Question

Madhav’s father is 26 years younger than Madhav’s grandfather and 29 years older than Madhav. The sum of the ages of all the three is 135 years. What are the ages of each one of them?  ​

Answer 1

madhava's age = x

his father's age = x+29

his grandfather's age = x+29+26

therefore,

x = x+x+29+x+29+26

3x + 29 + 29 + 26 = 135

3x + 58 + 26 = 135

3x + 84 = 135

3x = 135 - 84

3x = 51

x = 51/3

x = 17

madhava's age = 17

his father's age = 17 + 29

= 46

his grandfather's age = 17 + 29 + 26

= 46 + 26

= 72

17 + 46 + 72 = 135

Answer 2

Answer:

Madhav's present age is 17 years. His father is 46 years old and grandfather is 72 years old.

Step-by-step explanation:

Let the ages be :

• Grandfather = x
• Father = y
• Madhav = z

Madhav's father is 26 years younger than grandfather,

$\longrightarrow$ x = 26 + y --- (Equation I)

Madhav's father is 28 years older than Madhav,

$\longrightarrow$ z = y - 29 --- (Equation II)

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According to the Question,

Sum of all three ages is 135.

$\longrightarrow$ x + y + z = 135

$\longrightarrow$ (26 + y) + y + (y - 29) = 135

(Substitution of equation I and II)

$\longrightarrow$ -3 + 3y = 135

$\longrightarrow$ 3y = 135 + 3

$\longrightarrow$ 3y = 138

$\longrightarrow$ y = 138/3

$\longrightarrow$ y = 46

Madhav's father is 46 years.

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★ Madhav's age = z

Substitute value of y in equation II,

$\longrightarrow$ z = 46 - 29

$\longrightarrow$ z = 17

Madhav's present age is 17 years.

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★ Grandfather's age = x

Substitute value of y in equation I

$\longrightarrow$ x = 26 + 46

$\longrightarrow$ x = 72

Grandfather's age is 72 years.

Therefore, Madhav's present age is 17 years. His father is 46 years old and grandfather is 72 years old.