Question

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
A) 1
B) \[\dfrac{7}{2}\]
C) 7
D) 49

Answer 1

Hint:
Here, we will use the concept of proportion to find required days. Proportion is defined as the two ratios which are equal. We will assume the required number of days to be some variable. Then we will use the given information and apply the condition of direct and indirect proportion. We will then use the formula of proportion to find the required value.

Formula Used:
A proportion is given by the formula \[a:b = c:d\] and \[e:f = c:d\] then \[\dfrac{{a \times d}}{e} = \dfrac{{b \times c}}{f}\]

Complete step by step solution:
We are given that 7 spiders make 7 webs in 7 days.
We will find the number of days that 1 spider needs to make 1 web.
Let \[x\] be the required number of days.
If the number of spiders is less, then the number of days is more to make a web. So it is in indirect proportion. So, we have
\[1:7::7:x\]
If the number of webs is more, then the number of days is more to make a web. So it is in direct proportion. So, we have
\[7:1::7:x\]
Now, we get
Spiders : Days
Webs : Days
So, we get
\[\left. \begin{array}{l}1:7\\7:1\end{array} \right\}::7:x\]
A proportion is given by the formula \[a:b = c:d\] and \[e:f = c:d\] then \[\dfrac{{a \times d}}{e} = \dfrac{{b \times c}}{f}\].
\[1 \times 7 \times x = 7 \times 1 \times 7\]
Multiplying the terms, we get
\[ \Rightarrow 7x = 49\]
Dividing both the sides by 7, we get
\[\begin{array}{l} \Rightarrow x = \dfrac{{49}}{7}\\ \Rightarrow x = 7\end{array}\]
Therefore, the required number of days is 7.

Thus Option(C) is the correct answer.

Note:
When two quantities are in direct proportion, then when one amount increases, then another amount also increases at the same rate. So, we can write as \[x = y\]. When two quantities are in indirect proportion, then when one amount increases, then another amount decreases at the same rate. So, it can be written as \[x = \dfrac{1}{y}\] . So, in order to solve the question we should remember these formulas while writing a proportion with direct and indirect variation.