1. A cricketer scored some runs in his 21st innings, as a result, his average runs increased by 3. If the present average run is 40, how many runs he scored in the final innings?

a) 85

b) 103

c) 82

d) 100

Explanation: Let he scored x runs in final innings

Now,

37 × 20 + x = 40 × 21

x = 840 - 740

x = 100

2. Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.

a) 82

b) 89

c) 93

d) 98

Explanation: Total of 80 numbers

= 80 × 42 = 3360

Now, total of 85 numbers

= 85 × 45 = 3825

Hence, sum of 5 numbers

= 3825 - 3360 = 465

Average of five numbers

= $$\frac{{465}}{5}$$ = 93

3. The average age of A, B, C, D and E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is :

a) 46 years

b) 45 years

c) 48 years

d) 42 years

Explanation: A + B + C + D + E = 40 × 5 = 200

A + B = 35 × 2 = 70

C + D = 42 × 2 = 84

Therefore,

E = (A + B + C + D + E) - (A + B + C + D)

E = 200 - 70 - 84

E = 46 years

4. A man travels equal distances of his journey at 40, 30 and 15 km/h. respectively. Find his average speed for whole journey.

a) 24

b) 25

c) 27

d) 28

Explanation: Required average speed,

$$ = {\frac{{\left( {3 \times 40 \times 30 \times 15} \right)}}{{ {\left( {40 \times 30} \right) + \left( {40 \times 15} \right) + \left( {30 \times 15} \right)} }}} $$

$$ = 24\,{\text{km/hr}}$$

5. A batsman makes a score of 270 runs in the 87^{th} inning and thus increase his average by a certain number of runs that is a whole number. Find the possible values of the new average.

a) 12

b) 98

c) 184

d) All of these

Explanation: Part of the runs scored in the 87

^{th}innings will go towards increasing the average of the first 86 innings to the new average and remaining part of the runs will go towards maintaining the new average for the 87

^{th}innings. The only constraint in this problem is that there is increase in average by a whole number of runs. This is possible for all three options.

6. A school has only four classes that contain 10, 20, 30 and 40 students respectively. The pass percentage of these classes are 20%, 30%, 60% and 100% respectively. Find the pass % of the entire school.

a) 76%

b) 66%

c) 56%

d) 34%

Explanation: The number of pass candidates are 2 + 6 + 18 + 40 = 66 out of total 100.

Hence, Pass percentage = 66%

7. One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.

a) $$\frac{{600}}{{53}}$$ km/h

b) $$\frac{{1200}}{{53}}$$ km/h

c) $$\frac{{1800}}{{53}}$$ km/h

d) $$\frac{{1600}}{{53}}$$ km/h

Explanation: Let distance be 120 km

Hence 30 km is covered by 25 kmph and 40 km covered by 30 kmph and rest 50 km has been covered 50 kmph

$$\eqalign{ & {\text{average}} = {\frac{{120}}{{{\text{total}}\,{\text{time}}\,{\text{taken}}}}} \cr & = \frac{{120}}{{\frac{{30}}{{25}} + \frac{{40}}{{30}} + \frac{{50}}{{50}}}} \cr & = \frac{{3600}}{{106}} \cr & = \frac{{1800}}{{53}}\,{\text{km/h}} \cr} $$

8. A man started his journey from Lucknow to Kolkata, which is 200 km, at the speed of 40 kmph then he went to Banglore which is 300 km, at the speed of 20 kmph. Further he went to Ahmedabad which is 500 km, at the speed of 10 kmph. The average speed of the man is :

a) 15.6 kmph

b) 16.1 kmph

c) 14$${\frac{5}{7}}$$ Kmph

d) 14$${\frac{2}{7}}$$ kmph

Explanation:

$$\eqalign{ & {\text{Average}}\,{\text{speed}}, \cr & = {\frac{{{\text{Total}}\,{\text{Distance}}}}{{{\text{Total}}\,{\text{time}}}}} \cr & = {\frac{{ {200 + 300 + 500} }}{{ { {\frac{{200}}{{40}}} + {\frac{{300}}{{20}}} + {\frac{{500}}{{10}}} } }}} \cr & = \frac{{1000}}{{70}} \cr & = 14{\frac{2}{7}}\, \text{kmph} \cr} $$

9. Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 49 yr. How old is E?

a) 45 years

b) 25 years

c) 64 years

d) 40 years

Explanation: Total present age of A, B, C and D

= (45 × 4) + (4 × 5)

= 200 years

Total age present age of A, B, C, D and E

= 49 × 5

= 245 years

So, Age of E = 45 years

10. There are five boxes in cargo hold. The weight of the first box is 200 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box's weight. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.

a) 51.5 kg

b) 75 kg

c) 37.5 kg

d) 112.5 kg

Explanation: The weight of boxes is :

1

^{st}box = 200 kg

2

^{nd}box = 300 kg

3

^{rd}box = 250 kg

4

^{th}box = 350 kg

5

^{th}box = 500 kg

difference between heavier 4 and lighter 4 is 300

difference in average is 75