Question

The average age of persons in Group A,B,C are 37,23,41. If Average age of persons in Groups A and B is 29, B and C is 33 and in C and A is 39.5, then the average age of all the persons age combined in three groups is??​

Answer 1

Answer:

34.5

Step-by-step explanation:

can't explain, I think it's a logical question.

Answer 2

The average of age of all the persons age combined in three groups is 34

Step-by-step explanation:

The average age of persons in Group A,B,C are 37,23,41

Let x number of people in Group A

Let y number of people in Group B

Let z number of people in Group C

The average age of persons in Group A is 37.

The sum of age of all persons in Group A is 37x

The average age of persons in Group B is 23.

The sum of age of all persons in Group B is 23y

The average age of persons in Group C is 41.

The sum of age of all persons in Group C is 41z

• If Average age of persons in Groups A and B is 29

$\dfrac{37x+23y}{x+y}=29$

$37x+23y=29x+29y$

$8x=6y$

$4x=3y$

$y=\dfrac{4}{3}x$

• If Average age of persons in Groups B and C is 33

$\dfrac{41z+23y}{z+y}=33$

$41z+23y=33y+33z$

$8z=10y$

$4z=5y$

$z=\dfrac{5}{4}y=\dfrac{5}{3}x$

• If Average age of persons in Groups C and A is 39.5

$\dfrac{41z+37x}{z+x}=39.5$

$41z+37x=39.5x+39.5z$

$1.5z=2.5x$

$z=\dfrac{5}{3}x$

The average age of all the persons age combined in three groups

$\Rightarrow \dfrac{37x+23y+41z}{x+y+z}$

$\Rightarrow \dfrac{37x+23\times \dfrac{4}{3}x+41\times \dfrac{5}{3}x}{x+\dfrac{4}{3}x+\dfrac{5}{3}x}$

$\Rightarrow \dfrac{37\times 3+23\times 4+41\times 5}{3+4+5}$

$\Rightarrow 34$

Hence, the average of age of all the persons age combined in three groups is 34

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