## Average Questions and Answers Part-9

1. Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:
a) 20
b) 21
c) 28
d) 32

Explanation: Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings.
In the 10th inning, he scored 100 runs then average became (x+8). And he scored (x + 8) × 10 runs in 10 innings.
\eqalign{ & 9x + 100 = 10 \times \left( {x + 8} \right) \cr & 9x + 100 = 10x + 80 \cr & x = 100 - 80 \cr & x = 20 \cr & {\text{New}}\,{\text{average}} = \left( {x + 8} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 28\,{\text{runs}} \cr}

2. The average temperature for Wednesday, Thursday and Friday was 40°C. The average for Thursday, Friday and Saturday was 41° C. If temperature on Saturday was 42° C, what was the temperature on Wednesday?
a) 39° C
b) 44° C
c) 38° C
d) 41° C

Explanation: Average temperature for Wednesday, Thursday and Friday = 40° C
Total temperature = 3 × 40 = 120° C
Average temperature for Thursday, Friday and Saturday = 41° C
Total temperature = 41 × 3 = 123° C
Temperature on Saturday = 42° C
(Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123 - 120;
Saturday - Wednesday = 3
Wednesday = 42 - 3 = 39° C

3. The average of the first five multiples of 9 is:
a) 20
b) 27
c) 28
d) 30

Explanation:
\eqalign{ & {\text{Required}}\,{\text{average}} \cr & = {\frac{{{\text{total}}\,{\text{sum}}\,{\text{of}}\,{\text{multiple}}\,{\text{of}}\,9}}{5}} \cr & = {\frac{{9 + 18 + 27 + 36 + 45}}{5}} \cr & = 27 \cr}
Average of 9 and 45 is also 27.
And average of 18 and 36 is also 27.

4. 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

Explanation:
\eqalign{ & {\text{Average speed}}, \cr & = \frac{{ {2 \times x \times y} }}{{ {x + y} }} \cr & = \frac{{ {2 \times 100 \times 150} }}{{ {100 + 150} }} \cr & = \frac{{ {200 \times 150} }}{{250}} \cr & = 120\,{\text{km/hr}} \cr}

5. Find the average of first 97 natural numbers
a) 47
b) 37
c) 48
d) 49

Explanation: Average of 1st n natural number is given by
$$= \frac{{ {\frac{{ {{\text{n}} \times \left( {{\text{n}} + 1} \right)} }}{2}} }}{{\text{n}}}$$
Average of 1st 97 natural number is given by
\eqalign{ & {\frac{{ {\frac{{ {97 \times \left( {97 + 1} \right)} }}{2}} }}{{97}}} \cr & = 49 \cr}

6. There are two sections A and B of a class, consisting of 36 and 44 students' respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class.
a) 30 kg
b) 35 kg
c) 42.5 kg
d) 37.25 kg

Explanation: The total weight of (36 + 44) Students of A and B,
= (36 × 40 + 44 × 35) kg = 2980 kg.
Average weight of the whole class = $$\frac{{2980}}{{80}}$$ kg
Average weight = 37.25 kg

7. Distance between two stations A and B is 778km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find the average speed of train during the whole journey
a) 60 km/hr
b) 30.5 km/hr
c) 57 km/hr
d) 67.2 km/hr

Explanation:
\eqalign{ & {\text{Average speed}} \cr & = {\frac{{2xy}}{{ {x + y} }}} \,\,{\text{km/hr}} \cr & x = 84{\kern 1pt} \,{\text{kmph}} \cr & y = 56\,{\kern 1pt} {\text{kmph}} \cr & {\text{Average speed}} \cr & = {\frac{{ {2 \times 84 \times 56} }}{{ {84 + 56} }}} \cr & = 67.2\,{\kern 1pt} {\text{kmph}} \cr}

8. The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded, then the average of the remaining numbers is nearly
a) 28.32
b) 29.68
c) 28.78
d) 29.27

Explanation:

Total sum of 48 numbers
= (50 × 30) – (35 +40)
= 1500 – 75
= 1425
Average = $$\frac{{1425}}{{48}}$$ = 29.68

9. The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.
a) 33.25
b) 33.5
c) 34.25
d) 35

Explanation: Total sum of last 4 matches
= (10 × 38.9) - (6 × 42)
= 389 - 252 = 137
Average = $$\frac{{137}}{4}$$ = 34.25

10. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.:
a) 40
b) 39
c) 52
d) 55

Explanation: Let the average after 17th innings = x
Then average after 16th innings = (x - 3)
16 × (x - 3) + 87 = 17x
x = 39