Question

6. Class B has 50% more students than class A. Number of girls in class A is equal to number of
boys in class B. The percentage of girls is the same in both classes. What percentage of the
student group are boys?
1. 33.33%
2. 40%
3.25%
4. 60%
​

Answer 1

$\bf \implies \underline{GIVEN}$

• Class B has 50% more students than class A.
• No. of girl is class A = No. of boys in class B.
• Percentage of girls in class A = Percentage of girls in class B.

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$\bf \implies \underline{TO \: FIND}$

• The percentage of the boys student group.

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$\bf \implies \underline{SOLUTION}$

➸ First scenario, class B has 50% more students than class A.

Let the total number of students in class A = 100.

Then the total number of students in class B = 100+50=150.

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➸ Second scenario, number of girls in class A is equal to number of boys in class B.

Let x = number of girls in class A

Also, x = number of boys in class B

∴ 100 - x = number of boys in class B

And 150 - x = number of girls in class B

ㅤ

➸ Third scenario, percentage of girls in class A is similar to percentage of girls in class B.

⇒For class A, The proportion of girls to the total class members

= x / total no. of students

= x/100

⇒For class B, The proportion of girls to the total class members

= (150-x) / total no. of students

= (150-x)/150

• From the 3rd given scenario,

$\sf \: \: \: \: \: \: \implies\dfrac{x}{100} = \dfrac{150 - x}{150}$

$\sf \: \: \: \: \: \: \implies \: 150x = 100(150 - x)$

$\sf \: \: \: \: \: \: \implies150x = 15000 - 100x$

$\sf \: \: \: \: \: \: \implies \: 250x = 15000..... \{ \small{\bf{added \: 100 \: to \: both \: sides \}}}$

$\sf \: \: \: \: \: \: \implies \: x = \dfrac{ \cancel{15000}}{ \cancel{250} }$

$\sf \: \: \: \: \: \: \implies \: \boxed{{ \purple{x = 60}}}$

∴ x = Girls in class A = Boys in class B = 60

Boys in class A = 100 - no. of girls = 100-60 = 40 boys.

Total number of boys = 60 + 40 = 100

Total population = 100 + 150 = 250

☛ So the percentage of boys:

$\sf \implies \: \: \: \: \: \dfrac{100}{250} \times 100$

$\sf \implies \: \: \: \: \: \: \boxed{\boxed{ \purple{= 40 \% }}}$

$\bf \therefore \underline{the \: percentage \: of \: boys \: in \: class \: is \: 40 \%}$