Top

# Average

1.

A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

Let the sale in the sixth month $$=x$$
Then, $$\dfrac{6435+6927+6855+7230+6562+x}{6}=6500$$
$$\Rightarrow 6435+6927+6855+7230+6562+x=6 \times 6500\\ \Rightarrow 34009 + x = 39000\\ \Rightarrow x = 39000 - 34009 = 4991$$

Enter details here

2.

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

Since the month begins with a Sunday, to there will be five Sundays in the month.
Required average
$$\left( \dfrac {510 \times 5 + 240 \times 25}{30} \right)\\ =\dfrac{8550}{30}\\ =285$$

Enter details here

3.

A student's mark was wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by $$\dfrac12$$. What is the number of students in the class?

Let the total number of students $$=x$$
The average marks increased by $$\dfrac12$$ due to an increase of $$83 - 63 = 20$$ marks.
But total increase in the marks
$$\dfrac{1}{2}\times x = \dfrac{x}{2}$$
Hence we can write as,
$$\dfrac{x}{2}=20\\ \Rightarrow x = 20 \times 2 = 40$$

Enter details here

4.

A motorist travel to a place 150 km away at an average speed of 50 km/hr and returns ar 30 km/hr.His average speed for the whole journey in km/hr is:

Average speed will be,
$$\dfrac{2xy}{x+y} \text{ km/hr}\\ = \dfrac{2(50)(30)}{50+30} \text{ km/hr}\\ = 37.5 \text{ km/hr}$$

Enter details here

5.

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:

Required average
$$\left( \dfrac {55 \times 50 + 60 \times 55 + 45 \times 60}{55+60+45} \right)\\ =\left( \dfrac {2750 + 3300 + 2700}{160} \right)\\ =\dfrac{8750}{160}\\ =54.68$$

Enter details here

6.

The average monthly income of A and B is Rs. 5050. The average monthly income of B and C is Rs. 6250 and the average monthly income of A and C is Rs. 5200. What is the monthly income of A?

Let monthly income of A = a
monthly income of B = b
monthly income of C = c

$$a + b = 2 \times 5050~\cdots(Equation 1)\\ b + c = 2 \times 6250 ~\cdots(Equation 2)\\ a + c = 2 \times 5200 ~\cdots (Equation 3)\\ (Equation 1) + (Equation 3) - (Equation 2)\\ \Rightarrow a + b + a + c - (b + c) = (2 \times 5050) + (2 \times 5200) - (2 \times 6250)\\ \Rightarrow 2a = 2(5050 + 5200 - 6250)\\ \Rightarrow a = 4000$$

i.e., Monthly income of A = 4000

Enter details here

7.

A student needed 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 is the value of $$x$$?

$$\dfrac{\text{3+11+7+9+15+13+8+19+17+21+14+}x}{12} = 12\\ \Rightarrow \dfrac{137 + x}{12} = 12\\ \Rightarrow 137 + x = 144\\ \Rightarrow x = 144 - 137 = 7$$

Enter details here

8.

The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?

Total increase in weight $$= 8 \times 2.5 = 20$$
If $$x$$ is the weight of the new person, total increase in weight $$= x-65$$
$$\Rightarrow 20 = x - 65\\ \Rightarrow x = 20 + 65 = 85$$

Enter details here

9.

Average of first five multiples of 3 is:

Average:
$$=\dfrac{3(1+2+3+4+5)}{5}\\ = \dfrac{45}{5}\\ = 9$$

Enter details here

10.

A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 30 days starting with Sunday is:

$$= \left (\dfrac{510 \times 5 + 240 \times 25}{30}\right)\\ = \left( \dfrac{8550}{30} \right)\\ = 285$$