Average

Average ( SET 2 : Q6-Q10 )

6. The average age of 3 people is 46 years. When another man joins the group, the average reduces to 42 years. Now, another woman with age 4 years more than the new man replaces one of the first three people. The average age of these 4 is then 40 years. What is the age of the replaced person?
1
21
2
34
3
42
Correct Answer
4
None of the above

Solution: 3

Total age of first 3 people = 46 × 3 = 138

Let the age of the fourth man be x

⇒ (138 + x)/4 = 42

⇒ x = 30 years

Age of the new man is 30 years. Age of woman is 4 years more than this man

⇒ Age of woman = 34 years

Woman replaces one of the first three people.

Let the age of this replaced person be y

⇒ Age of the remaining two person = 138 – y

⇒ Sum of age of the man and woman = 34 + 30 = 64

⇒ New average = (64 + 138 – y)/4

⇒ 40 = (202 – y)/4

⇒ 160 = (202 – y)

∴ y = 42 years

7. The average revenues of 11 consecutive years of a company is Rs. 77 lakhs. If the average of first 6 years is Rs. 72 lakhs and that of last 6 years is Rs. 84 lakhs, What is the revenue for the sixth year.
1
Rs. 91 lakhs
2
Rs. 87 lakhs
Incorrect
3
Rs. 85 lakhs
4
Rs. 89 lakhs
Correct Answer


Solution: 4
Average revenue for 11 years = Sum of all revenues/11

⇒ 77L = Sum/11

⇒ Sum of revenues for 11 years = 77 × 11 = 847L

Average revenue for first 6 years = Sum of revenues for first 6 years/6

⇒ 72L = Sum of revenues for first 6 years/6

⇒ Sum of revenues of first 6 years = 72 × 6 = 432L

Similarly, Sum of revenues for last 6 years = 84 × 6 = 504L

⇒ Sum of revenues for first 5 years = total sum – sum of revenues of last 6 years

⇒ Sum of revenues for first 5 years = 847 – 504 = 343L

⇒ Revenue in the 6th year = Sum of revenues in first 6 years – sum of revenues in first 5 years

∴ Revenue for 6th year = 432 – 343 = 89 Lakhs

 

The sum of revenues for the first six years = 6 × 72 = 432 lakhs 

The sum of revenues for the last six years = 6 × 84 = 504 lakhs

And the sum of revenues for 11 years = 11 × 77 = 847 lakhs

So, the revenue of sixth year is 432 + 504 - 847 = 89 lakhs 

∴ the required revenue of sixth year is 89 lakhs 


8. The arithmetic mean of the scores of a group of students in a test was 64. The brightest 15% of them secured a mean score of 90 and the dullest 20% secured a mean score of 28. The mean score of remaining 65% is:

1
58.63
2
66.09
3
44.89
4
69.07
Correct Answer

Solution: 4

Given:

Arithmetic mean of scores of all students = 64

Average of brightest 15%  of students = 90

Average of dullest 20% of students = 28

Formula Used:

Average = Sum of observations/Number of observations

Calculation:

Let the total number of students be 100

According to the question

⇒ Average of 100 students = 64

⇒ Total score of 100 students = 64 × 100 = 6400

Then,

⇒ Total score of first 15 students = 15 × 90 = 1350

⇒ Total score of last 20 students = 20 × 28 = 560

⇒ Total score of remaining 65 students = 6400 – (1350 + 560)

⇒ 4490

∴ Average of 65 students = 4490/65 = 69.07


9. There are 500 seats in a classroom placed in a similar row. After the reconstruction of the classroom, the total number of seats became 10% less. The number of rows was reduced by 5 but each row contained 5 seats more than before. How many rows and how many seats in a row were there initially in the classroom?
1
20 rows 25 seats
Correct Answer
2
25 rows 20 seats
3
50 rows 10 seats
4
10 rows 50 seats

Solution: 1

Let there are x rows and number of seats in each row is y

So, according to the question,

⇒ xy = 500

Also, after the reconstruction of classroom,

The seats became 10% less than before

⇒ 500 – 10% of 500 = 500 – 50 = 450

⇒ (x – 5) (y + 5) = 450

⇒ xy + 5x – 5y – 25= 450

Putting the value of xy, we get,

⇒ 500 + 5x – 5y = 475

⇒ y – x = 5

⇒ y = x + 5

So,

⇒ x (x + 5) = 500

⇒ x2 + 5x – 500 = 0

⇒ x2 + 25x – 20x – 500 = 0

⇒ (x + 25) (x – 20) = 0

⇒ x = 20, -25

Since, -25 is not possible

⇒ x = 20

⇒ y = 25

∴ Number of rows are 20 and number of seats are 25



10 . A truck owner buys petrol at Rs. 6.50, Rs. 7 and Rs. 7.50 per litre for three successive years. What approximately will be the average cost per litre of petrol if he spends Rs. 3200 each year?
1
6.1
2
6.23
Incorrect
3
6.97
Correct Answer
4
7.12


Solution: 3

⇒ Amount spend yearly on petrol = Rs. 3200

⇒ Total amount of petrol consumed = (3200/6.50) + (3200/7) + (3200/7.50) = 1376.11 litres

⇒ Total amount spent in 3 years on petrol = 3200 × 3 = Rs. 9600

⇒ Average cost per litre of petrol = Total amount spent in 3 years on petrol/ Total amount of petrol consumed

⇒ Average cost per liter of petrol = 9600/1376.11 = 6.97

∴ Average cost per liter of petrol is Rs. 6.97

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