Question
A $80\ m$ by $64\ m$ rectangular lawn has two roads, each $5\ m$ wide, running through its middle, one parallel to its length and the other parallel to its breadth. Find the cost of gravelling the roads at $₹ 40\ per\ m^2$.
✓
Answer
Area of the road ABCD $= 80 \times 5 = 400m^2$
Area of the road EFGH $= 64 \times 5 = 320m^2$
Area of the road PQRS $= 5 \times 5 = 25m^2$
Road PQRS is common to both the roads ABCD and EFGH.
$\therefore$ Area of the road to be gravelled
= Area of the road ABCD + Area of the road EFGH - Area of the road PQRS
$= (400 + 320 - 25)m^2$
$= 695m^2$
Now, cost of gravelling the roads $= ₹ 40\ per\ m^2$
$\therefore$ Cost of gravelling $695m^2$ road $= ₹ 40 \times 695 = ₹ 27800.$
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