Question

the present ages of A and B are in the ratio 5:3. four years after, the ratio is 3:2. find their present ages.

Answer 1

Answer :-

• The present age of A is 20 years.

• The present age of B is 12 years.

Given :-

• The present ages of A and B are in the ratio 5 : 3.

• After four years, the ratio of their ages will be 3 : 2.

To find :-

• Their present ages.

Step-by-step explanation :-

• It has been given that the present ages of A and B are in the ratio 5 : 3.

• So let the present ages of A and B be 5x and 3x respectively.

After 4 years,

• A's age will be 5x + 4.
• B's age will be 3x + 4.

• It has been given that after 4 years, the ratio of their ages will be in the ratio 3 : 2.

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$\sf\longmapsto \dfrac{5x + 4}{3x + 4} = \dfrac{3}{2}$

By cross multiplication,

$\sf \longmapsto 2 \: (5x + 4) = 3 \: (3x + 4)$

Removing the brackets,

$\sf \longmapsto 10x + 8 = 9x + 12$

Putting the constant and variable terms on different sides by the method of transposing,

$\sf \longmapsto 10x - 9x = 12 - 8$

On simplifying,

$\longmapsto \underline{ \boxed{\sf x = 4}}$

• The value of x is 4.

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So, their present ages are as follows :-

$\bf A's \: age = 5x = 5 \times 4 = 20.$

$\bf B's \: age = 3x = 3 \times 4 = 12.$

Answer 2

Given :

• The present ages of A and B are in the ratio 5:3.
• After 4 years, the ratio of their ages will be 3:2.

To Find :

• Their Present Ages

Solution :

⟶ Let the Present age of A be 5x

⟶ Let the Present age of B be 3x

After 4 years :

⟶ Present age of A = 5x + 4

⟶ Present age of B = 3x + 4

According to the Question :

⟹ 5x + 4 / 3x + 4 = 3/2

⟹ 2 (5x + 4) = 3 (3x + 4)

⟹ 10x + 8 = 9x + 12

⟹ 10x - 9x = 12 - 8

⟹ x = 4

Therefore :

• Present age of A = 5x = 5 × 4 = 20 years
• Present age of B = 3x = 3 × 4 = 12 years

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