## Average Related Problems

*(Quantitative Reasoning)*

The average of given set of numbers can be expressed as:

A = | Sum of the quantities of same kind |

Number of quantities of the same kind. |

*Important Points:*

*① Sum of Quantities = Number of quantities × Average*

② Average is also called the Arithmetic Mean.

③ If all the given quantities have the same value, then the vaue itself is the average.

④ If each of the given quantities is increased/decreases by a constant N, then their average is also increased/decreased by N.

⑤ If each of the given quantities is multiplied by a constant N, then their average is also multiplied by N.

*Solved Problems*:

**Q1: Fnd the average of first five even numbers.**

Answer: A = (2 + 4 + 6 + 8 + 10)/5 = 30/5 =

**6**

**Q2: If the average of p and q is 58 and the average of q and s is 64, what is the value of s-p?**

Answer: (p + q)/2 = 58 ⇒ p + q = 116 ...(i)

(q + s)/2 = 64 ⇒ q + s = 128 ...(ii)

Subtract (i) from (ii),

q + s - p - q = 128 - 116

s - p =

**12**

**Q3: The average weight of 10 men is increased by 1½ kg, when one of the men who weighs 68 kg is replaced by a new man. Find the weight of the new man.**

Answer: Average increase in weight = 1½ kg

No. of men = 10

Total increase = 10 × 1½ = 15kg

Weight of new man = Weight of previous man + Total increase in weight

= 68 + 15 =

**83kg.**

**Q4: The average of 10 numbers is 7. If each number is multiplied by 12, then the average of new set of numbers is ___?**

Answer: 12 × 7 =

**84**.

If each of the given quantities is multiplied by a constant N, then their average is also multiplied by N.

**Q5: Of three numbers, the first is two times the second and the second is thrice the third. If the average of three numbers is 10, find the numbers.**

Answer: Let 3rd no. = x

2nd number = 3x

1st number = 6x

Ratio of 1st : 2nd : 3rd = 6 : 3: 1

Sum of ratios = 6x + 3x + x = 10x

Average of three numbers = 10x/3 = 10

⇒ x = 3

First No. = 6 × 3 =

**18**

2nd No. = 3 × 3 =

**9**

3rd No. =

**3**