If we multiply a certain two-digit number by the sum of its digits, we get $405$ . If we multiply the number consisting of the same digits written in the reverse order by the sum of the digits, we get $486$ . Find the number.

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Solution

Given condition:
Number $\times$ Sum of the Digits $= 405$
Now, factors of $405$ will give the required number.
Factors of $405 = 5 \times 3 \times 3 \times 3 \times 3 = 15 \times 27 = 45 \times 9$
$45 \times 9 = 405$
Also, $54 \times 9 = 486$
So, Required number $= 45$

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If we multiply a certain two-digit number by the sum of its digits, we get 405. If we multiply the number consisting of the same digits written in the reverse order by the sum of the digits, we get 486. Find the number.

Given condition:Number × Sum of the Digits =405Now, factors of 405 will give the required number.Factors of 405=5×3×3×3×3=15×27=45×945×9=405Also, 54×9=486So, Required number =45

If we multiply a certain two-digit number by the sum of its digits, we get $405$ . If we multiply the number consisting of the same digits written in the reverse order by the sum of the digits, we get $486$ . Find the number.

Given condition:
Number $\times$ Sum of the Digits $= 405$
Now, factors of $405$ will give the required number.
Factors of $405 = 5 \times 3 \times 3 \times 3 \times 3 = 15 \times 27 = 45 \times 9$
$45 \times 9 = 405$
Also, $54 \times 9 = 486$
So, Required number $= 45$