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Q.

In an acoustics class, 120 students are male and 100 students are female. 25% of the male students and 20% of the female students are engineering students.

20% of the male engineering students and 25% of the female engineering students passed the final exam.

What percentage of engineering students passed the exam?

 A.

5%

 B.

10%

 C.

16%

 D.

22%

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Solution:
Option(D) is correct

There are 100 female students in the class, and 20% of them are Engineering students.

Now, 20% of 100 equals $(\dfrac{20}{100})× 100 = 20.$
Hence, the number of female engineering students in the class is 20.

Now, 25% of the female engineering students passed the final exam:
$25% of 20 = (\dfrac{25}{100})×20 = 5$.
Hence, the number of female engineering students who passed is 5.

There are 120 male students in the class. And 25% of them are engineering students.

Now, 25% of 120 equals$( \dfrac{25}{100})×120 = (\dfrac{1}{4})×120 = 30$.
Hence, the number of male engineering students is 30.

Now, 20% of the male engineering students passed the final exam:
$20% of 30 = (\dfrac{20}{100})×30 = 6$.
Hence, the number of male engineering students who passed is 6.

Hence, $\text{the total number of engineering students who passed is:}$
$\text{(Female Engineering students who passed)} +$
$\text{(Male Engineering students who passed)}$

$= 5 + 6 = 11$

$\text{The total number of engineering students in the class is:}$
$\text{(Number of female engineering students)} +$
$\text{(Number of male engineering students)} =$

$= 30 + 20 = 50$

Hence, the percentage of engineering students who passed is
$\left(\dfrac{\text{Total number of engineering students who passed}}{\text{Total number of engineering students}}\right)×100 $
$= (\dfrac{11}{50}) ×100$
= 22%


(1) Comment(s)


Rohit
 ()

Good solution but here is my take on making it short one yet complete,

Total no. of Engg. students = 25% of total male + 20% of total female

Total engg students:

$= \dfrac{120*25}{100} \text{from male} + \dfrac{100*20}{100} \text{from female}$

$= 30+20= 50$

Now total percentage of engg. who passed:

$=\dfrac{30*20}{100} \text{from male}+ \dfrac{20*25}{100} \text{from female}$

$=6+5= 11$

So. total engg students $=50$

Total passed engg. $=11$

Pass percentage $=\dfrac{11}{50}\times 100=  22\%$