Question

114. In an auditorium, the ratio of the number of girls to the number of boys was 5:9. When 203 girls entered the
auditorium, the new ratio of the number of girls to the number of boys became 4:3. How many pupils were in the
auditorium at first?
(a) 406
(b) 326
(c) 580
(d) 428​

Answer 1

$\large\mathfrak \red{Solution:-}$

$\underline \mathbb{GIVEN:-}$

☯Ratio of girls : boys = 5 : 9

☯When 203 girls entered ratio become = 4 : 3

$\underline \mathbb{TO \: FIND:-}$

☯Pupils present in the auditorium at first.

$\underline \mathbb{ASSUMPTION:-}$

☯Let, the present number of girls be 5x .

☯$\therefore$ the present number of boys is 9x .

★After 203 girls entered into the auditorium ,

☯Then, total number of girls is 5x + 203

☯And the number of boys is 9x.

$\underline \mathbb{BY \: THE \: PROBLEM:-}$

$5x + 203 : 9x = 4 :3 \\ \\ \implies \: \frac{5x +203 }{9x} = \frac{4}{3} \\ \\ \implies \:3(5x + 203) = 4 \times 9x\\ \\ \implies \:15 {x} + 609 = 36 {x} \\ \\ \implies \:36 {x} - 15 {x} = 609 \\ \\ \implies \: 21 x= 609 \\ \\ \implies \: 21 x = 609 \\ \\ \implies \: x = \frac{609}{21} \\ \\ \implies \: x = 29$

☯Present number of girls = 5x = 5 × 29 = 145

☯Present number of boys = 9x = 9 × 29 = 261

★So, Total pupils = (145 + 261) = 406

$\underline \mathbb{ANSWER:-}$

$\implies \boxed{ \blue{ Total \: pupils = 406}}$