Question

Rajeev's present age is 100/3% of his father's age and his father's age is half of Rajeev's grandfather's age. The average of the present ages of all of them is 110/3 years. What was the ratio of their ages 10 years ago?​

Answer 1

Answer:

The ratio of their ages 10 years ago is 1:23:56.

Step-by-step explanation:

Given:

• Rajeev's present age is 100/3% of his father's age.

• And His father's age is half of Rajeev's grandfather's age.

• The average of the present ages of all of them is 100/3. Years.

To find:

• The ratio of their ages 10 years ago?

Required Solution:

Let Rajeev's present age = x

His father's present age = 3x

Now grandfather's present age = 6x

$\boxed{\red{Average = \dfrac{Sum \: of \: Terms}{Number \: of \: Terms}}} \bigstar$

Then equation is:-

$\implies \dfrac{x + 3x + 6x}{3} = \dfrac{110}{3} \\ \\ \implies \frac{10x}{3} = \dfrac{110}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies10x \times \cancel3 = 110 \times \cancel 3 \: \\ \\ \implies10x = 110 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies x = \cancel\dfrac{110}{10} \: \normalsize\bf^{11} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \implies x = \bf 11 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

Rajeev's present age = x = 11 years

So,

10 years ago Rajeev's age = 11 – 10

= 1 years

His Father's present age = 3x = 3×11

= 33 years

10 years ago father's age = 33 – 10

= 23 years

Grandfather's present age= 6x = 6 × 11

= 66 years

10 years ago = 66 – 10 = 56 years

Therefore,

Required Ratio = 1:23:56

The ratio of their ages 10 years ago is 1:23:56.