## Average Questions - 1

The average price of 3 Mangoes and 2 apples is Rs.8. The average price of 3 Apples and 3 Oranges is Rs.4.50. The average price of 3 Mangoes and 3 Oranges is Rs.7. What is the price of 1 Mango ?
• Rs.5
• Rs.15
• Rs.10
• Rs.12
• Rs.8
Explanation

Let Mango be M, Apple be = A, Orange be = O

3M + 2A = 5(8) = 40, 3A + 3O = 27, 3M + 3O = 42

(3M + 5A + 3O) = 67 – (3M + 3O) = 42, => 5A = 25 => A = Rs.5, Mango = Rs.10, Orange = Rs.4

Workspace
Walking simultaneously, 4 persons walk 10 km in 2 hrs. How many kilometres will 6 persons cover in 1 hour by walking simultaneously at the same speed ?
• 5 km
• 10 km
• 15 km
• 18 km
• 12 km
Explanation

As all are walking together/simultaneously then 6 person’s walk 5 km in 1 hour.

Workspace
My age after 12 years will be twice as much as my age 8 years ago. What is my present age?
• 30 years
• 28 years
• 32 years
• 34 years
• 26 years
Explanation

Let present age be x then

2(x - 8) => (x + 12) => 2x – 16 = x + 12 => x = 16 + 12 = 28.

Workspace
In a farm, the number of hens and goats are 80. The average of legs are 2.5. What is the number of goats in the farm ?
• 30
• 20
• 25
• 32
• 15
Explanation

Let Hens be H, Goats be = G

H + G = 80, legs = 80 x 2.5 = 200, Hen has 2 legs, Goat has 4 legs.

2(H + G = 80)

2H + 4G = 200

 2H + 2G = 160 2H + 4G = 200

2G = 40 => G = 20 or Goats = 20

Hens = 80 – 20 = 60

Workspace
A trader purchases Brand A at Rs.8/kg, and Brand B at Rs.10/kg. At what ratio should both these brands be mixed to sell at an average price of Rs.9.50 ?
• 1:3
• 3:1
• 4:1
• 1:4
• 5:3
Workspace
The average age of Mr. A and his wife Mrs. B is 26 years, and the average age of Mr. A and his child ‘C’ is 17 years, and the average age of Mrs. B and C is 15 years. What is the age of C ?
• 10 years
• 8 years
• 6 years
• 4 years
• 2 years
Explanation

A + B = 52, A + C = 34, B + C = 30.

(A + B) + (A + C) = 52 + 34 => 2A + B + C = 86 - (B + C) = 30 => 2A = 56.

A = $\displaystyle \frac{56}{2}$ = 28

A + C = 34

28 + C = 34

C = 34 – 28 = 6

Workspace
The present ages of a father and his son is in the ratio of 3 : 1. 6 years ago their average age was 18 years. What will be the age of the son after 10 years ?
• 22 years
• 24 years
• 18 years
• 20 years
• 26 years
Explanation

Let father be F, son = S.

Sum of ages of 6 years ago => F + S = 2 x 18 = 36.

Present ages of F + S = 36 + 12 = 48.

Father = 48 $\displaystyle \times \frac{3}{4}$ = 36 years, Son = 48 $\displaystyle \times \frac{1}{4}$ = 12 years.

Workspace
The average of two numbers is ‘x’. The value of the one of the numbers is ‘n’. What is the value of the other number ?
• x – n
• 2n
• $\displaystyle \frac{3\text{n}}{2}$
• 2x – n
• None
Explanation

Sum of the numbers = 2x, one of the numbers = n

Other number = 2x – n

Workspace
The age of a father is 4 times that of his son, and their average age is 25 years. What is the age of the father ?
• 32 years
• 42 years
• 40 years
• 36 years
• 34 years
Explanation

Sum of ages = 2 x 25 = 50, Father to son = 4 : 1.

Father = 50 $\displaystyle \times \frac{4}{5}$ = 40, son = 40 $\displaystyle \times \frac{1}{5}$ = 10.

Workspace
The average age of a family of 8 persons is 16 years, and the age of the youngest is 2 years. What is the average age of the remaining persons ?
• 21 years
• 17 years
• 20 years
• 18 years
• 24 years
Explanation
Sum of ages of 8 persons = 8 x 16 = 128.
[Less] age of younger = 2

128 - 2 = 126.

Total age of remaining 7 persons = 126 => $\displaystyle \frac{126}{7}$ = 18 years.

Workspace

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## Average Important Formulas

Average is the mean value of a set of numbers.

1. Arithmetic Mean (A.M):

Average = $\displaystyle \frac{\text{Sum of observations}}{\text{Number of observations}}$

2. Harmonic Mean:

Average = $\displaystyle \frac{2[\text{v}_1 \times \text{v}_2]}{\text{v}_1 \ + \ \text{v}_2}$

3. Average of first ‘n’ Natural numbers = (n + 1 ) ÷ 2.

4. Average of first ‘n’ Even numbers = n + 1.

5. Average of first ‘n’ Odd Numbers = n.

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