Question

the product of digits of two digit number is 16 when 54 is added to the number the digits interchange their places find the number

Answer 1

Hey Friends!!

Here is your answer↓⬇


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▶⏩ Let the ten's digit be ‘x’.
and, the unit's digit be ‘y’.

A/Q.

=> The product of two-digit number is 16.

$\huge \bf{=> xy = 16.}$


▶ Required number = ( 10x + y ).

▶ Number obtained on reversing its digit are
= ( x + 10y ).


▶⏩ Now, A/Q.

=> When 54 is added to the required number then the digit are reversed their places.


$\bf{=> ( 10x + y ) + 54 = ( x + 10y ).}$


$\bf{=> 54 = x + 10y - 10x - y.}$


$\bf{=> 54 = 9y - 9x .}$


$\bf{=> 9 ( y - x ) = 54.}$


$\bf{=> y - x = \frac{54}{9} }.$


$\huge \bf{=> y - x = 6..........(1).}$


▶⏩ Now, using identity:-)

$\boxed{( {a + b)}^{2} = {(a - b)}^{2} + 4ab}$

$\bf = > {(y + x)}^{2} = {(y - x)}^{2} + 4yx.$

$\bf = > (y + x) = \sqrt{ {(y - x)}^{2} + 4yx } .$

↪➡ Now, put the values.


$\bf = > (y + x) = \sqrt{ {(6)}^{2} + 4 \times 16} .$

$\bf = > y + x = \sqrt{36 + 64} .$


$\bf = > y + x = \sqrt{100} .$


$\huge \bf = > y + x = 10........(2).$



↪➡ Add in equation (1) and (2).


y - x = 6.
y + x = 10.
(+)...(+)..(+)
_________
2y = 16.

$\bf = > y = \frac{16}{2} .$

$\huge \boxed{=> y = 8.}$


↪➡Put the value of ‘y’ in equation (2).


$\bf{=> 8 + x = 10.}$


$\bf = > x = 10 - 8.$


$\huge \boxed{ = > x = 2.}$

▶ Hence, the required number
= 10x + y.

= 10 × 2 + 8.

$\huge \boxed{= 28.}$


✅✅ Hence, the required number is founded ✔✔.




$\huge \boxed{THANKS}$



$\huge \bf \underline{Hope \: it \: is \: helpful \: for \: you}$

Answer 2

$\huge{hey}$


$\huge \bf{here \: is \: the \: answer}$


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this refers to the pic


$\huge \underline{hope \: it \: helps}$

$\huge{thanks}$