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 appear and 7% percent got selected with 80 more candidates got selected than A, then what was the number of candidates that appeared from each state?
A. 7600
B. 8000
C. 8400
D. Data inadequate

Answer 1

Hint: Here in order to solve this problem we have to understand the question and the situation completely. Given that there is a competitive examination held in both states named A and B, and a same no. of candidates appeared in both states. Here we use basic arithmetic based algebraic math. Also given that from both the states only a few percentage of candidates are selected from the total number of appeared candidates. We are asked to find the number of appeared candidates from both states.

Complete step by step answer:
Given that the number of candidates appearing for the competitive examination are the same in both the states A and B.
Let the number of candidates appearing for the competitive examination in each state be $'x'$
Total number of candidates appeared for the examination in both states = $x$
Given that the number of candidates got selected in state A = 6% of the total number of appeared candidates.
$ \Rightarrow $No. of candidates got selected in state A = \[\dfrac{{6x}}{{100}}\]
Also given that the number of candidates got selected in state B = 7% of the total number of appeared candidates.
$ \Rightarrow $No. of candidates got selected in state B = $\dfrac{{7x}}{{100}}$
It is given that the number of candidates got selected in state B more than in of state A = 80
Which means that, as given below:
Number of candidates selected in state B is more than state A by 80 candidates, which is expressed mathematically below:
$ \Rightarrow \dfrac{{7x}}{{100}} = \dfrac{{6x}}{{100}} + 80$
$ \Rightarrow \dfrac{x}{{100}} = 80$
$ \Rightarrow x = 8000$
Total number of candidates appeared for the examination from both states = 8000.
$\therefore $The 8000 candidates appeared for the competitive examination in both the states.

8000 candidates appeared from each state.

Note: The most important thing to understand and analyze here is how to write the mathematical expression of what is given in the information. Here it is given that 80 more candidates are selected in state B than state A, hence we add the 80 candidates to the selected percentage of candidates in state A, in order to equate it to the selected percentage of candidates in state B.