Question

The cost of painting a square with 10 percent greater dimensions by using 10 percent cheaper paint will be?

Answer 1

Let the side of square = $a$ units

We know that Area of square = $side^{2}$

$\Rightarrow \text{Area = } a^{2}$ square units

Let the cost to paint 1 square unit be $x\ Rs.$

Total cost to paint the square = Area $\times$ Cost to paint 1 square unit

$\Rightarrow \text{Initial Cost, C } = a^{2} \times x ..... (1)$

Side is increased by 10%.

So, new side becomes:

$a + a \times \dfrac{10}{100}\\\Rightarrow \dfrac{11a}{10}$

Cost is decreased by 10%

So, new side becomes:

$x - x \times \dfrac{10}{100}\\\Rightarrow \dfrac{9x}{10}$

Total New Cost = New Area $\times$ New Cost

$\Rightarrow (\dfrac{11a}{10})^2 \times \dfrac{9x}{10}\\\Rightarrow \dfrac{1089}{1000} \times a^2\times x ..... (2)$

Using equations (1) and (2) :

Total New cost = $\frac{1089}{1000}$ $\times$ Initial Cost

Total New cost = $(1+\frac{89}{1000})$ $\times$ Initial Cost

Total New Cost = Initial Cost + $8.9\%$ $\times$ Initial Cost

i.e. New Cost of painting the new square is increased by $8.9\%$ if side of square is increased by 10 % and paint used is 10% cheaper.