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.

• A. $100$
• B. $22$
• C. $76$
• D. $83$

Answer 1

The correct option is D $83$

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

Then the number is $10x+y$.

By the first condition-

$(x+y)\times 8-5=10x+y$

$\Rightarrow 2x-7y=-5$ ........(i)

By the second condition-

$(x-y)\times 16+3=10x+y$

$\Rightarrow 6x-17y=-3$ ..........(ii)

Multiplying (i) by $3$, we get

$6x-21y=-15$ .......(iii)

Subtracting (ii) from (iii), we get

$-4y=-12$

$\Rightarrow y=3.$

Substituting $y=3$ in (i)

$2x-7\times 3=-5$

$\Rightarrow x=8$

$\therefore$ The number is $10\times 8+3=83$.