Practice MCQ Questions and Answer on Average

11.

The speed of the train going from Nagpur to Allahabad is 100 km/h while when coming back from Allahabad to Nagpur, its speed is 150 km/h. find the average speed during whole journey.

(A) 125 km/hr
(B) 75 km/hr
(C) 135 km/hr
(D) 120 km/hr

Solution: $\begin{aligned} Average speed, \\ = \frac{2 \times x \times y}{x + y} \\ = \frac{2 \times 100 \times 150}{100 + 150} \\ = \frac{200 \times 150}{250} \\ = 120 km/hr \end{aligned}$

12.

The difference between two angles of a triangle is 24ÃÂÃÂÃÂÃÂ°. The average of the same two angles is 54ÃÂÃÂÃÂÃÂ°. Which one of the following is the value of the greatest angle of the triangle?

(A) 45°
(B) 60°
(C) 66°
(D) 72°

Solution: Let a and b be the two angles in the question, with a > b. We are given that the difference between the angles is 24°. ⇒ a – b = 24 Since the average of the two angles is 54°, we have $\frac{a + b}{2}$ = 54 Solving for b in the first equation yields b = a – 24, and substituting this into the second equation yields, $\frac{{a + (a - 24)}}{2} = 54$ 2a − 24 = 54 × 2 2a − 24 = 108 2a = 108 + 24 2a = 132 a = 66 Also, b = a − 24 = 66 − 24 = 42 Now, let c be the third angle of the triangle. Since the sum of the angles in the triangle is 180°, a + b + c = 180° Putting the previous results into the equation yields 66 + 42 + c = 180° Solving for c yields c = 72° Hence, the greatest of the three angles a, b and c is c, which equal.

13.

The average weight of three boys A, B and C is $54 \frac{1}{3}$ kg, while the average weight of B, D and E is 53 kg. What is the average weight of A, B, C, D and E?

(A) 52.4 kg
(B) 53.2 kg
(C) 53.8 kg
(D) Data inadequate

Solution: Total weight of (A + B + C) =( $54 \frac{1}{3}$ × 3 ) kg= 163 kgTotal weight of (B + D + E)= (53 × 3) kg= 159 kg Adding both, we get: = A + 2B + C + D + E = (163 + 159) kg= 322 kg So, to find average weight of A, B, C, D and E, we ought to know B's weight, which is not given. So, the data is inadequate.

14.

The average age of 10 children is 9 years 9 months. The average of 9 children is 8 years 11 months. What is the age of the tenth child ?

(A) 17 years 3 months
(B) 18 years 4 months
(C) 17 years 5 months
(D) 18 years 3 months

Solution: Average age of 10 children = 9 years 9 months Sum of ages of 10 children = 9 × 10 + $\frac{9}{12}$ × 10 = $\frac{390}{4}$ Average age of 9 children = 8 years 11 months Sum of age of 9 children = 8 × 9 + $\frac{11}{12}$ × 9 = $\frac{321}{4}$ Age of 10th child = $\frac{390}{4}$ - $\frac{321}{4}$ = $\frac{69}{4}$ = 17 years 3 months

15.

What is the average of first 93 natural numbers?

(A) 45
(B) 46
(C) 47
(D) 49

Solution: Average of first 'n' natural number $\begin{aligned} = \frac{(n + 1)}{2} \\ = \frac{93 + 1}{2} \\ = 47 \end{aligned}$

16.

A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What was the difference of the two digits a and b?

(A) 8
(B) 6
(C) 2
(D) 4

17.

The mean of 9 observation is 16. One more observation is included and the new mean becomes 17. The 10^th observation is :

(A) 9
(B) 16
(C) 26
(D) 30

18.

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

(A) 35 km/hr
(B) 37 km/hr
(C) 37.5 km/hr
(D) 40 km/hr

Solution: Average speed $\begin{aligned} = (\frac{2 x y}{x + y}) km/hr \\ = (\frac{2 \times 50 \times 30}{50 + 30}) km/hr \\ = 37.5 km/hr \end{aligned}$

19.

The mean monthly salary paid to 75 workers in a factory is Rs. 5680. The mean salary of 25 of them is Rs. 5400 and that of 30 others is Rs. 5700. The mean salary of the remaining workers is-

(A) Rs. 5000
(B) Rs. 6000
(C) Rs. 7000
(D) Rs. 8000

Solution: Required average $= Rs .$ $[\frac{(5680 \times 75) - {(5400 \times 25) + (5700 \times 30)}}{75 - (25 + 30)}]$ $= Rs . [\frac{426000 - (135000 + 171000)}{20}]$ $\begin{aligned} = Rs . (\frac{120000}{20}) \\ = Rs . 6000 \end{aligned}$

20.

If the average of 5 consecutive integers is x then, find the average of next to next 5 consecutive integers.

(A) x + 5
(B) x + 15
(C) x + 10
(D) x + 25

Solution: $\begin{aligned} Let numbers be a, a + 1, a + 2, a + 3, a + 4 \\ Next, a + 5, a + 6, a + 7, a + 8, a + 9 \\ Next to Next, a + 10, a + 11, a + 12, a + 13, a + 14 \\ I^{st} condition = \frac{5 a + 10}{5} = x \\ 5 a + 10 = 5 x . . . . . . (i) \\ I I^{nd} condition \\ = \frac{a + 10 + a + 11 + a + 12 + a + 13 + a + 14}{5} \\ = \frac{5 a + 50 + 10}{5} \\ From equation (i) \\ = \frac{5 x + 50}{5} \\ = x + 10 \end{aligned}$

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Practice MCQ Questions and Answer on Average

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