Question

two thirds of the area of a farm land was covered by wheat fields half of the remaining was covered by pound and the rest was garden. the area of the garden is 420 sq.m what is the total area of the farm land

Answer 1

Answer:

The total area of the farm land is  2520 sq. m

Step-by-step explanation:

Let us assume the total area of the farm land  = P sq. m

Now, two thirds of the area of a farm land was covered by wheat fields.

So, the area covered in Wheat field = $\frac{2}{3} \times P = (\frac{2}{3})P$

The area left which is not covered in wheat

= Total land - Land covered  in Wheat  

= $P - (\frac{2}{3}) P = (\frac{1}{3})P$

Also, the half of the remaining land is covered by pound.

So, the area covered in pound  = $\frac{1}{2} \times (\frac{P}{3} ) = (\frac{P}{6} )$

The other half is empty garden.

⇒The area empty garden  =   $\frac{1}{2} \times (\frac{P}{3} ) = (\frac{P}{6} )$

Also, the area of the garden = 420 sq. m

⇒$(\frac{P}{6}) = 420\\\implies P = 6 \times 420 = 2520$

or, P  = 2520 sq. m

Hence, the total area of the farm land is  2520 sq. m