## Results

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### #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:

Solution:
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.
Now,

9x 100=10×(x 8) or,

9x 100=10x 80 or,

x=10080 or,

x=20

New average=(x 8)=28runs

### #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?

Solution:

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
Now,
(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:

Solution:
Required average
= (total sum of multiple of 9/5)
= (9 18 27 36 45/5)
= 27 Required average
= (total sum of multiple of 95)
= (9 18 27 36 455) = 27

Note that, 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.

Solution:
Average speed,
= (2×x×y) / (x y)
= (2×100×150) / (100 150)
= (200×150) / 250
= 120km/hr

### #5. Find the average of first 97 natural numbers.

Solution:

1st Method:
Average of 1st n natural number is given by

= ([n×(n 1)] / 2) / n

= ([n×(n 1)]2) / n

Average of 1st 97 natural number is given by

= ([97×(97 1)] / 2) / 97)
= 49{([97×(97 1)] / 2)97}
= 49

2st Method:

These numbers are in AP series so average.

= (sum of corresponding term) / 2
= (1 97) / 2=49
or, (2 96) / 2=49
or, (3 95) / 2=49
And so on.
=(sum of corresponding term) / 2
=(1 97) / 2=49
or, (2 96) / 2=49
or, (3 95) / 2=49
And so on.

### #6. The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is

Solution:

Sum of ages of three boys = 45 years
Now, (3x 5x 7x) = 45
⇒ 15x = 45
⇒ x = 3
So, age of youngest boy = 3x
= 3 × 3
= 9 years

### #7. The average of a group of men is increased by 5 years when a person aged of 18 years is replaced by a new person of aged 38 years. How many men are there in the group?

Solution:

Let N be the no. of persons in the group.
Required number of person is given by;
Member in group × aged increased = difference of replacement
N × 5 = 38 – 18
Or, 5N = 20
Or, N = 4

### #8. In a boat there are 8 men whose average weight is increased by 1 kg when 1 man of 60 kg is replaced by a new man. What is weight of new comer?

Solution:

Member in group × age increased = difference of replacement
Or, 8 × 1 = new comer – man going out
Or, new comer = 8 60;
Or, new comer = 68 years.

### #9. The average of 25 results is 18. The average of first 12 of those is 14 and the average of last 12 is 17. What is the 13th result?

Solution:

Sum of 1st 12 results = 12 × 14
Sum of last 12 results = 12 × 17
13th result = x (let)
Now,
12 × 14 12 × 17 x = 25 × 18
Or, x = 78