## 52nd SSC CGL level Question Set, 1st exclusively on Average

This is the 52nd question set of 10 practice problem exercise for SSC CGL exam and 1st exclusively on topic Average.

For maximum gains, the test should be taken first, that is obvious. But more importantly, to absorb the concepts, techniques and deductive reasoning elaborated through these solutions, one must solve many problems in a systematic manner using this conceptual analytical approach.

Learning by doing is the best learning. There is no other alternative towards achieving excellence.

* After taking the test* you may refer to its companion detailed solution set,

**52nd SSC CGL solution set and 1st exclusively on Average.**Before starting with the questions, you may go through the basic concepts on **average**.

** Basic concepts on Average**

The average value $A$ of a set of $n$ number of values is,

$A=\displaystyle\frac{\text{Sum of }n\text{ values }S_n}{n}$.

Alternatively,

$\text{Sum of }n\text{ number of values }S_n=n\times{\text{Average of }n\text{ values }A}$.

Using these two of the most basic concepts on average, the problems on average are solved.

### 52nd question set - 10 problems for SSC CGL exam: 1st exclusively on topic Average - answering time 15 mins

**Problem 1.**

The average height of 40 students in a class is 163 cm. When the school opened after the vacation, three students were absent and the average height of the students present was found to be 162 cm. If the heights of the two students absent were equal to each other, and the height of the third absent student was 2 cm less than either of other two, what was the height of the third absent student?

- 170 cm
- 174 cm
- 172 cm
- 176 cm

**Problem 2.**

The average weight of three men is 84 kgs. When another man, the fourth one, joins the group, the average reduces to 80 kg. Now, a fifth man with weight 3 kg more than the fourth replaces one of the first three. The average weight of these four is then 79 kg. What is the weight of the replaced man?

- 72 kg
- 75 kg
- 76 kg
- 74 kg

**Problem 3.**

The average of three numbers is 42. The first is twice the second and the second is twice the third. What is the difference between the largest and the smallest number?

- 54
- 48
- 50
- 46

**Problem 4.**

The average of 25 results is 18, of the first 12 is 14, and of last 12 is 17. What is the value of the thirteenth result?

- 68
- 78
- 87
- 79

**Problem 5.**

If ages of three boys are in the ratio of 3 : 5 : 7 at an average of 15 years, the age of the youngest boy is,

- 8 years 3 months
- 9 years
- 8 years
- 9 years 3 months

**Problem 6.**

While calculating the average of ten numbers as 15 an error was made by reading 26 instead of 36 for one of the numbers. What should be the correct average?

- 16.5
- 14
- 15
- 16

**Problem 7.**

The average age of 8 members of a committee is 39 years. A year later, a member aged 55 retires and a new member aged 39 years joins the committee in his place. What is the average age of the committee members after the change?

- 39 years
- 38 years
- 40 years
- 36 years

**Problem 8.**

The average of first three numbers out of four numbers is 15, and that of last three is 16. If the last number is 19 what is the first number?

- 18
- 16
- 15
- 14

**Problem 9.**

The first number out of three is twice the second and half the third. If the average of the three numbers is 56, than what is the largest number?

- 50
- 75
- 96
- 48

**Problem 10.**

The average (arithmetic mean) of $3^{30}$, $3^{60}$, and $3^{90}$ is,

- $3^{60}$
- $3^{29}+3^{59}+3^{89}$
- $3^{27}+3^{57}+3^{87}$
- $3^{177}$

### Answers to questions

**Problem 1.** **Answer:** Option b: 174 cm.

**Problem 2. Answer:** Option b : 75 kgs.

**Problem 3.** **Answer:** Option a: 54.

**Problem 4.** **Answer:** Option b: 78.

**Problem 5.** **Answer:** Option b: 9 years.

**Problem 6.** **Answer:** Option d : 16.

**Problem 7. Answer:** Option b: 38 years.

**Problem 8.** **Answer:** Option b: 16.

**Problem 9.** **Answer:** Option c: 96.

**Problem 10.** **Answer: **Option b: $3^{29}+3^{59}+3^{89}$.

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