Question-87553

Question Number 87553 by TawaTawa1 last updated on 05/Apr/20

Answered by ajfour last updated on 05/Apr/20

l e t n o . o f b o y s i n A = 3 k

\dots \dots \dots . . g i r l s \dots . A = 2 k

l e t n o . o f g i r l s i n B = x

& n o . o f b o y s i n B = y

n o . o f g i r l s i n C = z

n o . o f b o y s i n C = t

\Rightarrow x + y = 5 k \dots (i)

\frac{x}{4} + z = 16 + x \dots (i i)

\frac{y}{t} = \frac{5}{8} \dots . (i i i)

z + t = 100 \dots . (i v)

10 k + 100 = 220 \dots (v)

Q = \frac{3 k + y + t}{2 k + x + z} = ?

f r o m (v) : k = 12

\Rightarrow x + y = 60 [u s i n g (i)]

z = 100 - t

y = \frac{5 t}{8}

N o w f r o m (i i)

\frac{x}{4} + 100 - t = 16 + x

\Rightarrow \frac{3 x}{4} + t = 84 \dots (I)

x + \frac{5 t}{8} = 60 \dots . (I I)

\Rightarrow 336 - 4 t + \frac{15 t}{8} = 180

\frac{17 t}{8} = 156

b u t t s h u d h a v b e e n a n i n t e g e r!

I s h a l l c h e c k g a i n a f t e r a w h i l e . .

Commented by TawaTawa1 last updated on 05/Apr/20

God bless you sir . I appreciate .

From your solution sir . I got 7 : 4

Commented by TawaTawa1 last updated on 05/Apr/20

I said let total number of students be = x

Let the number of boys be = p

Let the number of girls = q

So that, p + q = x

No of boys and girls in A = \frac{3 x}{5} and \frac{2 x}{5}

Number of girls in B = 0 . 25 q

Number of girls in C = 0 . 25 q + 16

Number of boys in B and C = \frac{5 x}{13} and \frac{8 x}{13}

And 100 students in C (no of boys + number of girls)

\frac{8 x}{13} + 0 . 25 q + 16 = 100

\frac{8 x}{13} + 0 . 25 q = 84 \dots \dots . (i)

Number of students in B (Boys + Girls)

\frac{5 x}{13} + 0 . 25 q = 60 \dots \dots (ii)

Then solving (i) and (ii) q = 80

And p = 220 - 80 = 140

Hence, p : q = 140 : 80 \Rightarrow 7 : 4

It is the 60 you got that made me to solve further .

God bless you sir .