Question

In a town of 1,000 people, the number of women are greater than the number of men. If the average age of men is 30 years, whereas the average age of women is 40 years, which of these could be the average age (in years) of all the people in the town?​

Answer 1

This is ur answer i hope it helps u

Answer 2

Answer:

According to the information available, the exact age cannot be determined but the average age of the town is greater than 35

Step-by-step explanation:

• Average also known as the arithmetic mean, is calculated by the sum of all observations divided by a number of observations.

• Let the number of women in the town be x and men be y

        Women - x

        men - y

• Since the number of people in town are 1000, that means

                                     x + y = 1000      - (1)

• And also we are given that the average age of men is 30 years and the average age of women is 40 years
• We are asked to find the average age of the whole town.

Step 1 :

• First, we must find the sum of the age of all the people in the town.
• For that, we must find the sum of the age of all the women and men
• Let the sum of the age of all women be sum1 and men be sum2
• We are given that the average age of women is 40 years, which means  

                                                 $\frac{sum1}{x} = 40$

                                          ⇒  sum1 = 40x     - (2)

• Similarly, we are given the average age of men i.e. 30

                                                 $\frac{sum2}{y} = 30$

                                            ⇒ sum2 = 30y       -(3)

Step 2 :

The average age of all the people in town will be given by sum of the age of all the people divided by 1000

i.e.  $\frac{sum1+sum2}{1000}$

substitute the value of sum1 and sum2 from (2) and (3)

we get,

Avg age =   $\frac{40x+30y}{1000}$

Now replace y by 1000-x using (1)

⇒Avg age = $\frac{40x+30(1000-x)}{1000}$

Avg age = $\frac{40x+30000-30x}{1000}$

Avg age = $\frac{10x+30000}{1000}$  -(4)

Since we know that the number of women is greater than men

therefore x>y

putting the value of y we get

x>1000-x

2x>1000

x>500

Now let us create the same equation as (4) on the left-hand side

10x > 5000 (multiplied 10)

10x + 30000 > 35000 (Addition of 30000)

$\frac{10x+30000}{1000} > \frac{35000}{1000}$   (division by 1000)

Avg age > 35

Therefore the average age of the town is greater than 35