Question

In a hotel the tariff for every odd date is Rs. 1000 and for even dates is Rs. 2000. If a man paid a total of 30,000Rs/-. For how many days did he stay in the hotel given that the first day is\[{{5}^{th}}\] date of the month?

Answer 1

Hint: For solving this problem we assume that the tariff of 2 consecutive dates one is an odd date and one even date as 3000/- and find for how many days will it take to reach 30,000/-. After evaluating if we get an answer as a natural number then it's fine but the problem is when the answer is in fractions because the number of days will always be in natural number. If the answer we get is in fraction then we take the quotient of that fraction and add one day to it to get the number of days because only one odd day will change the number of days to fractions.

Complete step by step answer:
We are given that the tariff for odd dates is 1000/- and that of even dates is 2000/-.
We are also given that the starting date is the fifth date which is odd.
Let us assume for two consecutive days the tariff is
\[2\text{ days}=1000+2000=3000\]
So, we can say that for 2 days the tariff will be 3000/-
Now, let us find for how many days the tariff will be 30000/- if the tariff for 2 days is 3000/-.
This is calculated as below
\[\begin{align}
  & \Rightarrow \text{Days}=\dfrac{2\times 30,000}{3,000} \\
 & \Rightarrow \text{Days}=20 \\
\end{align}\]
Here, we can see that the number of days we got in this method of solving is a natural number. So, there is no problem so that we can conclude that the answer is 20 days.

Therefore, we can say that it takes 20 days to get the total tariff of 30,000/-.

Note: Students may make mistakes in concluding the answer. Suppose if the question is asked to find the number of days for 31,000/- then the number of days is calculated in the same manner as
\[\begin{align}
  & \Rightarrow \text{Days}=\dfrac{2\times 31,000}{3,000} \\
 & \Rightarrow \text{Days}=\dfrac{62}{3} \\
\end{align}\]
Here, the number of days is not a natural number then we must add ‘1’ to the quotient to the above division to get the number of days.
\[\Rightarrow \text{Days}=20+1=21\]
Therefore, the number of days it will take to get 31,000/- is 21 days.