Question

The sum of a two-digit number and the number obtained by reversing the order of its digits is
165.If the digit differ by 3. Find the number.

Answer 1

Answer:

Step-by-step explanation:

The sum of 2 digit number and the number obtained by reversing the order of the digit is 165. If the digit differ by 3, find the number , when ten's digit is bigger than the unit 's digit. Hence both the conditions are verified. 96 is the required number.

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Answer 2

S O L U T I O N :

Let the ten's place digit be x & one's place digit be y respectively.

$\boxed{\bf{Original\:number=10x+y}}$

$\boxed{\bf{Reversed\:number=10y+x}}$

A/q

$\mapsto\tt{x-y = 3}$

$\mapsto\tt{x = 3+y..............(1)}$

&

$\mapsto\tt{(Original\:number ) +(Reversed\:number) = 165}$

$\mapsto\tt{(10x+y) +(10y+x) = 165}$

$\mapsto\tt{10x+y +10y+x= 165}$

$\mapsto\tt{10x + x+y +10y= 165}$

$\mapsto\tt{11x+11y= 165}$

$\mapsto\tt{11(x+y)= 165}$

$\mapsto\tt{x+y= \cancel{165/11}}$

$\mapsto\tt{x+y = 15}$

$\mapsto\tt{(3+y)+y = 15\:\:\:[from(1)]}$

$\mapsto\tt{3+y + y =15}$

$\mapsto\tt{3+2y=15}$

$\mapsto\tt{2y=15-3}$

$\mapsto\tt{2y=12}$

$\mapsto\tt{y=\cancel{12/2}}$

$\mapsto\bf{y=6}$

∴ Putting the value of y in equation (1),we get;

$\mapsto\tt{x = 3 + 6}$

$\mapsto\bf{x = 9}$

Thus,

The number = 10x + y

The number = 10(9) + 6

The number = 90 + 6

The number = 96 .