9	D) 8,7

Answer & Explanation Answer: B) 10,16

Explanation:

Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)]

= Rs. (120 - 94) = Rs. 26.

let the price of one book be Rs. x

Then, the price of other book = Rs. (x + 60% of x) = Rs.(x+(3/5)x) = Rs. (8/5)x

So, x+(8/5)x =26 <=> x =10

The prices of the two books are Rs. 10 and Rs. 16

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Q:

The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?

A) 62 degrees	B) 64 degrees
C) 65 degrees	D) 66 degrees

Answer & Explanation Answer: B) 64 degrees

Explanation:

Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)

Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)

Subtracting (1) From (2), we get :

Temp, on 5th day - Temp on 1st day = 8 degrees.

Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.

Then, 8x - 7x = 8 or x = 8.

Temperature on the 5th day = 8x = 64 degrees.

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56 27568

Q:

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?

A) 20 years	B) 21 years
C) 23 years	D) 25 years

Answer & Explanation Answer: C) 23 years

Explanation:

Let the average age of the whole team be x years.

11x - (26 + 29) = 9 (x - 1)

=> 11x - 9x = 46

=> 2x = 46

=> x = 23.

So, average age of the team is 23 years.

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57 27531

Q:

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of $\frac{a^{2} + b^{2} + c^{2}}{3}$ is :

A) M	B) 3 M^2
C) 2 (M/3)	D) M^2

Answer & Explanation Answer: B) 3 M^2

Explanation:

We have : ( a + b + c) / 3 = M or (a + b + c) = 3M.

Now. ${(a + b + c)}^{2} = {(3 M)}^{2} = 9 M^{2}$ .

$< = > a^{2} + b^{2} + c^{2} + 2 (a b + b c + c a) = 9 M^{2}$

$a^{2} + b^{2} + c^{2} = 9 M^{2}, (a b + b c + c a = 0)$

Required mean = $(\frac{a^{2} + b^{2} + c^{2}}{3}) = \frac{9 M^{2}}{3} = 3 M^{2}$ .

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35 26460

Q:

A student was asked to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x ?

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

Answer & Explanation Answer: B) 7

Explanation:

Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.

or 137 + x = 144 or x = 144 - 137 = 7.

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