Question

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

Answer 1

Answer:

$\huge {\pink{\green {\sf\boxed {\therefore Ones\:digit = 5}}}}$

$\huge {\pink{\green {\sf\boxed{Tens\:digit = 8}}}}$

Step-by-step explanation:

$\bold{\underline {Given:}}$

• The number is differ by 3.
• If resulting number added to original number we get 143.

$\bold{\underline {To \:Find :}}$

• The original number = ?

$\huge {\red{\boxed{SOLUTION→ }}}$

Let the ones digit of two digit number be $</strong><strong>=</strong><strong>{x}$

Then the tens digit of two digit number be $</strong><strong>=</strong><strong>{</strong><strong>x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>3</strong><strong>}$

Original number $</strong><strong>=</strong><strong> {</strong><strong>10</strong><strong>(</strong><strong>x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>13</strong><strong>)</strong><strong> </strong><strong>+</strong><strong> </strong><strong>x</strong><strong>}$

$= {10x </strong><strong>-</strong><strong> </strong><strong>13</strong><strong> </strong><strong>+ </strong><strong>x</strong><strong>}</strong><strong>$

$= {</strong><strong>10x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>30</strong><strong>}$

$= {</strong><strong>10x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>30</strong><strong>}$

$= {</strong><strong>11x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>30</strong><strong>}$

When we interchange the digits, then

Ones digit $= {</strong><strong>x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>3</strong><strong>}$

Tens digit $= {</strong><strong>x}$

Resulting number $= {10(x</strong><strong>) + </strong><strong>x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>3</strong><strong>}$

$= {</strong><strong>10x</strong><strong> + x - 3}$

$= {</strong><strong>11</strong><strong>x - 3}$

$\Large\boxed{</strong><strong>According</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>to</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>the</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>given</strong><strong> </strong><strong>\</strong><strong>:</strong><strong>question</strong><strong>⟹</strong><strong>}$

$⟹ {</strong><strong>11x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>30</strong><strong> </strong><strong>+</strong><strong> </strong><strong>11x</strong><strong> </strong><strong>-</strong><strong> </strong><strong>3</strong><strong>} = {</strong><strong>143</strong><strong>}$

$⟹ {11x</strong><strong> + 11x} = {</strong><strong>143</strong><strong> </strong><strong>+</strong><strong> </strong><strong>30</strong><strong> </strong><strong>+</strong><strong> </strong><strong>3</strong><strong>}$

$⟹ {</strong><strong>22x</strong><strong>} = {</strong><strong>176</strong><strong>}$

$⟹ {</strong><strong>x</strong><strong>} </strong><strong>=\dfrac</strong><strong>{</strong><strong>176</strong><strong>}</strong><strong>{</strong><strong>22</strong><strong>}</strong><strong>$

$⟹ {</strong><strong>x</strong><strong>} = {</strong><strong>8</strong><strong>}$

$\Large\boxed{</strong><strong>Hence</strong><strong>}$

Ones digit ⟹ x - 3= 8 - 3 = 5

Tens digit ⟹ x= 8

$\</strong><strong>huge</strong><strong>{\pink{\green {\sf\boxed{</strong><strong>Original</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>number</strong><strong> </strong><strong>=</strong><strong> </strong><strong>85</strong><strong>}}}}$ [taking ones =5 and tens digit =8]

#Be_Brainly

Answer 2

Answer:

8

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