Question

5. The average age of Mahesh and Deepak is 13 years and that of Deepak and Aarati
is 20 years. If the sum of ages of Aarati and Mahesh is 36 years, then what is
Aarati's age ?
(1) 13 years
(2) 18 years
(3) 20 years
(4) 25 years
​

Answer 1

Solution -

Let us assume that the age of Mahesh is x years , the age of Deepak is y years and the age of Aarati is z years .

Now , the following conditions are given -

The average age of Mahesh and Deepak is 13 years .

=> [ x + y ] / 2 = 13

=> x + y = 26 .......... { 1 }

The average age of Deepak and Aarati is 20 years.

=> [ y + z ] / 2 = 20

=> y + z = 40 ......... . { 2 }

The sum of the ages of Aarati and Mahesh is 36 years .

=> z + x = 36 ..... ... { 3 } .

Now , adding the three equations -

=> 2 [ x + y + z ] = 102

=> x + y + z = 51. . . ... { 4 }

Subtracting the first equation from the 4th equation -

z = 25 years .

Thus , the age of Aarati is 25 years .

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Answer 2

Answer:

4) 25 years

Step-by-step explanation:

Assume that the age of Mahesh is x years and Deepak is y years.

As per given condition,

→ (x + y)/2 = 13

→ x + y = 26

→ y = 26 - x ..........(1)

Assume that the age of Aarati is z years. So,

→ (y + z)/2 = 20

→ y + z = 40

→ 26 - x + z = 40 [From (1)]

→ z - x = 14

→ z = 14 + x ................(2)

Similarly,

→ z + x = 36

→ 14 + x + x = 36 [From (2)]

→ 2x = 22

→ x = 11

Hence, the age of Mahesh is 11 years.

Substitute value of x in (2)

→ z = 14 + 11

→ z = 25

Hence, the age of Aarati is 25 years.