Question

Reena climbs up \[5\] stairs every second and then climbs down \[2\] stairs over the next second. How many seconds will it take to climb the\[60\]stairs?

Answer 1

Hint: A little bit Knowledge of direct and inverse proportion will help you to solve this question easily. If you know the basic conditions for direct and inverse proportion and some basic formula to solve this then it will be easy to get the answer to this question. First, write all the things given in the question, and then it will be easy for you to solve the problem.

Complete answer:
According to the question, we are given that Reena climbs \[5\] stairs in one second and climbs down 2 stairs in one second.
Which means she climbs 3 stairs in 2 seconds.
Similarly, she will climb 6 stairs in 4 seconds and so on.
A direct and inverse proportion are used to determine how the quantities and amounts are correlated with each other.
\['\propto '\] is the symbol used to denote proportionality.
If x is directly proportional to y, then it is represented by \[x\propto y\].
If x is inversely proportional to y, then it is represented by\[x\propto \dfrac{1}{y}\].
Two quantities x and y are said to be in directly proportional if they fulfill the following criteria:
1) If x increases, y also gets increased.
2) If x decreases, y also decreases.
Similarly,
Two quantities x and y are said to be in inversely proportional if they fulfill the following criteria:
1) If x increases, then there is a decrease in y.
2) If x decreases, then there is an increase in y.
So according to the definition, we can see that this question is based on direct proportion as we can see that if we increase the number of stairs then the time taken to climb the stairs will also increase.
She has to climb 60 stairs, so let the time taken to climb 60 stairs be \[x\] seconds.
So now, \[\begin{align}
  & 3\text{ Stairs 2 sec} \\
 & \text{60 Stairs x sec} \\
\end{align}\]
Now cross multiplying it we will have,
\[60\times 2=3\times x\]
Now,
\[x=\dfrac{60\times 2}{3}\]
\[\therefore \]\[x\]=\[40\]seconds
So, the time taken by Reena to climb 60 stairs is 40 seconds.

Note: Direct proportion is also known as direct variation. The problems of stairs can also be solved with the help of recursion. We can also find the work done in moving upwards on the stairs with the help of this question. In the above question, Reena will not fall at the last second. She will reach there before the last second.