Question

Consider the mess charges for $35$ students for $24$ days is rs.$6300$. How much will be the mess charges for $25$ students for $18$ days.

Answer 1

Here we have 3 quantities i.e., mess charges, number of students and number of days.

Mess charges in Rs.	Number of students	Number of days
$6300$	$35$	$24$
$?\left(x\right)$	$25$	$18$
$6300:x$	$35:25=7:5$	$24:18=4:3$

Mess charges is directly proportional to number of students.
Mess charges $\propto$ number of students
$6300:x=7:5$
Again mess charges are directly proportional to number of days.
Mess charges $\propto$ number of days
$6300:x=4:3$
Since, mess charges depends upon both the value i.e number of students and number of days so we will take a compound ration of these two variables.
Mess charges $\propto$ compound ratio of ratio of number of students and ratio of number of days
$6300:x=$compound ratio of $7:5$ and $4:3$
$6300:x=7\times 4:5\times 3$
Product of extremes $=$ product of means.
$28\times x=15\times 6300$
$x=\frac{15\times 6300}{28}$
$x=$ Rs.$3375$
hence, the required mess charges is Rs.$3375$