Question

A two-digit number is obtained by either multiplying the sum of the digits by 8 and
then subtracting 5 or by multiplying the difference of the digits by 16 and then adding 3
Find the number,​

Answer 1

Answer:

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.