Question

When 6 new boys were admitted and 6 girls were left from the class the percentage of boys in the class increased from 60% to 75% find the original no. of boys and girls in the class

Answer 1

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Answer 2

Answer:

Number of boys = 24 and number of girls = 16

Step-by-step explanation:

Given : When 6 new boys were admitted and 6 girls were left from the class the percentage of boys in the class increased from 60% to 75%.

To find : The original number of boys and girls in the class ?

Solution :

Let the number of boys be 'x'

Number of girls be'y'.

Percentage of boys = 60%

i.e. $\frac{x}{x+y}=0.6$

$x=0.6x+0.6y$

$x-0.6x-0.6y=0$

$0.4x-0.6y=0$

$2x-3y=0$  ....(1)

6 boys were admitted ⇒ number of boys = (x + 6)

Percentage of boys = 75%

i.e. $\frac{x+6}{(x+6)+(y-6)}=0.75$

$x+6=0.75x+0.75y$

$x-0.75x-0.75y=-6$

$0.25x-0.75y=-6$

$x-3y=-24$  ....(2)

Solving equations (1)and (2),

We get, x = 24, y = 16

i.e. Number of boys = 24 and number of girls = 16