169+ Problems on Average With Explanation

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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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 28315

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 27620

Q:

In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?

A) 55.5 kg	B) 66.5 kg
C) 77.5 kg	D) 88.5 kg

Answer & Explanation Answer: B) 66.5 kg

Explanation:

Let Arun's weight be X kg.

According to Arun, 65 < X < 72.

According to Arun's brother, 60 < X < 70.

According to Arun's mother, X < 68.

The values satisfying all the above conditions are 66 and 67.

Required average = (66 + 67) / 2 = 66.5 kg

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21 25984

Q:

David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?

A) 75	B) 68
C) 65	D) 60

Answer & Explanation Answer: A) 75

Explanation:

Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5 = 75.

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24 25185

Q:

The mean temperature of Monday to Wednesday was 37C and of Tuesday to Thursday was 34C . If the temperature on Thursday was (4/5) th that of Monday, the temperature on Thursday was?

Answer

$\inline \fn_jvn M+T+W =(37\times 3)^{0}=111^{0}C$ -----------(1)

$\inline \fn_jvn T+W+Th=(34\times 3)^{0}=102^{0}C$

$\inline \fn_jvn \Rightarrow T+W+\frac{4}{5}M = 102^{0}C$ --------------(2)

(1) - (2) gives

$\inline \fn_jvn \frac{1}{5}$ th of temperature on Monday = $111^{0}-102^{0}=9^{0}C$

$\inline \fn_jvn \Rightarrow$ Temperature on Monday = $\inline \fn_jvn 45^{0}C$

$\inline \fn_jvn \therefore$ Temperature on Thursday = $\inline \fn_jvn \frac{4}{5}\times 45^{0}=36^{0}$

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160 25176

Q:

The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?

A) 3600	B) 3700
C) 3800	D) 3900

Answer & Explanation Answer: A) 3600

Explanation:

Manager's monthly salary Rs. (1600 * 21 - 1500 * 20) = Rs. 3600.

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20 24309

Q:

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years, The ratio of the number of boys to the number of girls in the class is :

A) 1 : 2	B) 2 : 3
C) 3 : 4	D) 4 : 5

Answer & Explanation Answer: B) 2 : 3

Explanation:

Let the ratio be k : 1. Then,

k * 16.4 + 1 * 15.4 = (k + 1) * 15.8

<=> (16.4 - 15.8) k = (15.8 - 15.4) <=> k = 0.4/0.6 = 2/3.

Required ratio = 2/3 : 1 = 2 : 3.

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