Question

If the distance between two places on the map is 3 cm and scale of the map is 2 cm = 2000km. Find the actual distance between the two places.​

Answer 1

$\large\sf\underline{Given}$

• Distance between two places on the map = 3cm .

• Scale of the map is 2 cm = 2000km .

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$\large\sf\underline{To\:find}$

• Actual distance between two places .

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$\large\sf\underline{Solution}$

We know ,

If the actual distance increases oR decreases then the distance in the map also increases oR decreases .

Therefore ,

Actual distance directly vary with the distance in the map .

So ,

$\small{\underline{\boxed{\mathrm\pink{\frac{x₁}{x₂}=\frac{y₁}{y₂}}}}}$

Here ,

• x₁ = 2 ⠀,⠀⠀⠀ x₂ = 2000

• y₁ = 3 ⠀,⠀⠀⠀ y₂ = x ( say )

Substituting the value in :

$\sf➞\:\frac{x₁}{x₂}=\frac{y₁}{y₂}$

$\sf➞\:\frac{2}{2000}=\frac{3}{x}$

$\sf➞\:2x=2000 \times 3$

$\sf➞\:2x=6000$

$\sf➞\:x=\frac{6000}{2}$

$\small{\underline{\boxed{\mathrm\pink{➠\:x=3000\:kms}}}}$

$\dag\:\underline{\sf So\:the\:actual\:distance\:is\:3000\:kms\:.}$

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!! Hope it helps !!