Question

One of the two digits of a two digit number is three times the other digit. If you interchange the digits of this two-digit number and add the resulting number to the original number, you get 88. What is the original number?
26​

Answer 1

AnswEr :

$\:\bullet\:\sf\ Let \: the \: one's \: place \: digit \: be \: \bf\ x$

$\:\bullet\:\sf\ So, \: ten's \: place \: digit \: number \: is \: \bf\ 3x$

$\rule{100}1$

$\normalsize\star{\boxed{\sf{Original \: number = 10 \times\ Ten's \: place \: digit + one's \: place \: digit }}}$

$\normalsize\twoheadrightarrow\sf\ Original_{no.} = 10 \times\ 3x + x \\ \\ \normalsize\twoheadrightarrow\sf\red\ Original_{no.} = 31x$

$\normalsize\star{\boxed{\sf{Reversing \: number = 10 \times\ One's \: place \: digit + ten's \: place \: digit }}}$

$\normalsize\twoheadrightarrow\sf\ Reversing _{no.} = 10 \times\ x + 3x \\ \\ \normalsize\twoheadrightarrow\sf\green\ Reversing_{no.} = 13x$

$\underline{\dag\:\textsf{According \: to \: the \: question \: now:}}$

$\normalsize\dashrightarrow\sf\ Original_{no.} + Reversing_{no.} = 88$

$\normalsize\dashrightarrow\sf\ 31x + 13 x = 88$

$\normalsize\dashrightarrow\sf\ 44x = 88$

$\normalsize\dashrightarrow\sf\ x = \frac{\cancel{88}}{\cancel{44}}$

$\normalsize\dashrightarrow\sf\ x = 2$

$\rule{100}1$

$\normalsize\dashrightarrow\sf\ Original_{no.} = 31x$

$\normalsize\dashrightarrow\sf\ Original_{no.} = 31 \times\ 2$

$\normalsize\dashrightarrow\sf\ Original_{no.} = 62$

$\therefore\:\underline{\textsf{Hence, \: the \: Original \: number \: is} {\textbf{ \: \: 62 }}}$

Answer 2

Answer:

★ Number will be 26 or 62 ★

Step-by-step explanation:

Given:

• One of the two digits of a two digit number is three times the other digit.
• After interchanging digits and adding resulting number we get 88

To Find:

• The original number

Solution: Let the ones digit be x , So the other digit will be 3x

∴ The number will be 10x + 3x

$\small\implies{\sf }$ 13x

★ After interchanging the digits the number will be 10(3x) + x= 30x + x = 31x

A/q

→ After adding the both numbers = 88

$\small\implies{\sf }$ 13x + 31x = 88

$\small\implies{\sf }$ 44x = 88

$\small\implies{\sf }$ x = 88/44 = 2

∴ The Number will be 10x + 3x

$\small\implies{\sf }$ 10(2) + 3(2) [ putting value of x ]

$\small\implies{\sf }$ 20+6 = 26

Or, It can also be ,

$\small\implies{\sf }$10(3x) + x = 10(6) + 2 = 60 + 2 = 62