# Average Aptitude Questions, Answers with Solutions:

#### Overview:

 Questions and Answers Type: MCQ (Multiple Choice Questions). Main Topic: Quantitative Aptitude. Quantitative Aptitude Sub-topic: Average Aptitude Questions and Answers. Number of Questions: 10 Questions with Solutions.

1. Find the average of prime numbers between $$10$$ and $$20 \ ?$$

1. $$18$$
2. $$16$$
3. $$17$$
4. $$15$$

Answer: (d) $$15$$

Solution: Prime numbers between $$10$$ and $$20$$ = $$11, 13, 17, 19$$, then $$Average = \frac{11 + 13 + 17 + 19}{4}$$ $$= \frac{60}{4} = 15$$

1. If a man received salary of $$20,000 \ Rs.$$ in first quarter of the year, $$30,000 \ Rs.$$ in second quarter of the year, $$50,000 \ Rs.$$ in third quarter of the year and $$70,000 \ Rs.$$ in last quarter of the year. Find the average salary of the man for whole year?

1. $$43,000$$
2. $$42,000$$
3. $$43,500$$
4. $$42,500$$

Answer: (d) $$42,500$$

Solution: $$Average = \frac{20,000 + 30,000 + 50,000 + 70,000}{4}$$ $$= \frac{170,000}{4} = 42,500 \ Rs.$$

1. If the ratio of age of two friends is $$3 : 5$$ and after $$2$$ years ratio of their age becomes $$4 : 6$$ then find the present age of friends and average age of the friends after five years?

1. Present age $$6$$ and $$10$$ years, average age after five years is $$13$$ years
2. Present age $$8$$ and $$12$$ years, average age after five years is $$15$$ years
3. Present age $$6$$ and $$13$$ years, average age after five years is $$12$$ years
4. Present age $$6$$ and $$11$$ years, average age after five years is $$13$$ years

Answer: (a) Present age $$6$$ and $$10$$ years, average age after five years is $$13$$ years.

Solution: Let the present age of the friends are $$3x$$ and $$5x$$.

then ages after $$2$$ years $$\frac{3x + 2}{5x + 2} = \frac{4}{6}$$ $$18x + 12 = 20x + 8$$ $$x = 2$$ The present age of the friends are $$6$$ years and $$10$$ years.

After $$2$$ years the age of the friends will be $$8$$ years and $$12$$ years.

After $$5$$ years the age of the friends will be $$6 + 5 = 11$$ years and $$10 + 5 = 15$$ years.

The average age of the friends after $$5$$ years $$= \frac{11 + 15}{2} = \frac{26}{2} = 13 \ years$$

1. Find the average of first $$20$$ natural numbers?

1. $$13.5$$
2. $$11.5$$
3. $$10.5$$
4. $$12.5$$

Answer: (c) $$10.5$$

Solution: Sum of the first $$n$$ natural numbers $$= \frac{n \ (n + 1)}{2}$$ $$= \frac{20 \ (20 + 1)}{2} = \frac{20 \times 21}{2}$$ $$= \frac{420}{2} = 210$$ $$Average = \frac{210}{20} = 10.5$$

1. Find the average of all prime numbers between $$20$$ and $$30 \ ?$$

1. $$25$$
2. $$26$$
3. $$28$$
4. $$24$$

Answer: (b) $$26$$

Solution: Prime numbers between $$20$$ to $$30$$ = $$23, 29$$. Then $$Average = \frac{23 + 29}{2} = \frac{52}{2} = 26$$

1. Find the average of first $$50$$ odd natural numbers?

1. $$45$$
2. $$48$$
3. $$50$$
4. $$49$$

Answer: (c) $$50$$

Solution: Sum of first $$n$$ natural numbers $$S_n = n^2$$, then $$S_{50} = (50)^2 = 2500$$ $$Average = \frac{2500}{50} = 50$$

1. Find the average of first $$70$$ even natural numbers?

1. $$70$$
2. $$71$$
3. $$72$$
4. $$73$$

Answer: (b) $$71$$

Solution: Sum of first $$n$$ even natural numbers $$S_n = n \ (n + 1)$$, then $$S_{70} = 70 \ (70 + 1) = 70 \times 71 = 4970$$ $$Average = \frac{4970}{70} = 71$$

1. Find the average of squares of first $$20$$ natural numbers?

1. $$142.3$$
2. $$143.5$$
3. $$141.5$$
4. $$140.3$$

Answer: (b) $$143.5$$

Solution: Sum of squares of first $$n$$ natural numbers, $$S_n = \frac{n \ (n + 1) \ (2n + 1)}{6}$$ $$S_{20} = \frac{20 \ (20 + 1) \ (40 + 1)}{6}$$ $$= \frac{20 \times 21 \times 41}{6}$$ $$= \frac{17220}{6} = 2870$$ $$Average = \frac{2870}{20} = 143.5$$

1. Find the average of cubes of first $$15$$ natural numbers?

1. $$850$$
2. $$900$$
3. $$955$$
4. $$960$$

Answer: (d) $$960$$

Solution: Sum of cubes of first $$n$$ natural numbers, $$S_n = \left[\frac{n \ (n + 1)}{2}\right]^2$$ $$S_{15} = \left[\frac{15 \ (15 + 1)}{2}\right]^2$$ $$= \left(\frac{15 \times 16}{2}\right)^2$$ $$= (120)^2 = 14,400$$ $$Average = \frac{14,400}{15} = 960$$

1. A train going from Delhi to Kanpur at the speed of $$60 \ km/hr$$ and returns from Kanpur to Delhi at the speed of $$80 \ km/hr$$. Find the average speed of the train during the whole journey?

1. $$67.57 \ km/hr$$
2. $$68.57 \ km/hr$$
3. $$69.57 \ km/hr$$
4. $$70.52 \ km/hr$$

Answer: (b) $$68.57 \ km/hr$$

Solution: Let the distance between Delhi to Kanpur is $$x \ km$$

Then the average speed of the train, $$= \frac{2x}{\frac{x}{60} + \frac{x}{80}}$$ $$= \frac{2x \times 240}{7x} = \frac{480}{7} = 68.57 \ km/hr$$