Question

one of the two digits of a two digit number is four times the other digit . if you interchange the digits of this number and add the resulting number to the original number , you get 110 . find the original number with full solution​

Answer 1

Answer:

Let the digit at tens place be x and ones place be 4x (as the two digit number is four times the other one).

Therefore,

$\\ \rm \: Original \: \: number = 10x + 4x \: \\ \\ \\ \implies \rm \: 14 \:x$

Now, if we interchange the digits at ones and tens place be x and 4x.

$\large{ \underline{ \green{ \rm{New \: \: number \: - }}}} \\ \\ \rm \: 10 \times 4x + x \\ \\ \\ \implies \rm \: 40x + x \\ \\ \\ \implies \rm \: 41 \: x$

According to the question,

New number + Original number = 110

→ 14x + 41x = 110

→ 55x = 100

→ x = 110/55

→ x = 2

________________________

$\\ \Large{ \underline{\rm{Original \: \: number \: - }}} \\ \\ \rm 14 \: x \\ \\ \\ \implies \sf \: 14 \times 2 = \rm{ \blue{28}} \\ \\ \\ \Large{ \underline{ \rm{New \: \: number \: - }}} \\ \\ \\ \rm 41x \\ \\ \\ \implies \rm \: 41 \times 2 = \red{82}$