Question

In the following multiplication, each of the different letter denotes a different integer. Each letter stands for the same integer through out. If 'B' stands for 6 and 'E' stands for 8, then what is the difference between 'F' and 'D'?
A B C
x D E
A C F B
E A G 0
F H F B

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (B)

4

Given that B = 6 and E = 8
A 6 C
x D 8
A C F 6
8 A G 0
F H F 6
As at the Thousand's place A+8=F, there is no carry over, thus the value of A can either be 0 or 1, but 0 will make it a 3-digit number. Hence, the value of A = 1 and thus that of F = 9.

Also, in the first multiplication, E$\times$C= B (units place), i.e., 8$\times$ C = 6 (units place).

So 'C' can either be 2 or 7.

By looking at the first row of multiplication, we see that 6 $\times$ 8 + carry over gives 9 ( value of F) in units place.

So, C = 2.

Therefore,

1 6 2
x D 8
1 2 9 6
+ 8 1 G 0
9 H 9 6
As 9+G=9, therefore, G should be '0' which can be obtained when D = 5,

Thus the difference between D & F is F - D = 9 - 5 = 4.(option B)