Question

The ages of A and B are in the ratio of 5: 7 four years from now the ratio of their ages will be 3 : 4 The persent age of B is
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Answer 1

Answer:

$\boxed{Present \: age \: of \: B = 28 \: years}$

Given:

Ratio of present ages of A and B is 5:7

After 4 years from now ratio of ages of A and B is 3:4

Step-by-step explanation:

Let present age of:

A = 5x

B = 7x

After 4 years:

Age of A = 5x + 4

Age of B = 7x + 4

As, ratio of ages after 4 years is given as 3:4

Therefore,

$= > \frac{5x + 4}{7x + 4} = \frac{3}{4} \\ \\ = > 4(5x + 4) = 3(7x + 4) \\ \\ = > (4 \times 5x) + (4 \times 4) = (3 \times 7x) + (3 \times 4) \\ \\ = > 20x + 16 = 21x + 12 \\ \\ = > 20x - 21x = 12 - 16 \\ \\ = > \cancel{- }x = \cancel{ -} 4 \\ \\ = > x = 4$

So,

Present age of A = 5x

= 5 × 4

= 20 years

Present age of B = 7x

= 7 × 4

= 28 years

Answer 2

Answer:

$\sf Present\:Age \:\:\xrightarrow{After\:4\:Years} \:\:Future\:Age \\{\qquad\sf A : B \qquad \qquad \qquad\qquad A : B} \\{\qquad\sf 5 \::\:7 \qquad \qquad \qquad\qquad 3 : 4}$

⠀

Let the Present Age of A be 5n and of B be 7n respectively.

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf \dfrac{A+4}{B+4}=\dfrac{3}{4}\\\\\\:\implies\sf \dfrac{5n + 4}{7n + 4} = \dfrac{3}{4} \\\\\\:\implies\sf (5n + 4) \times 4 = 3 \times (7n + 4)\\\\\\:\implies\sf 20n + 16 = 21n + 12\\\\\\:\implies\sf 16 - 12 = 21n - 20n\\\\\\:\implies\sf n = 4\:years$

$\rule{130}{1.5}$

☯ $\underline{\textsf{Present Age of B :}}$

$\dashrightarrow\sf\:\:B=7n\\\\\\\dashrightarrow\sf\:\:B= 7 \times 4\:years\\\\\\\dashrightarrow\underline{\boxed{\sf B=28\:years}}$

⠀

$\therefore\:\underline{\textsf{Hence, Present Age of B is \textbf{28 years}}}.$