Question

Which of the following could be the distant of Allyson's map

Answer 1

The real distance from Mumbai to Bangalore is 845 km.

The real distance from Mumbai to Dehli is 1160 km.

Allyson has made a map in which distance is in cm and is proportional to the real distance.

Since the real distance and the distance on the map are proportional then their ratio must be equal.

Let us compare the ratio of real distance with the distance in given options.

Option A:

Bangalore to Mumbai = 116.5 cm

Mumbai to Dehli = 174 cm

`\begin{gathered} (845)/(1160)=(116.5)/(174) \\ 0.728\\e0.669 \end{gathered}`

As you can see, the ratio is not equal so this is wrong.

Option B:

Bangalore to Mumbai = 42.25 cm

Mumbai to Dehli = 58 cm

`\begin{gathered} (845)/(1160)=(42.25)/(58) \\ 0.728=0.728 \end{gathered}`

As you can see, the ratio is equal so this is correct.

Option C:

Bangalore to Mumbai = 23.4 cm

Mumbai to Dehli = 29 cm

`\begin{gathered} (845)/(1160)=(23.4)/(29) \\ 0.728\\e0.807 \end{gathered}`

As you can see, the ratio is not equal so this is wrong.

Option D:

Bangalore to Mumbai = 16.9 cm

Mumbai to Dehli = 23.2 cm

`\begin{gathered} (845)/(1160)=(16.9)/(23.2) \\ 0.728=0.728 \end{gathered}`

As you can see, the ratio is equal so this is correct.

Option E:

Bangalore to Mumbai = 25.35 cm

Mumbai to Dehli = 34.8 cm

`\begin{gathered} (845)/(1160)=(25.35)/(34.8) \\ 0.728=0.728 \end{gathered}`

As you can see, the ratio is equal so this is correct.

Therefore, the following can be the possible distances on Allyson's map

Option B

Option D

Option E