Problems on Averages - Aptitude Questions and Answers Part 3

11. Average of 3rd and 5th number in 5 consecutive number is 12. Find the sum of 5 numbers.

a. 10.25
b. 22.5
c. 50
d. 55

Answer: d. 55

Explanation:

Average=Sum of Observations
Number of Observations


Let first of the 5 consecutive numbers be N.
So the 5 numbers will be,
N, N+1, N+2, N+3, N+4

Also,
Average of 3rd and 5th =(N+2)+(N+4)=12
2
∴  N =18
2
Sum = N+(N+1)+(N+2)+(N+3)+(N+4) = 5N+10 = 55


12. Rajat carried two types of pens with him. The ratio of cost of Pen A : Pen B was 10:4. There were two pens of type B with him and the average cost of all the three pens together was Rs 60/-. Find the cost of Pen A.

a. Rs 72/-
b. Rs 75/-
c. Rs 100 /-
d. Rs 150/-

Answer: c. Rs 100 /-

Explanation:

Total cost of 3 pens = 3 x 60 = Rs 180/- .

Ratio of cost of Pen A : Pen B = 10:4

Let K be common factor.

So, Cost of Pen A = 10K; Cost of both Pen B = 4K (As they are similar)

∴ 10K + 4K + 4K = 180

∴  K = 10

Cost of Pen A will be = 10K = Rs 100/-


13. There are some history books and some geography books in a library. The books that were read were read cover to cover. The average number of pages read for all these books is 158. If the average number of pages read for history books is 164 and that for geography books is 154, find the ratio of no. of history books to that of geography books.

a. 2:3
b. 3:2
c. 3:5
d. 5:3
e. 77:82
                                                                                                                                                                                                                                  

Answer: a. 2:3

Explanation:

This problem becomes easier when we treat this as problem of mixture and alligation.

Ratio can directly be found out by following subtractions:-

All books average - Geography books average = History books Ratio
∴ 158 - 154 = 4 = History books Ratio

History books average - All books pages average = Geography books Ratio
∴ 164 - 158 = 6 = Geography books Ratio

Ratio of History books to Geography books = 4:6 = 2:3

Tip: Diagrammatically it is easier

average 13


14. Rishabh's current average of runs is 64. He wanted it to be 66 and this could have been achieved if he had scored 22 runs more in all his innings put together. How many innings has he played till now?

a. 10
b. 11
c. 12
d. 15

Answer: b. 11

Explanation:

Let number of innings be N.

Since increase in average is by 2 runs (from 64 to 66), runs in each innings would increase by 2 runs

Total increase in runs = 2 x N = 2N

Also, Rishabh needs to score 22 runs more to increase average.

∴ 2N = 22

∴ N = 11 = Number of innings


15. In a big joint family of 42 people, the difference between the ages of Great Grandfather and Great Grandson is 100 years. Leaving these two members out, the average age of remaining members is 28 years. The average age of the family otherwise is 30 years. Find the age of the Great  Grandfather.

a. 101 years
b. 103 years
c. 115 years
d. 120 years

Answer: d. 120 years

Explanation:

Total age of all people of group = 42 x 30

Total of age of 40 people = 40 x Average age of 40 people = 40 x 28

If Great Grandson is 'N' years old, Great Grandfather is '100+N' years old.

∴ N + (100+N) + (40 x 28) = 42 x 30

∴ N = 20

The Great Grandfather is 100+N = 100 + 20 = 120 years old

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