Question

In a hostel of $ 50 $ girls, there are food provisions for $ 40 $ days. If $ 30 $ more girls join the hostel, how long will these provisions last? (in days)

Answer 1

Hint: Identify the known and unknown ratios and set up the ratio and proportion and solve accordingly. In these ratio and proportion types of questions, take any variable as the reference number where applicable and frame the word statements into the form of mathematical expressions.

Complete step-by-step answer:
Total number of girls in a hostel is equal to the sum of girls already there and the more who joined later.
Total number of girls $ = 50 + 30 = 80 $
Let us assume that “x” is the number of days for which food provisions last for $ 80 $ girls.
 $ 50 $ Girls, there are food provisions for $ 40 $ days.
 If $ 80 $ girls then it lasts for “x”
Since, with the increase in the number of girls then the food will last for less number of days. This is the inverse ratio and proportion –
 $ \Rightarrow 50 \times 40 = 80x $
Simplify the above expression-
 $ \Rightarrow 2000 = 80x $
Make the required variable as the subject –
 $ \Rightarrow x = \dfrac{{2000}}{{80}} $
Simplify –
 $ \Rightarrow x = 25 $ Days
Hence, the required numbers of days are $ 25 $ days.
So, the correct answer is “25”.

Note: Always read the question twice and frame the word statement in the mathematical form. Segregate all the known and unknown terms and form the corresponding ratios and the proportions accordingly.
Ratio is the comparison between two numbers without any units.
Whereas, when two ratios are set equal to each other are called the proportion.
Four numbers a, b, c, and d are said to be in the proportion. If $ a:b = c:d $ whereas, four numbers are said to be in continued proportion if the terms \[\] $ a:b = b:c = c:d $