Question

The digits of a two digit number differ by 3. If the digits are interchanged and the resulting number is added to original number, we get 143. Find the original number.

Answer 1

Step-by-step explanation:

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Answer 2

S O L U T I O N :

Let the ten's place digit be r & one's place digit be m respectively.

$\boxed{\bf{Original\:number=10r+m}}$

$\boxed{\bf{Reversed\:number=10m+r}}$

A/q

$\underbrace{\bf{1^{st}\:case\::}}$

$\mapsto\tt{r-m=3}$

$\mapsto\tt{r=3+m...................(1)}$

$\underbrace{\bf{2^{nd}\:case\::}}$

$\mapsto\tt{10m+r + 10r+m=143}$

$\mapsto\tt{10m+m+r + 10r=143}$

$\mapsto\tt{11m+ 11r=143}$

$\mapsto\tt{11(m+r) =143}$

$\mapsto\tt{m+r=\cancel{143/11}}$

$\mapsto\tt{m+r=13}$

$\mapsto\tt{m + 3+m = 13\:\:\:[from(1)]}$

$\mapsto\tt{2m + 3 = 13}$

$\mapsto\tt{2m=13 - 3}$

$\mapsto\tt{2m=10}$

$\mapsto\tt{m=\cancel{10/2}}$

$\mapsto\bf{m=5}$

∴ Putting the value of m in equation (1),we get;

$\mapsto\tt{r=3+5}$

$\mapsto\bf{r=8}$

Thus;

The original number = 10r + m

The original number = 10(8) + 5

The original number = 80 + 5

The original number = 85 .