Question

A car's rectangular number plate was to be painted equally in blue and red as shown in the figure. What will be the total cost of painting the car's number plate if red paint costs ₹2 per$c{m}^2$ and blue paint costs ₹1 per $c{m}^2$?

• A. ₹300
• B. ₹360
• C. ₹350
• D. ₹420

Answer 1

The correct option is B ₹360

Since the number plate is a rectangle, the diagonal divides it into two triangles of equal areas.
This means that the areas of the red triangle and the blue triangle are equal.
$\Rightarrow$ Area of the number plate = Area of red triangle + Area of blue triangle
$\Rightarrow 2\times \text{Area of red/blue triangle}=\text{Area of the number plate}$

$\text{Area of the number plate}=20\times 12c{m}^2$
$\Rightarrow \text{Area of red/blue triangle}=\frac{1}{2}\text{(Area of the number plate)}$

$=\frac{1}{2}\left(240\right)=120c{m}^2$

Therefore cost of painting the number plate
= cost of painting the red triangle + cost of painting the blue triangle
= $₹\left[\right(120\times 2)+(120\times 1\left)\right]$
=₹[(120) (2 + 1)] = 120 x 3 = ₹360
Hence, the total cost of painting the number plate is ₹360.