Question

22. The ages of A and B are in the ratio 5:7. Four years from now the ratio
of their ages will be 3:4. The Present age of B is. *
O(a) 20 years
O (b) 28 years
0 (c) 15 years
0 (d) 21 years​

Answer 1

Answer :–

• Correct option is (b) 28 years.

Given :–

• Ages of A and B are in ratio of 5:7.
• After four years from now the ratio of their ages are 3:4.

To Find :–

• Present age of B.

Solution :–

Let,

The age of A = 5x

And the age of B = 7x

• Fraction of their ages = $\dfrac{5x}{7x}$

• Fraction of their ages after 4 years = $\dfrac{3}{4}$

First, we need to find the value of x.

According to the question,

⟹ $\sf \dfrac{Age \: of \: A + 4}{Age \: of \: B + 4} = \dfrac{3}{4}$

⟹ $\dfrac{5x + 4}{7x + 4} = \dfrac{3}{4}$

By cross multiplication,

⟹ 4(5x + 4) = 3(7x + 4)

⟹ 20x + 16 = 21x + 12

⟹ 16 – 12 = 21x – 20x

⟹ 4 = x

• x = 4

Now, we have to find the age of B,

Age of B = 7x

⟹ 7 × 4

⟹ 28 years.

Hence,

The correct option is (b).

Answer 2

Answer:

Answer is Option b) 28 years

Step-by-step explanation:

Let the present age of A be 5x

Let the present age of B be 7x

Let the age of A after 4 years be 5x + 4 i.e. 3x

Let the age of B after 4 years be 7x + 4 i.e. 4x

Therefore,

5x + 4 =   3x

7x + 4      4x

(5x + 4) 4x = 3x (7x + 4)

20x² + 16x = 21x² + 12x

16x - 12x = 21x² - 20x²

4x = x²

4 = x²/x

4 = x

Present age of B = 7x

                            = 7(4)

                            = 28 years

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