The Gateway to Computer Science Excellence

+2 votes

The sum of the digits of a two digit number is $12$. If the new number formed by reversing the digits is greater than the original number by $54$, find the original number.

- $39$
- $57$
- $66$
- $93$

+4 votes

Best answer

Let the two digits be $x$ and $y$.

Original number$=xy=10x+y$

$ x + y = 12 \quad \to(1)$

Given that new number formed by reversing the digits is greater than the original number by $54,$

$ y * 10 + x = 10 * x + y + 54 $

$ 10 y + x = 10 x + y +54 $

$ 9y-9x = 54 $

$ x - y = -6 \quad \to(2)$

From $(1)$ and $(2)$

$ 2 x = 6 $

$ x = 3 $ and $ y = 9$

Hence, Original number $=xy=10x+y= 39$

Correct Answer: $A$

Original number$=xy=10x+y$

$ x + y = 12 \quad \to(1)$

Given that new number formed by reversing the digits is greater than the original number by $54,$

$ y * 10 + x = 10 * x + y + 54 $

$ 10 y + x = 10 x + y +54 $

$ 9y-9x = 54 $

$ x - y = -6 \quad \to(2)$

From $(1)$ and $(2)$

$ 2 x = 6 $

$ x = 3 $ and $ y = 9$

Hence, Original number $=xy=10x+y= 39$

Correct Answer: $A$

+4 votes

Original no is 54 less than Reversed no.

66 Not possible as reversal of 66 is 66 itself.

93 and 57 also not possible because by adding 54 it will become 3 digit no.

Only option left is 39, which is correct answer. :-P

i.e. 39+54=93

66 Not possible as reversal of 66 is 66 itself.

93 and 57 also not possible because by adding 54 it will become 3 digit no.

Only option left is 39, which is correct answer. :-P

i.e. 39+54=93

0 votes

x+y=12

10y+x=54+10x+y

solving the above equation we will get 9x-9y=-54

solving both equations we will get x=3,y=9

10y+x=54+10x+y

solving the above equation we will get 9x-9y=-54

solving both equations we will get x=3,y=9

0 votes

Let's assume the unit digit of the number is $y$ & $x$ is the digit of ten's place.

∴ The number is $10x+y$

Now, given $x+y =12$

if the number is $yx$, then $\{(10y+x)-(10x+y)\}=54$

Now, we know, $x+y =12$

∴ $y=12-x$

Now, $\{(10y+x)-(10x+y)\}=54$

$10y+x-10x-y=54$

$10(12-x)+x-10x-(12-x)=54$

Or,$120-10x+x-10x-12+x=54$

Or, $120-20x+2x-12=54$

Or,$108-18x=54$

Or,$108-54=18x$

Or,$18x=54$

Or,$x=3$

∴$ y = 12-x = 12-3 = 9$

The original number is $39$ which is option A)

∴ The number is $10x+y$

Now, given $x+y =12$

if the number is $yx$, then $\{(10y+x)-(10x+y)\}=54$

Now, we know, $x+y =12$

∴ $y=12-x$

Now, $\{(10y+x)-(10x+y)\}=54$

$10y+x-10x-y=54$

$10(12-x)+x-10x-(12-x)=54$

Or,$120-10x+x-10x-12+x=54$

Or, $120-20x+2x-12=54$

Or,$108-18x=54$

Or,$108-54=18x$

Or,$18x=54$

Or,$x=3$

∴$ y = 12-x = 12-3 = 9$

The original number is $39$ which is option A)

52,315 questions

60,433 answers

201,778 comments

95,257 users