If a firm sells 7000 units it's loss is $ 40,000. But if it sells 10,000 units it's profit is $ 20,000 . What is it's Fixed Cost :?

b)180,000

Hmm... with the assumption that total cost and other cost elements was not given to obtain the variable cost since Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC).

1. Profit / Loss = Total Revenue (TR) - Total Cost (TC) since VC is easily obtained FC will be taken in this circumstance as total cost
2. TR = Quantity (output unit) x Selling Price (SP) per uni since selling price per unit is not given let represent it by 'X'

Hence the equation7,000X - FC = -40,000  (1) multiply by -1 will be -7,000X + FC =40,000 (3)

                                  10,000X - FC =20,000  (2)                                     10,000X - FC =20,000  (2)

Add equation (3) and (2) will be -7,000X +10,000X =40,000 +20,000 thus FC will cancel out

                                                                     3,000X =60,000 hence X (SP) =60,000/3,000 = $20

Putting X into any of the above equation let say (2)

10,000(20) - FC =20,000

200,000 -20,000 = FC hence FC = $180,000

In the normal process this would have been the total cost but VC cannot be computed using it with the various VC formulas example1. VC = TC - FC  2. VC = Output x variable cost per unit

3. The Change in total cost as agianst outputs at different level of production

B), 

based on fomula, Profit or loss = (number of units*contibution margine per unit) - Fixed cost

(1) : -, = (* C.M) -F.C        &      (2):    , = (0 * C.M) - F.C

Then (1) -(2) :, = C.M so, C.M per unit =

F.C =,  (Total fixed cost and variable cost per unit remain constant within the relevant range)

 1,80,000.

Change in quantity = (10,000 -7,000) =3,000 units.

Change in Profit =20,000 - (-40,000) = `60,000.

Therefore, unit contribution = (change in profit) / (change in output) =60,000 /3,000 = `20.

So, when output =10,000 units, total contribution =20 x10,000 = `2,00,000

Fixed Cost = Total Contribution - Profit =2,00,000 -20,000 = `1,80,000.