Question

A rectangular lawn $80m\times 60m$ has two roads each $10m$ wide running in the middle of it, one parallel to the length and the other parallel to the breadth. Find the cost of gravelling the roads at Rs. $30$ per square metre.

• A. $Rs.35000$
• B. $Rs.42000$
• C. $Rs.40000$
• D. $Rs.39000$

Answer 1

The correct option is D $Rs.39000$

In rectangular road $PQRS$, $l=60m,b=10m$

$\Rightarrow$ Area of rectangle $PQRS=l\times b=60\times 10=600m^2$

$\Rightarrow$ In rectangular road $ABCD$, $l=80m,b=10m$

$\Rightarrow$ Area of rectangle $ABCD=l\times b=80\times 10=800m^2$

$\Rightarrow$ Total area of two roads $=600m^2+800m^2=1400m^2$

$\Rightarrow$ But square $EFGH$ is common in both road.

$\therefore$ Area of $EFGH=10\times 10=100m^2$

$\therefore$ Final area of two roads $=1400-100=1300m^2$

$\therefore$ Cost of gravelling the roads $=1300\times 30=Rs.39000$