### Ques 1

**In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?**

#### Solution

→ Runs scored in the first 10 overs = 3.2*10 = 32

→ Remaining runs to be scored = 282-32=250

→ Run rate = 250/40 =6.25

So, the

→ Remaining runs to be scored = 282-32=250

→ Run rate = 250/40 =6.25

So, the

**required run rate in the remaining 40 overs is 6.25.**### Ques 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?**

#### Solution

→ Let X be the sale in 6th month

→ (6435+ 6927+ 6855+7230 +6562+X)/6=6500

→ 6435+ 6927+ 6855+7230 +6562+X = 6*6500

→ X= 4991

Solving the above equation,

→ (6435+ 6927+ 6855+7230 +6562+X)/6=6500

→ 6435+ 6927+ 6855+7230 +6562+X = 6*6500

→ X= 4991

Solving the above equation,

**we get 4991 as the sale in the 6th month.**### Ques 3.

**The average of 20 numbers is zero. Of them, how many of them may be greater than zero, at the most?**

#### Solution

→ Average of 20 numbers is 0.

→ Sum of 19 positive number is X.

→ 20th number be -X.

→ So, the average is 0.

→ Sum of 19 positive number is X.

→ 20th number be -X.

→ So, the average is 0.

**19 numbers are positive.**### Ques 4.

**The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team.**

#### Solution

→ Average age of the team is X.

→ Sum of the age of all the 11 members = 11X

→ Age of captain = 26

→ Age of wicket keeper = 29

→ Average age of 9 remaining members = (11X – (26+29))/9 = (X-1)

→ Solving this we get

→ Sum of the age of all the 11 members = 11X

→ Age of captain = 26

→ Age of wicket keeper = 29

→ Average age of 9 remaining members = (11X – (26+29))/9 = (X-1)

→ Solving this we get

**X = 23 years.**### Ques 5.

**The library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with a Sunday?**

#### Solution

→ In a month of 30 days beginning with a Sunday, there will be 4 complete weeks and another two days which will be Sunday and Monday.

→ Hence there will be 5 Sundays and 25 remaining days in a month begin with Sunday.

→ Average visitors in a month of 30 days = (510*5) + (240*25)/30 = 285.

So, the

→ Hence there will be 5 Sundays and 25 remaining days in a month begin with Sunday.

→ Average visitors in a month of 30 days = (510*5) + (240*25)/30 = 285.

So, the

**average visitors in a month of 30 days is 28**### Ques 6.

**The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. What is the present age of the husband?**

#### Solution

→ 3 years ago, (husband – 3) + (wife – 3) + (child -3) = 27*3 = 81

→ Husband + wife +child = 90

→ 5 years ago, (wife – 5) + (child – 5) = 20*2 = 40

→ Wife + child = 50

→ Husband + 50 = 90

→ Husband = 40 years

Hence

→ Husband + wife +child = 90

→ 5 years ago, (wife – 5) + (child – 5) = 20*2 = 40

→ Wife + child = 50

→ Husband + 50 = 90

→ Husband = 40 years

Hence

**husband’s present age is 40 years.**### Ques 7.

**The average weight of 8 person’s increases by 2.5 kg when a new person comes in place of one of them weighing 65kg. What is the weight of the new person?**

#### Solution

→ New person age = old person age + (increase in average * total number of person’s)

→ 65 + (2.5 *8)

→ 65 + 20

→ 65 + (2.5 *8)

→ 65 + 20

**New person’s age = 85 years**### Ques 8.

**A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?**

#### Solution

→ Average runs scored in 17th innings be X.

→ Total runs scored in 17th innings be 17X.

→ Average runs scored after 16th innings be (X-3)

→ Total runs scored in 16th innings = 16(X-3)

→ Total runs scored in 16th innings + 87 = 17th innings

→ 16(X-3) + 87 = 17X

→ X= 39

→ Total runs scored in 17th innings be 17X.

→ Average runs scored after 16th innings be (X-3)

→ Total runs scored in 16th innings = 16(X-3)

→ Total runs scored in 16th innings + 87 = 17th innings

→ 16(X-3) + 87 = 17X

→ X= 39

**Average after 17th innings is 39.**### Ques 9.

**The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. Find out the teacher’s age in years?**

#### Solution

→ After including teacher number of person’s is 37 and average is added by one. So, 14+1=15.

36 14

Difference is +1 Difference is +1

37 15

→ (36*1) +(15*1) = 51 years.

So,

Difference is +1 Difference is +1

37 15

→ (36*1) +(15*1) = 51 years.

So,

**the age of the teacher is 51 years.**### Ques 10.

**Suresh drives his car to a place of 150 km away at an average speed of 50 km/hr and returns at 30km/hr. What is the average speed for the whole journey?**

#### Solution

→ Average speed = (2*x*y)/(x+y)

Where x = 50km/hr

→ Y = 30km/hr

→ 2*50*30/ 50+30

→ 37.5 km/hr

Where x = 50km/hr

→ Y = 30km/hr

→ 2*50*30/ 50+30

→ 37.5 km/hr

**The average speed for the whole journey is 37.5km/hr.**
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