Question

10years ago 'A'was 1/3rd of 'Q's age if the ratio of the present ages of 'A' and 'Q' are 4:7 what is the total sum of their ages after 5 years? ​

Answer 1

Answer:

54

Step-by-step explanation:

Given:

• 10 years ago, A was ⅓ of Q's age.
• The ratio of their present ages = 4:7

To find:

• The total sum of their ages after 5 years.

Solution:

Let the present age of A be 4x years and the present age of Q be 7x years.

10 years ago,

• Age of A = (4x-10) years
• Age of Q = (7x-10) years

According to the question,

$\implies$ (4x-10) = ⅓ × (7x-10)

$\implies$ 12x - 30 = 7x-10

$\implies$ 12x-7x = 30-10

$\implies$ 5x = 20

$\implies$ x = 20/5

$\implies$ x = 4

Therefore,

• A's present age = (4×4) = 16 years
• Q's present age = (7×4) = 28 years

After 5 years,

• Age of A = (16+5) = 21 years
• Age of Q = (28+5) = 33 years

Sum of their ages after 5 years,

= (21+33)

= 54

Hence, the sum of their ages after 5 years will be 54 .

Answer 2

Answer :-

Let the present age of 'A' be 4x and 'Q' be 7x.

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According to the question -

10 year ago 'A' was 1/3rd of 'Q's age -

ㅤ

➩ $\sf 4x - 10 = \dfrac{7x - 10}{3}$

ㅤ

By solving the linear equation, we can get the value of x -

➩ $\sf 4x - 10 = \dfrac{7x - 10}{3}$

➩ $\sf 3 ( 4x -10) = 7x - 10$

➩ $\sf 12x - 30 = 7x - 10$

➩ $\sf 12x - 7x = 30 - 10$

➩ $\sf 5x = 20$

➩ $\sf x = \dfrac{20}{5}$

➩ $\sf x = 4$

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• 'A' age = 4 × 4 = 16
• 'Q' age = 4 × 7 = 28

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ㅤ

Age after 5 years -

• 'A' age will be 16 + 5 = 21

• 'Q' age will be 28 + 5 = 33

ㅤ

Sum of their ages = 21 + 33 = 54

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Hence, Total sum of their ages = 54