Question

Product of digits of a 2­digit number is 12. If we add 36 to the number, the new number obtained is a number formed by interchange of the digits. What is the number.

A) 62 B) 34 C) 26 D) 43

Answer 1

AnSwer:-

• c) 26

ExPlanation:-

$\sf \: Let \: the \: units \: place \: digit \: be \: x$

$\sf \: tens \: place \: digit \: be \: y$

$\sf \: Number = 10y + x(as \: per \: given \: info) \\ \sf \: Interchanged \: Number = 10x + y$

${ \bigstar{ \underline{According \: to \: the \: Question,}}}$

$\longmapsto \sf \: xy = 12 \\ \longmapsto \sf \: x= 12/y ..... (i) \\ \longmapsto\sf \: 10y + x + 36 = 10x + y\\ \longmapsto \sf \: 10y + x - 10x - y = - 36 \\ \longmapsto \sf \: 9y - 9x = - 36 \\ \longmapsto \sf \: 9(y - x) = - 36 \\ \longmapsto\sf \: y - x = - 36/9 \\ \longmapsto\sf \: y - x = - 4 ....(ii)$

Substitute eqn (1) value in (2),

$\longmapsto \sf \: y - 12/y = - 4 \\ \longmapsto \sf \:{y}^{2} - 12/y = - 4 \\ \longmapsto \sf \:{y}^{2}+ 4y - 12 = 0 \\ \longmapsto \sf \: {y}^{2} + 6y - 2y -12 = 0 \\ \longmapsto \sf \: y(y + 6) - 2(y + 6) = 0 \\ \longmapsto \sf \:(y + 6)(y - 2) = 0 \\ \longmapsto \sf \:y = - 6, 2 (Neglect \: negative \: sign) \\ \longmapsto \sf \:y = 2$

$\sf \: Putting \: y \: value \: in \: Eqn (1), we \: get \\ \longmapsto \sf \: x = 12/y \\ \longmapsto \sf \: x = 12/2 \\ \longmapsto \sf \:x = 6$

$\sf \therefore \: Number = \\ \sf\implies \: 10y + x \\ \sf \implies \: 10\times2 + 6 \\ \sf \implies \: 20 + 6 \\ \sf\implies \: 26$

Hence, the number is 26.