A number consists of two digits whose product is 18. If 27 is added to the number, the digits interchange their places. Find the number.
Quadratic Equations
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Question

A number consists of two digits whose product is 18. If 27 is added to the number, the digits interchange their places. Find the number.

KnowledgeBoat · Accepted Answer

Let the ten's and unit's digits of required number be x and y respectively. Number = 10x + y Given, Product of digits = 18. ⇒ xy = 18 ⇒ x = .........(1) Given, If 27 is added to the number, the digits interchange the place. ⇒ 27 + 10x + y = 10y + x ⇒ 27 + 10x + y - 10y - x = 0 ⇒ 9x - 9y + 27 = 0 ⇒ 9(x - y + 3) = 0 ⇒ x - y + 3 = 0 ⇒ x - y = -3 .........(2) Substituting the value of x from equation (1) in equation (2), ⇒ - y = -3 ⇒ = -3 ⇒ 18 - y2 = -3y ⇒ y2 - 3y - 18 = 0 ⇒ y2 - 6y + 3y - 18 = 0 ⇒ y(y - 6) + 3(y - 6) = 0 ⇒ (y + 3)(y - 6) = 0 ⇒ (y + 3) = 0 or (y - 6) = 0 [Using zero-product rule] ⇒ y = -3 or y = 6. Since, digits must be positive y -3. Substituting value of y = 6 in equation (1), we get : x = = 3. The number is : 10 × 3 + 6 = 36. Hence, the required number is 36.

Mathematics

A number consists of two digits whose product is 18. If 27 is added to the number, the digits interchange their places. Find the number.

Quadratic Equations

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