Ratios & Proportion
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Q.

A sum of Rs.312 was divided among 100 boys and girls in such a way that the boy gets Rs.3.60 and each girl Rs.2.40 the number of girls is

 A.

35

 B.

40

 C.

45

 D.

50

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Solution:
Option(B) is correct

Step (i) Let $x$ be the number of boys and $y$ be the number of girls. 

Given total number of boys and girls = 100

\(\begin{align} x+y&=100 \end{align}\)

Step (ii) A boy gets Rs. 3.60 and a girl gets Rs. 2.40

The amount given to 100 boys and girls = Rs. 312

\(\begin{align} 3.6x+2.4y&=312 \end{align}\)

Step (iii) 

Solving (i) and (ii)

\(\begin{align*} 3.6x+3.6y&=360 \end{align*}\) multiplying by 3.6

\(\begin{align} 3.6x+2.4y&=312\\ 1.20y&=48\\ y&=40 \end{align}\)

The number of girls is $40$.

Edit: For an alternative solution, check comment by Sravan Reddy.

Edit 2: For yet another alternative solution, check comment by PULOK KHAN.


(6) Comment(s)


PULOK KHAN
 ()

Let, girls $=x$

So, boys $= 100-x$

Here, $x \times 2.40+(100-x) \times 3.60=312$

$x=40$



Sravan Reddy
 ()

If all 100 boys get money $=3.6*100 =360$

If all 100 girls get money $= 2.4*100 = 240$

But total amount is 312. So ratio of boys and girls is the ratio in which 312 divides 360 and 240 respectively.

So, if you go through this method, you will directly come to this step,

$(312-240):(360-312) = 72:48 = 6:4$

So 60% and 40%

P.S.Remember that 60 % is ratio of boys not girls as the ratio tells how far is the average from girls.

So, lesser ratio means more contribution. Think!!



Sam
 ()

B/G=3.60/2.40 calculate the ration between b & g.

=3/2

3:2

100*2/5=40.....


Fxyxy
 ()

Can you please elabotate more?

Manisha
 ()

Isn't the ratio btwn b and g the ratio of the money distributed ? and not the ratio of nmbr of boys to girls?


Sim
 ()

More easy solution--

Let number of girls $=x$

then boys will be $(100-x)$

$3.60*(100-x)+2.40x=312$

on solving above eq. u will get,

$x=40$

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