Question

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

Answer 1

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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.