Question

A meter is a measure of length, and 10 decimetres is equal in length to one meter. Calculate how many decimetres are in 12.5 meters.
(a) 125
(b) 1250
(c) 12.5
(d) None of these.

Answer 1

Hint: The constant is based on the concept of proportionality. Use the property that length on the decimetre scale is directly proportional to distance in meter scale. Use the definition of proportionality to remove the proportionality sign using the constant of proportionality to get an equation in terms of measurement in decimetre scale and measurement in meter scale. Use the data given in the question to find the constant of proportionality and solve to get the answer.

Complete step-by-step answer:
To start with the question, we let the length on the meter scale be l m, and the on decimetre scale be d dm.
Let us first try to interpret the question in mathematical terms. We know that the length on the map is directly proportional to the actual distance.
 $ \text{length on meter scale }\alpha \text{ length on decimetre scale}\text{.} $
 $ l\propto \text{d} $
Now according to the definition of proportionality, we can represent the above statement as:
 $ l=kd $
In the above equation, k is the constant of proportionality.
Now according to the question 1 meter on the meter scale represents 10 decimetre on decimetre scale. Representing it mathematically using the above equation, we get
 $ l=kd $
 $ \Rightarrow 1=10\times k $
 $ \Rightarrow k=\dfrac{1}{10}\text{ m/dm}.............(i) $
Therefore, the value of the constant of proportionality is $ \dfrac{1}{10}\text{ m/dm} $ .
So, if we put the value of k in the parent equation, we get
 $ l=\dfrac{1}{10}\times d $
Now we are asked the value of 12.5 meters on the decimetre scale. So, putting l=12.5.
 $ 12.5=\dfrac{1}{10}\times d $
 $ \Rightarrow 125dm=d $
Therefore, the answer to the above question is option (a).

Note: In the question related to proportionality, the key thing is to find the constant of proportionality. Also, the unit of the constant of proportionality is very important and needs to be used wisely. If you want you can directly solve the question using the unitary method as well.