Question

In a school, the ratio of boys to girls is 4: 5. When 1000 girls leave the school, the ratio changes to 6:7,
How many boys are there in the school?
(a) 13000
(b) 15000
(c) 16000
(d) 12000​

Answer 1

${{\underline{\underline{{\textsf{\textbf{Answer : }}}}}}}$

◩ Number of boys are 12,000

${{\underline{\underline{{\textsf{\textbf{Explanation : }}}}}}}$

Given statements,

✦ Ratio of number of boys to girls is 4 : 5

✦ If 1000 girls leave then the ratio turns to 6 : 7

❐ Step 1:

➡ Assuming number of :

→ Boys = 4x

→ Girls = 5x

❐ Step 2:

• Here, in the given question if 1000 girls left the school the remains will be in the ratio of 6 : 7

So, Number of girls present now :

➙ 5x - 1000

And also, the ratio now turns to 6 : 7

$\therefore$ Equation forms :

➙ $\frac{4x}{5x - 1000}$ = $\frac{6}{7}$

❐ Step 3:

Solving for x :

➙ 4x(7) = 6(5x - 1000)

➙ 28x = 30x - 6000

➙ 6000 = 30x - 28x

➙ 6000 = 2x

➙ 6000/2 = x

➙ x = 3000

❐ Final answer :

➡ Number of boys are 4x = 12,000

Hence, Option (d) 12,000 ☑

${{\underline{\underline{{\textsf{\textbf{Verification : }}}}}}}$

As the question says that if 1000 girls leaves then the ratio will be 6 : 7

A/q,

Number of girls after leaving of 1000 girls

→ 5x - 1000

→ 5(3000) - 1000

→ 15,000 - 1000

→ 14,000

Now

Forming in ratio :

➙ Number of boys : Number of girls

→ 12,000 : 14,000

→ 12 : 14

→ 6 : 7

${{\underline{\underline{{\textsf{\textbf{Hence, Verified ☑ }}}}}}}$

Answer 2

Answer:

(d)12000

Step-by-step explanation:

===>Ratio of number of boys to girls = 4:5.

===>1000 girls leave then the ratio turns = 6:7.

Lets boys = 4x

girls = 5x.

number of girls present now:-

5x-1000

Equation forms:-

$\frac{4x}{5x - 1000 \: \: = \frac{6}{7} }$

=>4x(7) = 6 (5x - 1000)

=>28x = 30x - 6000.

=>6000 = 2x.

=>6000/2 = x.

=>x = 3000.

Number of girls after leaving of 1000 girls

==>5x - 1000

==>5(3000) - 1000.

==>15,000 - 1000.

==>14,000.

In ratio:-

Number of girls : Number of boys

===>12000: 14000

===>12:14

===>6:7.

Hence,12000