Question

A two-digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.

Answer 1

Let the ones and tens digits be ‘a’ and ‘b’ respectively. 

10b + a = 4 ×(a + b) 

⇒ 6b = 3a 

⇒ a = 2b 

Also, 10b + a = 2ab 

⇒ 10b + 2b = 2 × 2b × b 

⇒ 4b² = 12b ⇒ b = 3 

Thus, a = 6 

Number is 36.