A two - digit number is 4 more than 6 times the sum of its digits. If

1.	A two - digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.
Answer» Let the one’s digit be ‘a’ and ten’s digit be ‘b’ Given, two - digit number is 4 more than 6 times the sum of its digits. ⇒ 10b + a = 6(a + b) + 4 ⇒ 4b = 5a + 4 ------- (1) Also, if 18 is subtracted from the number, the digits are reversed. ⇒ 10b + a – 18 = 10a + b ⇒ b – a = 2 ------- (2) Multiplying eq2by 4 and subtracting from eq1 ⇒ 4b – 5a – 4b + 4a = 4 – 8 ⇒ a = 4 Thus, b = 6 Number is 64

A two - digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.

Answer»

Let the one’s digit be ‘a’ and ten’s digit be ‘b’

Given, two - digit number is 4 more than 6 times the sum of its digits.

⇒ 10b + a = 6(a + b) + 4

⇒ 4b = 5a + 4 ------- (1)

Also, if 18 is subtracted from the number, the digits are reversed.

⇒ 10b + a – 18 = 10a + b

⇒ b – a = 2 ------- (2)

Multiplying eq2by 4 and subtracting from eq1

⇒ 4b – 5a – 4b + 4a = 4 – 8

⇒ a = 4

Thus, b = 6

Number is 64