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Q48 (CISF/2024) Miscellaneous & General Knowledge › Important Days, Places & Events

Consider the following sum :
@37 + 46@ + 5@3 = 1@@@
In the above sum, @ stands for which one among the following?

Explanation

Let the digit represented by @ be x. We can express the terms of the sum using their place-value expansions:

  • @37 = 100x + 37
  • 46@ = 460 + x
  • 5@3 = 500 + 10x + 3
  • 1@@@ = 1000 + 100x + 10x + x = 1000 + 111x

Now, calculate the Left Hand Side (LHS) of the equation:
LHS = (100x + 37) + (460 + x) + (500 + 10x + 3)
LHS = (100x + x + 10x) + (37 + 460 + 500 + 3)
LHS = 111x + 1000

Comparing the LHS with the Right Hand Side (RHS):
111x + 1000 = 111x + 1000

Since the LHS and RHS are identical, the equation holds true for any digit x ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Therefore, @ stands for all digits.

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