Question

the present ages of Ram and Rahim are in the ratio 4: 3 four years laters with their ages will be in the ratio 6:5 what are their present ages

Answer 1

Given, present ages of Ram and Rahim are in the ratio 4 : 3

Let the constant be x

So, let the present age of Ram be 4x and Rahim be 3x

After 4 years, age of Ram = 4x + 4 and age of Rahim = 3x + 4

After 4 years, the ratio of their ages will be 6 : 5


According to the question,

$\dfrac{4x + 4}{3x + 4} = \dfrac{6}{5}$

➾ 5(4x + 4) = 6(3x + 4)

➾ 20x + 20 = 18x + 24

➾ 20x - 18x = 24 - 20

➾ 2x = 4

➾ x = 2


∴ Present age of Ram ➾ 4x

➾ 4 × 2

➾ $\green{\boxed{\green{\boxed{\red{\textsf{8\:years}}}}}}$


∴ Present age of Rahim ➾ 3x

➾ 3 × 2

➾ $\green{\boxed{\green{\boxed{\red{\textsf{6\:years}}}}}}$

Answer 2

$The \: present \: ages \: of \: ram \: \\ and \: rahim \: are \: in \: the \: \\ ratio \: 4:3$

$let \: x \: be \: their \: common \: \\ multiple$

$then \: ram's \: presnt \: age \: is \: 4x \: years \: and \\ rahim's \: present \: age \: is \: 3x \: years$

$four\: years \: later \: \\ \\ ram's \: age \: will \: be(4x + 4)yrs \: and \: \\ rahim's \: age \: wil \: be \: (3x +4)yrs$

$from \: the \: given \: condition \\ \\ \frac{4x + 4}{3x + 4} = \frac{6}{5}$

$5(4x + 4) = 6(3x + 4) \\ \\ 20x + 20 = 18x + 24$

$20x - 18x = 24 - 20$

$2x = 4 \\ \\ x = \frac{4}{2} \\ x = 2$

$the \: present \: age \: of \: ram \: = 4x = 4 \times 2 = 8yrs$

$present \: age \: of \: rahim \: = 3x = 3 \times 2 = 6yrs \:$

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