Question

A two digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. The number isImmersive Reader

Answer 1

Answer

The original number is 64

$\bf \large \underline{Given : }$

• A two digit number is 4 more than 6 times the sum of its digits.
• When 18 is subtracted from the number , the digits are reversed.

$\bf \large \underline{To \: Find : }$

• The number

$\bf \large \underline{Solution : }$

Let the digits of the two digit number be x and y respectively

Therefore, the number is :

$\sf \longrightarrow 10x + y$

$\sf \underline{ \underline{ \dag \: \: According \: to \: question}}$

$\sf \implies 10x + y = 6(x + y) + 4 \\\\ \sf\implies 10x + y = 6x + 6y + 4 \\\\ \sf\implies 10x - 6x + y - 6y = 4 \\\\ \sf\implies 4x - 5y = 4 \dashrightarrow(1)$

$\sf \underline{ \underline{ \dag \: \: Again \: by \: question}}$

$\sf\implies 10x + y - 18 = 10y + x \\\\ \sf\implies 10x - x + y - 10y = 18 \\\\ \sf\implies 9x - 9y = 18 \\\\ \sf\implies x - y = 2 \\\\ \sf\implies x = 2+y \dashrightarrow (2)$

$\sf \underline{ \underline{Putting \: the \: value \: of \: x \: from \: (2) \: in \: (1) }}$

$\sf\implies 4(2 + y) - 5y = 4 \\\\ \sf\implies 8+4y-5y = 4 \\\\ \sf\implies -y = 4 - 8 \\\\ \sf\implies -y = -4 \\\\ \sf\implies y = 4$

$\sf \underline{ \underline{Again \: putting \: the \: value \: of \: y \: in \: (2)}} \\ \sf \underline{ \underline{ \: we \: have}}$

$\sf\implies x = 2 + 4 \\\\ \sf\implies x = 6$

Thus , the required two digit number is

$\sf\longrightarrow 10\times6 + 4 \\\\ \sf\longrightarrow 60 + 4 \\\\ \sf\longrightarrow 64$