Question

In $5A1 - 23A = 325$, 5Al and 23A are the three digits numbers, then the value of A.
A. 4
B. 6
C. 8
D. none

Answer 1

Hint: In these types of questions, first write all numbers in expanded form, keeping in mind their place values and then do the basic additions and subtractions. And after doing all mathematical operations, we get a linear equation in one variable. At last find the value of that variable from the obtained linear equation.

Complete step-by-step answer:
Given equation is $5A1 - 23A = 325$.
Also given that, 5A1 and 23A are three digits numbers.
The given equation can be written in expanded form as
$5 \times 100 + 10 \times A + 1 - (2 \times 100 + 3 \times 10 + A) = 325$
Simplifying the equation, we get
$500 + 10A + 1 - (200 + 30 + A) = 325$
$ \Rightarrow 500 + 10A + 1 - 230 - A = 325$
$ \Rightarrow 271 + 9A = 325$
Now, we get a linear equation in one variable.
Taking variable one side and all constants another side to get
$9A = 325 - 271$
$ \Rightarrow 9A = 54$
Dividing both sides by 6, we get
$A = \dfrac{{54}}{9} = 6$
Therefore, the value of A is 6 for which the given equation $5A1 - 23A = 325$ is satisfied.
Hence, option (B) is correct.

Note: These types of questions belong to basic mathematical concepts of numbers, their expanded forms etc. Be careful while writing the given numbers in expanded form, and doing mathematical operations like addition, subtraction, multiplication and division etc. Always keep the like terms together.
Alternatively, we can do these types of problems by writing in addition and subtraction format as we do in lower classes and by applying hit and trial methods or putting the different values for unknown numbers and checking the result whether satisfied or not. Hint and trial method will be useful for short operations. But if the problem given is complicated and involves many operations then go for the algebraic method to find the exact value without any approximation.