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A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.

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A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits. Find the number.
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Let the ten’s digit be x and unit’s digit = y

Number = 10x + y
10x + y = 4(x + y)  ⇒  6x = 3y  ⇒  2x = y

Again 10x + y = 3xy

10x + 2x = 3x (2x) ⇒ 12x = 6x2 ⇒ x = 2 (rejecting x = 0)

2x = y ⇒ y = 4

The required number is 24

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