Profit and Loss

Worked example

1. 1

   $\frac{2}{3}\times 24=16$ — How many sell at $9: two thirds of 24. Divide 24 by 3 to get 8, then times 2.

2. 2

   $24-16=8$ — The rest sell at $6. Take the 16 away from all 24 mugs.

3. 3

   $16\times 9=144$ — Money in from the $9 mugs: how many sold × the price of one.

4. 4

   $8\times 6=48$ — Money in from the $6 mugs, the same way.

5. 5

   $144+48=192$ — Add the two groups to get the total money in.

6. 6

   $192-150=42$ — Money in minus what you paid. 192 is more than 150, so this is a profit of $42.

7. 7

   $\frac{42}{150}\times 100=28\%$ — Divide the profit by the cost, then × 100 to turn the answer into a percentage.

Worked example

1. 1

   $40\times 2=80$ — The cost: you paid $2 for each of the 40 pens.

2. 2

   $\frac{1}{2}\times 40=20$ — Half the pens sell at $2.50. Half of 40 is 20.

3. 3

   $\frac{1}{4}\times 40=10$ — A quarter sell at $1.60. Divide 40 by 4.

4. 4

   $40-20-10=10$ — The rest sell at $1. Take both groups away from the 40 pens.

5. 5

   $20\times 2.50=50$ — Money in from the first group: how many × the price.

6. 6

   $10\times 1.60=16$ — Money in from the second group.

7. 7

   $10\times 1=10$ — Money in from the rest.

8. 8

   $50+16+10=76$ — Total money in. It is less than the $80 cost, so this is a loss.

9. 9

   $80-76=4$ — Cost minus money in, the bigger minus the smaller, so the loss is a positive $4.

10. 10

    $\frac{4}{80}\times 100=5\%$ — Divide the loss by the cost, then × 100. Just like profit, you compare with what you paid.

Worked example

1. 1

   $\frac{310}{270}=1.148148\dots$ — Divide the money in by the cost. Keep the full calculator number; do not round yet.

2. 2

   $1.148148\dots \times 100=114.8148\dots$ — × 100 turns it into a percentage: you sold for 114.8…% of what you paid.

3. 3

   $114.8148\dots -100=14.8148\dots$ — Take away 100%, which is the cost itself. What is left is the profit.

4. 4

   $14.8\%\text{profit}$ — Round only at the end: 14.8148… is 14.8 to 3 significant figures.

Worked example

1. 1

   $\frac{215}{250}\times 100=86$ — The phone sold for 86% of what it cost.

2. 2

   $86-100=-14$ — Take away 100. The answer is negative because the money in is less than the cost.

3. 3

   $\text{loss of }14\%$ — A negative answer means a loss. Write it as a 14% loss, not a −14% profit.

Worked example

1. 1

   $100\%+30\%=130\%$ — She wants her cost back (100%) plus 30% more on top.

2. 2

   $130\%=1.30$ — Change the percentage into a multiplier: divide by 100.

3. 3

   $160\times 1.30=208$ — The cost × the multiplier: $208 is the lowest price that gives 30% profit.

4. 4

   $200<208$ — She sold for $200, which is less than $208.

5. 5

   $\text{No}$ — So she did not make 30% profit. Always write Yes or No together with the numbers that prove it.

Worked example

1. 1

   $150\times 12=1800$ — The cost. You pay for all 150 boxes, even the ones that never sell.

2. 2

   $\frac{3}{5}\times 150=90$ — Boxes sold: 150 ÷ 5 = 30, and 3 × 30 = 90.

3. 3

   $90\times 25=2250$ — Money in. Only the 90 boxes that sold bring money in.

4. 4

   $2250-1800=\$450$ — Money in minus the cost. 2250 is bigger, so it is a profit of $450.

Worked example

1. 1

   $2+1=3$ — Add the ratio parts: 3 parts in total.

2. 2

   $300÷3=100$ — One part is 100 drinks.

3. 3

   $\text{tea: }2\times 100=200$ — Tea has 2 parts, so 200 teas.

4. 4

   $\text{coffee: }1\times 100=100$ — Coffee has 1 part, so 100 coffees.

5. 5

   $0.25\times 1.20=0.30$ — Profit on one tea: 25% of its price, and 25% = 0.25.

6. 6

   $0.40\times 2.50=1.00$ — Profit on one coffee: 40% of its price, and 40% = 0.40.

7. 7

   $200\times 0.30=60$ — Profit from all the teas: how many × the profit on one.

8. 8

   $100\times 1.00=100$ — Profit from all the coffees, the same way.

9. 9

   $60+100=\$160$ — Add the two groups for the total profit.