Question

In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?
A) 7600
B) 8000
C) 8400
D) Data inadequate.

Answer 1

Hint:
First assume the number of candidates appeared in the examination as ‘x’. Then compute 6% of it as selected from state A, and also compute 7% of it as selected from state B. Then make a simple linear equation based on these two facts and one more fact given in the question. After solving the equation in a single variable, we can get the answer easily.

Complete step by step solution:
First, let us assume that the total number of candidates appeared in the examination as ‘x’ from each state A and B.
Now, 6% candidates got selected from the total appeared candidates, so selected candidates from state A, will be,
=$
  x \times \dfrac{6}{{100}} \\
   \Rightarrow \dfrac{{6x}}{{100}} \\
 $ … (1)
Further, 7% candidates got selected from the total appeared candidates, so selected candidates from state B, will be,
=$
  x \times \dfrac{7}{{100}} \\
   \Rightarrow \dfrac{{7x}}{{100}} \\
 $ …(2)
It is given in the question that from state B , 80 more candidates got selected than the state A.
Therefore from equation (1) and (2), we get
$\dfrac{{7x}}{{100}} = \dfrac{{6x}}{{100}} + 80$
Then we do transformation of variable term towards LHS, then
$\dfrac{{7x}}{{100}} - \dfrac{{6x}}{{100}} = 80$
Now we do some more simplification as follows to get the value of x,
$
   \Rightarrow \dfrac{x}{{100}} = 80 \\
   \Rightarrow x = 8000 \\
 $
$\therefore $ The total number of candidates appearing in the examination from each state is 8000.

Thus the correct option is B.

Note:
Simple arithmetic based questions using the percentage value of some term, is very popular for many competitive examinations as well. Also, to enhance the mathematical logical and computational skill practice of such questions is very important. Also, here solving linear equations in a single variable is the case for solution.