Question

A two digits no. is 3 more than 4 times the sum of its digit . If 18 is added to the no. ,it's digit are reversed. Find the no.

Answer 1

Question should be "A two digit number is 3 more than 4 times the sum of its digit . If 18 is added to the number the digits are interchanged . Find the number." Solution:Let the digit in ones place be x and tens place be y Original number = 10y + x Number formed by reversing the digits = 10x + yGiven 10y + x = 4(x + y) + 3 ⇒ 10y + x − 4x − 4y = 3 ⇒ 6y� − 3x� = 3 ⇒ 2y� − x� = 1 → (1) Also given that when 18 is added to the number the digits gets interchanged.Hence (10y + x) + 18 = 10x + y ⇒ 9x − 9y = 18 ⇒ x − y = 2� → (2) Add (1) and (2), we get 2y� − x� = 1 x − y = 2 --------------- y = 3Put y=3 in x − y = 2, we get x − 3 = 2 ∴ x = 5Hence (10y + x) = 10(3) + 5 = 35