​Please solve in a diagrammed manner:


                      F i n d   t h e   v a l u e   o f   A ,   B   a n d   C   i n   :         8           A + 8           B _ _ _ _ _ _ _ _ _ C     B       3 _ _ _ _ _ _ _ _ _

Dear Student,

We have:
    8 A
+  8 B
_____
C B 3

​Since A, B and C are digits, they can only take values 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.
So, the minimum value of the sum above is 80 + 80 = 160 and the maximum value is 89 + 89 = 178. Thus, C = 1.

    8 A
+  8 B
_____
1 B 3

​Now, B can either be equal to 6 or 7.
​Let us assume that B = 6. Then the final sum is 163. Here, the only two numbers which add up to 163 are 82 and 81. So, 82 + 81 = 163, which gives B = 2 or 1, which is a contradiction since we had assumed B to be 6. Thus, the final sum must be 173. This gives B = 7.
So,
    8 A
+  8 7
_____
1 7 3

Now, 87 + 86 = 173, which gives A = 6.
Thus,
    8 6

+  8 7
_____
1 7 3

 

  • 1
What are you looking for?