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