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Average Questions and Answers

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1.

For the past \(m\) days, the average daily production at a company was 100 units per day.

If today’s production of 180 units changes the average to 110 units per day, what is the value of \(m\)?

Exam Year(s)

GATE AE - 2022,

Answer: C

The value of m is 7.

Total production over m days is 100m. Adding today's 180 units gives m + 1 days averaging 110:

\[ \begin{aligned} 100m + 180 &= 110(m + 1) \\ 180 - 110 &= 110m - 100m \\ m &= 7 \end{aligned} \]

Check: 7 days at 100 is 700, plus 180 is 880, and 880/8 = 110. Writing 110m on the right instead of 110(m + 1) gives m = 18, the first option, and the other options do not satisfy the equation.

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2.

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?

Answer: B

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

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3.

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:

Answer: D

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

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4.

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?

Answer: B

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,
\(\dfrac{x}{2}=20\\ \Rightarrow x = 20 \times 2 = 40\)

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5.

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:

Answer: B

Equal distances each way call for the harmonic mean.

\[ \bar{v} = \frac{2 \times 50 \times 30}{50 + 30} = \frac{3000}{80} = 37.5 \text{ km/hr} \]

The 150 km is not needed - it cancels. The arithmetic mean of 40 would be too high, since more time is spent on the slower return.

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6.

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:

Answer: B

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

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7.

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?

Answer: C

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

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8.

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 \(x\)?

Answer: C

The eleven known numbers sum to

\[ 3+11+7+9+15+13+8+19+17+21+14 = 137 \]

Twelve numbers averaging 12 must total

\[ 12 \times 12 = 144 \]

\[ x = 144 - 137 = 7 \]

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9.

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?

Answer: C

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

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10.

Average of first five multiples of 3 is:

Answer: A

The first five multiples of 3 are 3, 6, 9, 12 and 15 - equally spaced, so the average is the middle one.

\[ \frac{3 + 15}{2} = 9 \]

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