Question

A two digit number is four times the sum of its digits and twice the product of its digits. Find the number. ​

Answer 1

Answer:

36

Step-by-step explanation:

Let ten's digit be x and unit's digit be y. Therefore ,

➟ Sum of digits = x + y

➟ Product of digits = xy

➟ Number = 10 × x + y = 10x + y

A/q

10x + y = 4(x + y)

⟹ 10x + y = 4x + 4y

⟹ 10x – 4x = 4y – y

⟹ 6x = 3y

⟹ 2x = yㅤㅤㅤㅤ

Also ,

10x + y = 2xy

⟹ 10x + y = 2x × 2x

⟹ 10x + 2x = 4x²

⟹ 12x = 4x²

⟹ 12 = 4x

⟹ 3 = x

Putting the value of x in eqⁿ i

➮ 2 × 3 = y

➮ 6 = y

So ten's digit is 3 and unit's digit is 6. Hence, the number is 36.

Answer 2

$\large\underline\mathrm\pink{Question:-}$

• A two digit number is four times the sum of its digits and twice the product of its digits. Find the number.

$\large\underline\mathrm\green{given:-}$

• A two digit number is four times the sum of its digits and twice the product of its digits.

$\large\underline\mathrm\red{to \: find:-}$

• the number

$\large\underline\mathrm\purple{solution:-}$

let the number be X and y

$: \implies\sf10x + y = the \: number$

$: \implies\sf10x + y = (4x + y)$

$: \implies\sf10x + y = 4x + 4y$

$: \implies\sf10x - 4x = 4y - y$

$: \implies\sf6x = 3y$

divide both side by 3 :-

$: \implies\sf2x = y$

$: \implies\sf10x + 2x = 2x \times2x$

$: \implies\sf12x = 4 {x}^{2}$

$: \implies\sf3 = x$

putting 3 in place of X :-

$: \implies\sf \: y = 2x$

$: \implies\sf 2 \times 3$

$: \implies\sf \: y = 6$

so therefore the number is 36.