Average Questions and Answers

Q: 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:

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.

Q: 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 \(x\)?

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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41.

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:

A.36.5 km/hr
B.37.5 km/hr
C.35.5 km/hr
D.34.5 km/hr

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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42.

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:

A.53.33
B.54.68
C.55
D.None of these

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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43.

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?

A.2000
B.3000
C.4000
D.5000

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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44.

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 \(x\)?

A.12
B.5
C.7
D.9

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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45.

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?

A.75 Kg
B.50 Kg
C.85 Kg
D.80 Kg

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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46.

Average of first five multiples of 3 is:

A.9
B.11
C.13
D.15

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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47.

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:

A.280
B.285
C.290
D.295

Answer: B

As the month begin with Sunday, so there will be five Sundays in the month. So result will be:
\(= \left (\dfrac{510 \times 5 + 240 \times 25}{30}\right)\\ = \left( \dfrac{8550}{30} \right)\\ = 285\)

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48.

A batsman makes a score of 87 runs in the 17th match and thus increases his average by 3. Find his average after 17th match.

A.36
B.37
C.38
D.39

Answer: D

Let the average after 17th match is \(x\)
Then the average before 17th match is \(x-3\)
So,
\(16(x-3) + 87 = 17x\\ \Rightarrow x = 87 - 48 = 39\)

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