Question

Are you a math genius...
Plz answer the following question.. ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Ratio\:of\:their\:age\:=\:11\::\:53}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

Let,

• Tanya's present age be x years.
• Grandfather's present age be y years.

According to the question ,

$y - 16 = 8(x - 16) \\ ⇛y - 16 = 8x - 128 \\ y = 8x - 128+ 16 \\ y = 8x - 112..........(i)$

8 years from now,

• Tanya's age = (x + 8) years
• Grandfather's age = (y + 8) years

According to the question ,

$y + 8 = 3(x + 8) \\ ⇛8x - 112 + 8 = 3(x + 8) \\ ⇛8x - 104 = 3x + 24 \\ ⇛8x - 3x = 24 + 104 \\ ⇛5x = 128\\ ⇛x = \frac{128}{x}$

Substituting x = $\frac{</strong><strong>1</strong><strong>2</strong><strong>8</strong><strong>}{5}$ in eation (i)

$y = \frac{128 \times 8}{5} - 112 \\ \frac{1024 - 560}{5} = \frac{464}{5}$

8 years ago,

Tanya's age = $\frac{</strong><strong>1</strong><strong>2</strong><strong>8</strong><strong>}{5}$- 8 = $\frac{</strong><strong>8</strong><strong>8</strong><strong>}{5}$

Grandfather's age = $\frac{</strong><strong>4</strong><strong>6</strong><strong>4</strong><strong>}{5}$ - 8 = $\frac{</strong><strong>4</strong><strong>2</strong><strong>4</strong><strong>}{</strong><strong>5</strong><strong>}$

Ratio of their age = 88 : 424

ㅤㅤㅤㅤㅤㅤㅤ ㅤ=11 : 53