Question

The ratio of boys to girls in a junior band is 4:5. The band
has 63 members. The number of boys and the number of
girls in the band would be (a) 16 boys and 47 girls
(b) 20 boys and 43 girls
(c) 24 boys and 39 girls
(d) 28 boys and 35 girls
(e) None of the above

Answer 1

Question :

The ratio of boys to girls in a junior band is 4:5. The band has 63 members. The number of boys and the number of girls in the band would be?

Solution :

Let the no of boys in a band be 4x

and no of girls be 5x

Given :Band has 63members

thus, No of boys +No of girls = 63

$\implies \sf4x + 5x = 63$

$\sf \implies9x = 63$

$\sf \implies \: x = \cancel{\frac{63}{9}} = 7$

Now ,

No of boys in a band = 4x= 4×7 = 28

and no of girls in a band = 5x = 5×7 = 35

Correct option c) 28boys and 35 girls

_____________________

Verification:

•Total no of members is 63

Boys + girls = 28+35 = 63

•Ratio of boys to girls is 4:5

$\sf \dfrac{no \: of \: boys}{no \: of \: girls} = \cancel{ \dfrac{28}{35} } = \dfrac{4}{5}$

Hence verified!

Answer 2

Gɪᴠᴇɴ :

• Ratio of boys to girls = 4:5
• The band has = 63 members

Tᴏ ғɪɴᴅ :

• The number of boys and girls

Sᴏʟᴜᴛɪᴏɴ :

• Let, the number of boys be 4x and girls be 5x
• Given: the band has 63 members
• So, the number of girls + number of boys = total number of band

:$\implies\sf{4x + 5x = 63}$

:$\implies\sf{9x = 63}$

:$\implies\sf{x = \frac{63}{9}}$

:$\implies\sf{x = \frac{\cancel{63}}{\cancel{9}}}$

:$\implies\sf{7}$

$\rule{150}1$

• Now, the boys = 4$\sf{\cancel{x}}$
• Boys = 4 × 7 = 28
• Now, the girls = 5$\sf{\cancel{x}}$
• Girls = 5 × 7 = 35

Hence, boys are 28 and girls are 35

Hence, the correct option is D (28 boys and 35 girls)