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Q.

The value of A is: -


   A A A


+ B B B


+ C C C


B A A C


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a

9

b

7

c

6

d

1 

answer is A.

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Detailed Solution

Use the properties of place values of a digit in a number to add the unit digits, tens, and hundred digits separately. Consider the case of the carry process in the given sum and form three linear equations in A, B and C. Solve these equations for the value of A to get the answer.
We can see that at the units place we have a sum of digits A, B and C whose resultant is C. Since, none of the digits can be 0 so this sum is only possible if we have a carry.
Therefore, we have,
⇒A + B + C = C + 10
This is because the unit digits add up to form a ten in the case of carry. So, we have,
⇒ A + B = 10 – (1)
Now, this ten will add up with tens of place digits and form a hundred in the case of carry. So, considering tens place digits, we have,
⇒10A + 10B + 10C + 10 = 10A + 100
⇒10B + 10C + 10 = 100
⇒B + C + 1 = 10
⇒B + C = 9 – (2)
Finally, this hundred will add up with hundred place digits and form a thousand in the case of carry. So, considering hundred place digits, we have,
⇒100A + 100B + 100C + 100 = 100A + 1000B
⇒100B + 100C + 100 = 1000B
⇒B + C + 1 = 10B
⇒9B = C + 1 – (3)
Now, we have three variables A, B, and C, and three equations, so solving these equations for the value of A, we get,
⇒A = 9
Hence, option (1) is the correct answer.
 
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