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Question
Find the values of the letters in the following and give reasons for the steps involved.
A B
x 5
-------
C A B
-------
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Solution
The multiplication of B and 5 is giving a number whose ones digit is B again. This is possible when B = 5 or B = 0 only.
In case of B = 5, the product, B × 5 = 5 × 5 = 25
2 will be a carry for the next step.
We have, 5 × A + 2 = CA, which is possible for A = 2 or 7
The multiplication is as follows.
25
x 5
-----
125
-----
75
x 5
----
375
----
If B = 0,
B × 5 = B ⇒ 0 × 5 = 0
There will not be any carry in this step.
In the next step, 5 × A = CA
It can happen only when A = 5 or A = 0
However, A cannot be 0 as AB is a two-digit number.
Hence, A can be 5 only. The multiplication is as follows.
50
x 5
-----
250
-----
Hence, there are 3 possible values of A, B, and C.
(i) 5, 0, and 2 respectively
(ii) 2, 5, and 1 respectively
(iii) 7, 5, and 3 respectively
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