A picnic is being planned in a school for Class $V I I .$ Girls are $60 %$ of the total number of students and are $18$ in number. The picnic site is $55 k m$ from the school and the transport company is charging at the rate of $R s 12 p e r k m$ . The total cost of refreshments will be $R s 4280 .$ Find the cost per head if two teachers are also going with the class?

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Solution

Step 1- Finding the total cost
Distance of Picnic site from school $= 55 k m$
Total distance traveled $=$ Distance from school to picnic site $+$ Distance from picnic site to school
$= 55 + 55 = 110 k m$
Cost of Transportation per km $= R s 12$
So, the cost of transportation for $110 k m = R s 12 \times 110$
$= R s 1320$
Cost of Refreshment $= R s 4280$
Total Cost $=$ Total transportation cost $+$ Refreshment cost
$= 1320 + 4280$
$= R s 5600$
Step 2- Finding the cost per head
Let the total students be $x$
Number of girls $= 60 %$ of the total number of students
$\Rightarrow 18 = 60 %$ of $x$
$rightwards double arrow 18 equals space 60 over 100 cross times space x space space space space space space space space space space space space space space open parentheses because space o f space m e a n s space m u l t i p l i c a t i o n close parentheses rightwards double arrow 18 equals space fraction numerator 60 x over denominator 100 end fraction rightwards double arrow 18 equals fraction numerator 6 x over denominator 10 end fraction rightwards double arrow x equals fraction numerator 18 cross times 10 over denominator 6 end fraction rightwards double arrow x equals 3 cross times 10 rightwards double arrow x equals 30$
Total number of students = $30$
Given two teachers are also going with the class
Total person $=$ Number of Students $+$ Number of teachers
$= 30 + 2 = 32$
Cost per person = $\frac{T o t a l c o s t}{T o t a l p e r s o n}$
$= \frac{5600}{32} = R s 175$
Hence, cost per head $= R s 175$

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