Question

In the following multiplication, each of the different letters denotes a different integer. Each letter stands for the same integer through out. If ${}^{\prime }{B}^{\prime }$ stands for $6$ and ${}^{\prime }{E}^{\prime }$ stands for $8$, then what is difference between ${}^{\prime }{F}^{\prime }$ and ${}^{\prime }{D}^{\prime }$?

• A. $2$
• B. $4$
• C. $6$
• D. $8$

Answer 1

Answer: (B)

$4$

Given : $B=6$ and $E=8$.

So, $\left(A6C\right)\times 8=ACF6$.

Now, $6$ appears as unit digit when 8 is multiplied by either $2$ or $7$.

But as given $F+G=F$ and $B=6$, so $G=0$

But if $C=7$, then to get $0$ in place of $G$ the value of $D$ should be zero which is not possible.

So, $C=2$ and $D=5$.

Then, $\left(A62\right)\times 8=A2F6$, implies $F=9$.

i.e. $\left(A62\right)\times 8=A296$. So, $A=1$

i.e. $\left(162\right)\times 8=1296$.

And $\left(162\right)\times 5=810=EAG$.

And the sum is $=9396$

Thus, the difference between $D$ and $F$ is $9-5=4$.

Hence, option B is correct.