When a number consisting of two digits is multiplied by 9, it becomes

1.	When a number consisting of two digits is multiplied by 9, it becomes equal to twice the number obtained by reversing the digits of the original number. If the difference of two digits of the number is 7, find the number.
Answer» Let a two digit number be 10x + y in which x is tens place digit whereas y is units place digit. According to question 9(10x +y) = 2(10y + x) ⇒ 90x + 9y = 20y + 2x ⇒ 88x = 11y ⇒ 8x – y = 0 …(i) and x – y = -7 …(ii) [∴ Reject +ve value] Solving (i) and (ii), we get x = 1 and y = 8 Hence, required number is 10x + y = 10 x 1 + 8 = 18

When a number consisting of two digits is multiplied by 9, it becomes equal to twice the number obtained by reversing the digits of the original number. If the difference of two digits of the number is 7, find the number.

Answer»

Let a two digit number be 10x + y in which x is tens place digit whereas y is units place digit.

According to question

9(10x +y) = 2(10y + x)

⇒ 90x + 9y = 20y + 2x

⇒ 88x = 11y

⇒ 8x – y = 0 …(i)

and x – y = -7 …(ii) [∴ Reject +ve value]

Solving (i) and (ii), we get x = 1 and y = 8

Hence, required number is 10x + y

= 10 x 1 + 8

= 18