Question

The digit of two digit number differ by 3 if the digit are interchanged and the resulting number is added to the original number,we get 143 what can be the original number​

Answer 1

Answer:

Original number is 85.

Step-by-step explanation:

$\bold{\underline{\underline{Assume\::}}}$

Let the -

• Ten's digit be M
• One's digit be N

We have

• Original number = 10M + N
• Revered number = 10N + M

$\bold{\underline{\underline{Solution\::}}}$

According to question,

The two digits number are differ by 3.

$\implies\:M\:-\:N\:=\:3$

$\implies\:M\:=\:3\:+\:N$ ____ (eq 1)

If the digit are interchanged and the resulting number is added to the original number, we get 143.

$\implies\:10N\:+\:M\:+\:10M\:+\:N\:=\:143$

$\implies\:11N\:+\:11M\:=\:143$

$\implies\:N\:+\:M\:=\:13$

$\implies\:N\:+\:3\:+\:N\:=\:13$

[From (eq 1)]

$\implies\:2N\:=\:10$

$\implies\:N\:=\:5$

Substitute value of N in (eq 1)

$\implies\:M\:=\:3\:+\:5$

$\implies\:M\:=\:8$

Original number : 10M + N

→ 10(8) + 5

→ 80 + 5

→ 85

∴ Original number is 85.

Answer 2

Answer:

${\bold{\therefore Original\:number=85}}$

Step-by-step explanation:

${\bold{\huge{\underline{SOLUTION-}}}}$

• In the given question information given about a two digit number whose difference between their ones and tens place is given and their sum of original number and reversed number is given.

• We have to find the original number.

$\underline \bold{Given : } \\ \\ \implies Let\:Original \: number = 10x + y\\ \\ \implies Reversed \: number = 10y + x \\ \\ \underline \bold{To \: Find : } \\ \implies Original \: number = ?$

• According to given question :

$\bold{Difference \: between \:them \: is \: 3}\\ \implies x - y = 3 - - - - - (1) \\ \\ \bold{Sum \: of \: Original \:and \: Reversed \: number \: is \: 143}\\ \implies 10x + y + 10y + x = 143 \\ \\ \implies11x + 11y = 143 \\ \\ \implies 11(x + y) = 143 \\ \\ \implies x + y = \frac{ \cancel{143}}{ \cancel{11}} \\ \\ \implies x + y = 13 - - - - - (2) \\ \\ \bold{Subtracting \: (2) \: from \: (1).we \: get} \\ \implies x - y - (x + y) = 3 - 13 \\ \\ \implies \cancel x - y - \cancel x - y = - 10 \\ \\ \implies \cancel- 2y = \cancel- 10 \\ \\ \implies y = \frac{ \cancel{10}}{ \cancel2} \\ \\ \bold{\implies y = 5} \\ \\ \bold{Putting \: value \: of \: y \: in \: (1)} \\ \implies x - y = 3 \\ \\ \implies x - 5 = 3 \\ \\ \implies x = 3 + 5 \\ \\ \bold{\implies x = 8} \\ \\ \bold{\therefore Original \: number = 10x + y = 85}$