Question

The ratio of ages of jai and joy is 5:2 the sum of their ages is 63.After 9 years will be the ratio of their ages

Answer 1

Answer:

$\large{\underline{\boxed{\sf Ratio = 49:22}}}$

Step-by-step explanation:

Let the present ages of jai and joy be 5x and 2x respectively.

According to the question ;

Sum of their ages is 63.

⇒ 5x + 2x = 63

⇒ 7x = 63

⇒ x = $\sf \dfrac{63}{7}$

⇒ x = 9

Therefore,

Present age of jai = 5x = 45 years.

Present age of joy = 2x = 18 years.

_______________________

After 9 years,

Age of Jai = 5x + 4

Age of Joy = 2x + 4

Now ratio of their ages,

$\implies \tt \frac{5x + 4}{2x + 4} \\ \\ \implies \tt \frac{5(9) + 4}{2(9) + 4} \\ \\ \implies \tt \frac{45 + 4}{18 + 4} \\ \\ \implies \tt \frac{49}{22} \\ \\ \implies \tt 49 : 22$

Hence, the required ratio is 49:22

Answer 2

$\large\bf\underline\blue{ANSWER}$

Given:

The ratio of ages of jai and joy is 5:2

$\bf\underbrace{let \: x \: be\:the\:common \:multiple \:of \:this \:ratio}$

•°• Present age of Jai and that of Joy is 5x and 2x, respectively.

$\bf\underline\underline{According to the first condition}$

The sum of their ages is 63

5x + 2x = 63

$\bf\underbrace{Add\: the\:terms\:}$

7x = 63

$\bf\underbrace{shift\: the\: number\: 7\: to\:the\: RHS\: so\: it\: \:will\: be\: 63\:÷\:7}$

x = $\large\bf\frac{63}{7}$

x = 9

Now, gradually, multiply the value of x by the ratio i.e 5:2,

Jai = 5x = 5 × 9 = 45 years.

Joy = 2x = 2 × 9 = 18 years.

Second condition states:

the ratio of their ages after 9 years,

Jai = 5x + 9

Joy = 2x + 9

So, the ratio formed is,

$\bf\large\frac{5x + 9}{2x + 9}$

$\bf\large\frac{5 (9) + 9}{2 (9) + 9}$

$\bf\large\frac{45 + 9 }{18 + 9}$

$\bf\large\frac{54}{27}$

$\bf{54:27}$

Hence the ratio of their ages after 9 years will be 54:27.