GATE Electrical 2019 | GA | Question: 7

Question

The ration of the number of boys and girls who participated in an examination is $4:3.$ The total percentage of candidates who passed the examination is $80$ and the percentage of girls who passed the exam is $90.$ The percentage of boys who passed is _______.

• A. $55.50$
• B. $72.50$
• C. $80.50$
• D. $90.00$ 

Comments

Total no. of students = x

Boys = 4x / 7            Girls = 3x / 7

Let B is the percentage of boys passed.

(4x / 7) * B + (3x / 7)*0.90 = x*0.80

B = 0.725

percentage of boys passed = 72.50

Answer 1

$\text{Percentage of passed students} = \frac{\text{Percentage of boys passed} \times \text{#boys}+ \text{Percentage of girls passed}\times\text{#girls}}{\text{Total number of students}}$

Taking total number of students as $x$ and from the given statements,

$80 =  \frac{\text{Percentage of boys passed} \times \frac{4}{4+3}x + 90 \times \frac{3}{4+3}x}{x}$

$\implies80 \times 7 = 4 \times \text{Percentage of boys passed} + 3 \times 90 $

$\implies  \text{Percentage of boys passed} = \frac{560-270}{4} = \frac{290}{4} = 72.5$

Correct Answer: B

Answer 2

Let total candidates attempting the exam be $70$.

In these Boys:Girls are in ratio $4:3$

$\Rightarrow$ There are $40$ boys and $30$ girls.

$80$% of the total candidates passed the exam = $\frac{80}{100}*70$ = $56$

$90$% of the girls passed the exam = $\frac{90}{100}*30$ = $27$

So Number of boys who passed the exam

= total candidates who passed the exam – total girls who passed the exam

= $56-27$

=$29$

$\therefore$ Percentage of boys who passed the exam = $\frac{29}{40}*100$ = $72.50$

So Option B $72.50$ is the correct answer.

Answer 3

$\text{Let no of boys B  = 4k ,G = 3k and total students = 7k }$

$\text{total passed students} =  0.8 * 7k$

$\implies \text{0.9 * 3k + X * 4k } = \text{0.8 * 7k}$

$\implies X =  0.725$

$\therefore \text{pass percentage of boys }  X = 72.5$

Answer 4

Y= 0.75 X (given)

Let, Y= total no. of girls and X= total no. of Boys

80% of the total students passed the exam successfully; (X+Y)*0.8

And 90% of the girls passed the exam too; 0.9*Y

thus we can write, (X+Y)*0.8 = 0.9*Y + X* (percentage of the boys who passed the exam)

 

1.75*0.8*X = X( 0.9*0.75 + Percentage of the boys who passed the exam)

Percentage of the boys who passed the exam = 72.5%

Answer 5

B = 72.5