Question

Out of 8000 candidates, 60% were boys. If 80% of the boys and 90% of the girls passed the exam, find the number of candidates who failed.

Answer 1

Hint: In this question, we have the total number of students and the percentage of boys and girls and their passing percentage.
We need to find out the number of students who failed in the exam. For finding that we first need to evaluate the number of boys who failed in the exam and the number of girls who failed in the exam, then by adding these two numbers we will get the required solution.

Complete step-by-step solution:
It is given that out of \[8000\] candidates,\[60\% \] were boys. Also \[80\% \] of the boys and \[90\% \] of the girls passed the exam.
We need to find out the number of candidates who failed in the exam.
Now, the number of boys candidates are =\[8000 \times \dfrac{{60}}{{100}} = 4800\].
The number of girls candidates are =\[8000 - 4800 = 3200\] .
Here, \[80\% \] of the boys and \[90\% \] of the girls passed the exam.
Thus \[\left( {100 - 80} \right)\% = 20\% \] of the boys and \[\left( {100 - 90} \right)\% = 10\% \] of the girls failed in the exam.
Therefore the number of boys failed in the exam \[ = 4800 \times \dfrac{{20}}{{100}} = 960\]
The number of girls failed in the exam =\[ = 3200 \times \dfrac{{10}}{{100}} = 320\]
$\therefore $ The number of candidates who failed in the exam \[ = 960 + 320 = 1280\]

Note: Alternative Method:
Total candidates \[ = 8000\]
\[60\% \] Were boys, Number of boys \[ = 8000 \times \dfrac{{60}}{{100}} = 4800\]
Number of girls \[ = 8000 - 4800 = 3200\]
Number of boys passed \[ = 4800 \times \dfrac{{80}}{{100}} = 3840\]
Number of girls passed \[ = 3200 \times \dfrac{{90}}{{100}} = 2880\]
The number of candidates who failed in the exam,
Boys \[ = 4800 - 3840 = 960\] Boys
Girls \[ = 3200 - 2880 = 320\]Girls
Hence, the number of candidates who failed in the exam \[ = 960 + 320 = 1280\]