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

Answer:

10%

Step-by-step 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= $\frac{3}{4} \times 600= \ 450$

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

∴ Selling price of $\frac{3}{4}\ of\ lemon= 450- \frac{20}{100}\times 450$

Selling price= $450- 90= \ 360$

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

Now, the cost price of remaining lemon $(1-\frac{3}{4} )= (\ 600-\ 450)$

∴ The cost price of $\frac{1}{4}\ lemon = \ 150$

As given, remaining $\frac{1}{4} lemon\ sold\ at\ gain\ of\ 20\%$

∴ Selling price of $\frac{1}{4} \ lemon= (150\times \frac{20}{100}+150)$

Selling price of $\frac{1}{4} \ of\ lemon= (30+150)$

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

Loss\profit percent= $\frac{(SP-CP)}{CP} \times 100$

∴ Loss\profit percent= $\frac{60}{600} \times 100= 10\%$

Hence, the loss percentage is 10%