Question

Emily purchased lemons for $600. She sold 3/4 of these at a loss of 20% and the remaining at a gain of 20%. How much percent does she gain or lose in the whole transaction?

Answer 1

10%

Explanation:

Given: CP of lemon is $600.

3/4 of lemon sold at 20% loss

Remaining lemon at 20% gain.

Considering the quantity of lemon remain constant.

Cost price of 3/4 of lemon=
`(3)/(4) * 600= \$450`

As given, 3/4 of lemon sold at 20% loss.

∴ Selling price of
`(3)/(4)\ of\ lemon= 450- (20)/(100)* 450`

Selling price=
`450- 90= \$ 360`

Hence, selling price of 3/4 lemon is $360.

Now, the cost price of remaining lemon
`(1-(3)/(4) )= (\$ 600-\$ 450)`

∴ The cost price of
`(1)/(4)\ lemon = \$ 150`

As given, remaining
`(1)/(4) lemon\ sold\ at\ gain\ of\ 20\%`

∴ Selling price of
`(1)/(4) \ lemon= (150* (20)/(100)+150)`

Selling price of
`(1)/(4) \ of\ lemon= (30+150)`

Hence, selling price of 1/4 lemon is $180

Loss\profit percent=
`((SP-CP))/(CP) * 100`

∴ Loss\profit percent=
`(60)/(600) * 100= 10\%`

Hence, the loss percentage is 10%