Question

The number formed when 5 is after multiplying by 8 to the sum of digits of two digit number is equal to the number formed when 3 is added after multiplying by 16 to the difference of digits of number . What is the number?​

Answer 1

Let the tenth's digit be x and one's digit be y.

Then the number is 10x+y.  

By the first condition-

(x+y)×8−5=10x+y

⇒2x−7y=−5    ........(i)  

By the second condition-

(x−y)×16+3=10x+y

⇒6x−17y=−3     ..........(ii)

Multiplying (i) by 3, we get

6x−21y=−15     .......(iii)

Subtracting (ii) from (iii), we get

−4y=−12

⇒y=3.  

Substituting y=3 in (i)

2x−7×3=−5

⇒x=8  

∴ The number is 10×8+3=83.