Aptitude : Problems on Average

(16) The average of 6 numbers is 8. If the average of four of these numbers is 5, what is the average of the other two numbers?

• (a)11
• (b)14
• (c)25
• (d)31

Answer

Correct Answer : (b) 14
The total sum of the six numbers is the average times the number of values, or 6 * 8 = 48.
The total sum of the four numbers with an average of 5 is 4 * 5 = 20.
The total sum of the remaining two numbers is the total sum of all six numbers minus the sum of the first four numbers, or 48 – 20 = 28.
Therefore, the average of the remaining two numbers is their total sum divided by the number of values, or 28 / 2 = 14.

(17) The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, what is the price of the cheapest item?

• (a)8500 Rs
• (b)7500 Rs
• (c)9000 Rs
• (d)10000 Rs

Answer

Correct Answer : (c) 9000 Rs
The total price of the three items of furniture is 15000 x 3 = 45000.
The prices of the three items are in the ratio 3:5:7. This means that the prices of the items are 3x, 5x, and 7x, where x is a constant.
The total price of the three items is 3x + 5x + 7x = 15x.
Therefore, 15x = 45000
This means that x = 3000.
The price of the cheapest item is 3x = 3 x 3000 = 9000.
Therefore, the price of the cheapest item is Rs. 9000.

(18) The average score of a batsman in 13 innings is 42 runs. If his highest score, which is 102 runs, is not included, what is his average score for the remaining 12 innings?

• (a)35 Runs
• (b)36 Runs
• (c)38 Runs
• (d)37 Runs

Answer

Correct Answer : (d) 37 Runs
The total score of the batsman in 13 innings is 13 x 42 = 546 runs.
The total score of the batsman in 12 innings, excluding his highest score of 102 runs, is 546 – 102 = 444 runs.
Therefore, the average score of the batsman for the remaining 12 innings is 444/12 = 37 runs.

(19) The average of five numbers is 27. If one number is excluded, the average becomes 25. What is the excluded number?

• (a)30
• (b)33
• (c)35
• (d)31

Answer

Correct Answer : (c) 35
The total sum of the five numbers is the average times the number of values, or 27 * 5 = 135.
When one number is excluded, there are 4 numbers left with an average of 25. So, the sum of these 4 numbers is 25 * 4 = 100.
The excluded number is the total sum of all five numbers minus the sum of the remaining four numbers, or 135 – 100 = 35.
So, the excluded number is 35.

(20) The average height of 25 boys in a class is 150 cm. When 5 boys leave the class, the average height decreases by 2 cm. What is the average height of the 5 boys who left?

• (a)158 cm
• (b)150 cm
• (c)160 cm
• (d)151 cm

Answer

Correct Answer : (a) 158 cm
The average height of 25 boys is 150 cm. Therefore, the total height of the 25 boys is 25 x 150 = 3750 cm.
When 5 boys leave the class, the average height decreases by 2 cm. Therefore, the average height of the 20 boys is 148 cm. Therefore, the total height of the 20 boys is 20 x 148 = 2960 cm.
The total height of the 5 boys who left is 3750 – 2960 = 790 cm. Therefore, the average height of the 5 boys who left is 790 / 5 = 158 cm.