Aptitude : Problems on Average

(1) In the first 15 overs of a cricket game, the run rate was only 4.1. What should be the run rate in the remaining 35 overs to reach the target of 350 runs?

• (a)9.25 runs per over
• (b)8.24 runs per over
• (c)4.45 runs per over
• (d)8.55 runs per over

Answer

Correct Answer : (b) 8.24 runs per over
In the first 15 overs, the team scored 4.1 * 15 = 61.5 runs.
To reach the target of 350 runs, the team needs to score 350 – 61.5 = 288.5 runs in the remaining 35 overs.
Therefore, the required run rate is 288.5 / 35 = 8.24 runs per over.
This is a very high run rate and will be difficult to achieve. The team will need to score boundaries regularly and avoid losing wickets.

(2) A family consists of three grandparents, two parents and four grandchildren. The average age of the grandparents is 70 years, that of the parents is 40 years and that of the grandchildren is 10 years. What is the average age of the family?

• (a)35.5 years
• (b)36.25 years
• (c)37.5 years
• (d)36.7 years

Answer

Correct Answer : (d) 36.7 years
The total number of people in the family is 3 grandparents + 2 parents + 4 grandchildren = 9 people.
The total age of the grandparents is 3 x 70 = 210 years.
The total age of the parents is 2 x 40 = 80 years.
The total age of the grandchildren is 4 x 10 = 40 years.
The total age of the family is 210 years + 80 years + 40 years = 330 years.
The average age of the family is 330 years / 9 people = 36.7 years.
Here is a summary of the steps:
Total number of people in the family = 9
Total age of the grandparents = 210 years
Total age of the parents = 80 years
Total age of the grandchildren = 40 years
Total age of the family = 330 years
Average age of the family = 36.7 years

(3) A shopkeeper has a sale of Rs. 7435, Rs. 7927, Rs. 7855, Rs. 8230 and Rs. 7562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500?

• (a)5991 rupees
• (b)6552 rupees
• (c)5520 rupees
• (d)5458 rupees

Answer

Correct Answer : (a) 5991 rupees
To find out how much sale the shopkeeper must have in the sixth month to achieve an average sale of Rs. 7500, we need to calculate the total sales for the first five months and then determine the sixth-month sale.
Given sales for the first five months:
1st month: Rs. 7435
2nd month: Rs. 7927
3rd month: Rs. 7855
4th month: Rs. 8230
5th month: Rs. 7562
To find the total sales for the first five months, we sum up the sales for each month:
Total sales for the first five months = 7435 + 7927 + 7855 + 8230 + 7562
Total sales for the first five months = Rs. 39009
Now, let’s assume the sale in the sixth month as ‘x’.
To achieve an average sale of Rs. 7500, the total sales for all six months should be equal to the average sale multiplied by the total number of months (6):
Total sales for six months = Average sale × Total number of months
7500 × 6 = 45000
To find the sale in the sixth month, we subtract the total sales for the first five months from the desired total sales for six months:
x = Total sales for six months – Total sales for the first five months
x = 45000 – 39009
x ? Rs. 5991
Therefore, the shopkeeper must have a sale of approximately Rs. 5991 in the sixth month to achieve an average sale of Rs. 7500.

(4) The captain of a football team of 11 members is 28 years old and the goalkeeper is 2 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. What is the average age of the team?

• (a)28.59 years
• (b)27.5 years
• (c)26.85 years
• (d)24.5 years

Answer

Correct Answer : (a) 28.59 years
Let’s assume the sum of ages of the remaining 9 players (excluding the captain and the goalkeeper) is S.
According to the given information:
The captain’s age is 28.
The goalkeeper’s age is 28 + 2 = 30.
The average age of the remaining players is one year less than the average age of the whole team. This means that the average age of the remaining 9 players is (average age of the whole team – 1).
We know that the sum of ages of the whole team is equal to the sum of ages of the captain, goalkeeper, and the remaining players.
Sum of ages of the whole team = Sum of ages of captain + Sum of ages of goalkeeper + Sum of ages of remaining players
Let’s express it mathematically:
11 × (Average age of the whole team) = 28 + 30 + S
Now, we can express the average age of the whole team in terms of S:
Average age of the whole team = (28 + 30 + S) / 11
According to the given information, the average age of the remaining 9 players is (average age of the whole team – 1):
(S / 9) = [(28 + 30 + S) / 11] – 1
Let’s solve the above equation to find the value of S:
(S / 9) = [(58 + S) / 11] – 1
Multiply both sides of the equation by 9 and 11 to eliminate the denominators:
11S = 9(58 + S) – 9
11S = 522 + 9S – 9
2S = 513
S = 513 / 2
S = 256.5
Therefore, the sum of ages of the remaining 9 players (excluding the captain and goalkeeper) is 256.5.
To find the average age of the team, we need to calculate the sum of ages of all 11 players (including the captain and goalkeeper).
Sum of ages of the whole team = Sum of ages of captain + Sum of ages of goalkeeper + Sum of ages of remaining players
Sum of ages of the whole team = 28 + 30 + 256.5
Sum of ages of the whole team = 314.5
Finally, we can calculate the average age of the team by dividing the sum of ages of the whole team by the total number of players:
Average age of the team = Sum of ages of the whole team / Total number of players
Average age of the team = 314.5 / 11
Average age of the team ? 28.59
Therefore, the average age of the team is approximately 28.59 years.

(5) A bike owner buys petrol at Rs.8.50, Rs. 9 and Rs. 9.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 5000 each year?

• (a)9.25 Rs. per litre.
• (b)8.98 Rs. per litre.
• (c)8.55 Rs. per litre.
• (d)7.89 Rs. per litre.

Answer

Correct Answer : (b) 8.98 Rs. per litre.
If the bike owner spends Rs. 5000 each year on petrol, the quantity of petrol he bought each year would be:
In the first year, he bought 5000 / 8.50 = 588.24 litres approximately.
In the second year, he bought 5000 / 9.00 = 555.56 litres approximately.
In the third year, he bought 5000 / 9.50 = 526.32 litres approximately.
Therefore, the total quantity of petrol he bought over the three years is approximately 588.24 + 555.56 + 526.32 = 1670.12 litres.
The total amount of money he spent over the three years is Rs. 5000 * 3 = Rs. 15000.
The average cost per litre of petrol over the three years would be the total money spent divided by the total quantity of petrol, which is approximately 15000 / 1670.12 = Rs. 8.98 per litre.