A two-digit number is such that the product of the digits is 12. When 36 is added to the number the digits interchange their places. Determine the number.

**Let the ones digit be ‘a’ and tens digit be ‘b’. **

**Given, two-digit number is such that the product of its digits is 16. **

⇒ ab = 16 — **(1) **

**Also, **when 54 is subtracted from the number, the digits interchange their places

⇒ 10b + a – 54 = 10a + b

⇒ 9b – 9a = 54

⇒ b – a = 6

⇒ b = 6 + a

**Substituting in 1 **

⇒ a × (6 + a) = 16

⇒ a^{2 }+ 6a – 16 = 0

⇒ a^{2} + 8a – 2a – 16 = 0

⇒ a(a + 8) – 2(a + 8) = 0

⇒ (a – 2)(a + 8) = 0

⇒ a = 2

**Thus, b = 8 **

**Number is 82**

Let the ones digit be ‘a’ and tens digit be ‘b’.Given, two-digit number is such that the product of its digits is 12.⇒ ab = 12 —

(1)Also,when 36 is added to the number, the digits interchange their places⇒ 10b + a + 36 = 10a + b

⇒ 9a – 9b = 36

⇒ a – b = 4

⇒ a = 4 + b

Substituting in 1⇒ b × (4 + b) = 12

⇒ b

^{2}+ 4b – 12 = 0⇒ b

^{2 }+ 6b – 2b – 12 = 0⇒ b(b + 6) – 2(b + 6) = 0

⇒ (b – 2)(b + 4) = 0

⇒ b = 2

Thus, a = 6Number is 26