Question

A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.

Answer 1

Let this two digit number be XY. Then as per the question, 

XY = 18 ..... (i) 

XY - 63 = YX ..... (ii) 

Let this two digit number be 'Xi. Which means X=10x (as it comes in tens digit). 

Then as per the question, x x y = 1s ... 1ox+y-63=10y+x 

⇒  9x - 9y - 63 = 0

⇒  x - y - 7 = 0 

⇒ Puting x = `18/"y"` in above , we get

⇒ 18 - y² -7y = 0 

⇒ y² + 7y - 18=0 

⇒ y² + 9y -2y- 18=0 

⇒ (y+ 2) (y-9)=0. 

As y can't be negative, hence y= 9 

⇒ Hence x = `18/9 = 2`  (from (i))

⇒ Hence answer is 92

Alternate Answer: 

From (i), possible combinations are: 29, 36, 63, 92. 

From (ii), it's clear that the number 'Xi is more than 63 as that is the only case when we subtract this number by 63, we get a positive value. 

Hence, the number is 92 and when we delete it by 63, we get a number of 29 which is a numbers where the digits are interchanged. 

Hence answer is 92.