Question

1115 (2) 6 (3) 7 (4) 8
5. The average age of Mahesh and Deepak is
Mahesh and Deepak is 13 years and that of Deepak and Aarati
is 20 years. If the sum of ages of Aarati and 1
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

Answer: Opt.4) 25 years

Step by step explanation:

Let mahesh's age be x years, deepak's age be y years and Aarti's age be z years.

We know that:

Average age = Sum of ages of persons / Total persons

Sum of ages = Average age × no. of persons

Given: Average age of Mahesh and Deepak = 13 years

=> x + z = 13 × 2

x + y = 26 __ (1)

Avg. age of Deepak and Aarti = 20 years

y + z = 20 × 2

y + z = 40 __ (2)

Sum of ages of Arti and Mahesh = 36 years

z + x = 36 __ (3)

Now, Add (1) and (2),

(x + y) + (y + z) = 26 + 40

x + 2y + z = 66

x + z + 2y = 66

Substituting the value of x + z, from (3)

=> 36 + 2y = 66

2y = 66 - 36

2y = 30

y = 15

The age of Deepak is 15 years

________________________

Substituting the value of y in (2)

=> y + z = 40

15 + z = 40

z = 40 - 15

z = 25

Thus, Age of Aarti= 25 years.

Final Answer: Aarti’s age is 25 years [ Opt. 4 ]

Answer 2

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$\large \underline{ \blue{ \boxed{ \bf \green{Option \: 4}}}}$