Percentage Gain

Percentage Gain: Every Transaction is profitable, but when you sell article below its cost price, it is thus a Loss.

Gain:
= Selling Price(SP) – Cost Price(CP)

Example 1: Chisom bought an article #250 and sold it #300. What gain did she make?

Solution:
CP = #250
SP = #300
Gain = SP – CP = #300 – #250 = #50

Loss:
= CP – SP

Example 2: Mrs Bola bought an article #250 and sold it #230. What was her Loss?

Solution:
CP = #250
SP = #230
Loss = CP – SP = #250 – #230 = #20

Percentage Gain (PG):
This is the percentage of the profit made when the selling price is greater than the cost price.

= [(SP – CP)/CP] x 100

Example 3: Chisom bought an article #250 and sold it #300. What is her percentage gain?

Solution:
CP = #250
SP = #300

PG = [(SP – CP)/CP] x 100

= [(300 – 250)/250] x 100 = (50/250) x 100
= 20%

Percentage Loss(PL): This is the percentage of the Loss made when the cost price is greater than the selling price.

= [(CP – SP)/CP] x 100

Example 4: Mrs Bola bought an article #250 and sold it #230. What is her percentage Loss?

Solution:
CP = #250
SP = #230

PL = [(CP – SP)/CP] x 100

= [(250 – 230)/250] x 100 = (20/250) x 100
= 8%

QUESTIONS AND SOLUTIONS:

Q1: An article that costs #370 was sold at a loss of 14%. What is the selling price?

Solution:
CP = #370
SP = ?
PL = 14%

PL = [(CP – SP)/CP] x 100 = 14

[(370 – SP)/370] x 100 = 14

100(370 – SP) = 370 x 14
37000 – 100SP = 5180
-100SP = 5180 – 37000

100SP = -31820

SP = -31820/-100
SP = #318.20

Q2: A trader bought certain articles at 10 for #15.00 and sold them at #19.50 per dozen. Find the percentage gain or loss.

Solution:
The trader bought the articles at 10 for #15.00, and he sold them #19.50 per dozen.

A dozen = 12
Thus, (10/12) x #19.50 = SP.

SP= #16.25
CP = #15.00
PG = ?

PG = [(SP – CP)/CP] x 100

= [(16.25 – 15)/15] x 100 = (1.25/15) x 100
= 8.3% gain.

Q3: A dealer gains #142.00 when he sells an article to gain 20%. What is the selling price?

Solution:

The dealer gains #142.00 on an article he bought after selling it.

Let the cost price = y
and the selling price
= (y + #142)

PG = 20%

PG = [(y+142) – y]/y x 100

(142/y) x 100 = 20

14200/y = 20

20y 14200
y = 14200/20
y = #710.00

Therefore:
SP = (y + 142)
= 710 + 142
= #852.00

Q4: A trader bought 30 articles. He sold 20 of them at a gain of 16% and sold the remainder at a loss of 4%. Find the percentage profit/loss on the articles.

Solution:
Total number of articles bought = 30.

Let price per article be y.
30 of them cost 30y

20 of them cost 20y.

10 of the articles cost 10y.

INCOMES

20 articles @ 16% profit gives:
20y(100% + 16%) = 20y(1 + 0.16)
= 20y(1.16)
= 23.2y

10 articles @ 4% Loss gives:

10y(100% – 4%) = 10y(1 – 0.04)
= 10y(0.96)
= 9.6y

TOTAL INCOME

= 23.2y + 9.6y
= 32.8y

OVERALL PROFIT/LOSS

(Total income) ÷ (Total cost)

= 32.8y/30y = 1.0933
= (1.0933) = (1 + 0.093) = (100% + 9.3%)

Therefore, the percentage profit = 9.3%

Q5: In making cake, the costs of flour and sugar are in the ratio 3:2. A caterer sells for #150 to make a profit of 25%. What is the cost of the sugar for the cake?

Solution:
CP = ?
SP = #150
PG = 25%

(SP – CP)/CP = 25/100
(150 – CP)/CP = 1/4
4(150 – CP) = 1 x CP
600 – 4CP = CP
-4CP – CP = -600
-5CP = -600
CP = #120

The ratio of flour and sugar is 3:2

Cost of sugar = 2/5 x 120
= #48.00

Q6: By selling an article for #19.25, a trader makes a profit of 25%. How much must he sell the article to make a profit of 40%?

Solution:
CP = ?
SP = #19.25
PG = 25%

(SP – CP)/CP = 25/100
(19.25 – CP)/CP = 1/4
4(19.25 – CP) = 1 x CP
77 – 4CP = CP
77 = 5CP
CP = 77/5 = #15.40

For him to make a profit of 40%

CP = #15.40
SP = ?
PG = 40%

(SP – CP)/CP = 40/100
(SP – 15.4)/15.4 = 2/5
5(SP – 15.4) = 2 x 15.4
5SP – 77 = 30.8
5SP = 107.8
SP = #21.56

Q7: A woman bought 200 mangoes for #8. She discovered that 8 of the mangoes got spoilt, but then sold the rest at #0.60 a dozen. Find her Percentage profit on the sales.

Solution:
She bought 200 mangoes for #8 = CP

8 got spoilt
Good ones = 200 – 8
= 192 mangoes

She sold the rest at #0.60 a dozen

192/12 x 0.60
= 16 x 0.6
SP = #9.6

Percentage Gain = ?

PG = (9.6 – 8)/8 x 100
= 1.6/8 x 100
= 160/8 = 20%

Q8: The costs of flour and sugar are #1.40 and #1.60 respectively. To prepare cake the two items are mixed in the ratio 2:3, and the mixture is then sold at #2.40 per kg. Find the gain or loss percentage.

Solution:
Using the Ratio 2:3

Mass of the mixture = 5kg

Cost of the mixture = cost of flour + cost of sugar

= 2 x 1.40 + 3 x 1.60
= 2.8 + 4.8
CP = #7.6

SP of the mixture = 5 x 2.40 = #12.00

Since the CP is less than the SP, we are calculating the percentage gain.

PG = (SP – CP)/CP x 100

= (12 – 7.6)/7.6 x 100 = 4.4/7.6 x 100 = 440/7.6
PG = 57.89%
= 57.9%

Q9: Uguru sold an article to Bola to gain 20%. Thereafter Bola sold the same article to Hauwa to gain 25%. If the sales to Hauwa yielded #67.50, find what it cost Uguru to purchase the article.

Solution:

Bola’s CP = Uguru’s SP

Bola’s
CP = ?
SP = #67.50
PG = 25%

PG = (SP – CP)/CP = 25%

(67.50 – CP)/CP = 25/100
(67.50 – CP)/CP = 1/4

4(67.50 – CP) = 1 x CP
270 – 4CP = CP
-4CP – CP = -270
-5CP = -270
CP = #54.00

Remember that Bola’s CP = Uguru’s SP

Uguru’s
SP = #54.00
CP = ?
PG = 20%

PG = (SP – CP)/CP = 20%
(54 – CP)/CP = 20/100
(54 – CP)/CP = 1/5

5(54 – CP) = 1 x CP
270 – 5CP = CP
-5CP – CP = -270
-6CP = -270
CP = -270/-6
CP = #45.00

So the article cost Uguru #45.00 to purchase.

Q10: A man bought 8 dozen articles at #1.40 each. He sold 40 of them at a profit of 20%, 35 at a loss of 4% and the remainder at a profit of 15%. Find the:
(a) Overall selling Price to the nearest Kobo.

(b) Overall percentage gain or loss to 2 decimal places.

Solution:
Total number of items bought = 8 x 12 = 96

The item cost #1.40 per one.

Overall CP = 8 x 12 x #1.40
= #134.40

He sold 40 out of 96 items bought at a profit of 20%
CP(1) = 40 x #1.40 = #56.00

(SP – CP)/CP = 20%

(SP – 56)/56 = 1/5
5(SP – 56) = 1 x 56
5SP – 280 = 56
5SP = 336
SP(1) = #67.20

He sold 35 at a loss of 4%.
CP(2) = 35 x #1.40 = #49.00

(CP – SP)/CP = 4%
(49 – SP)/49 = 4/100

(49 – SP)/49 = 1/25
25(49 – SP) = 1 x 49
1225 – 25SP = 49

25SP = 49 – 1225
-25SP = -1176
SP(2) = #47.04

He sold the remainder at a profit of 15%.
The items remains 96 – (40 + 35) = 21 items

CP(3) = 21 x #1.40 = #29.40

(SP – CP)/CP = 15%

(SP – 29.4)/29.4 = 15/100

100(SP – 29.4) = 15 x 29.4

100SP – 2940 = 441
100SP = 3381
SP(3) = #33.81

Find the:
(a) Overall selling Price to the nearest Kobo.
Overall selling Price (OSP)
= SP(1) + SP(2) + SP(3) = #67.20 + #47.04 + #33.81 = #148.05

(b) Overall percentage gain or loss to 2 decimal places.

OCP = #134.40
OSP = #148.05

Since the overall selling price is greater than the overall cost price, thus it is a gain

PG = (SP – CP)/CP x 100

= [(148.05 – 134.40)/134.4] x 100

= (13.65/134.4) x 100 = 1365/134.4
=10.156%
= 10.16% (2 dp)

Q11: Sule bought 30 eggs for #450.00 and sold each egg for #12.00. What is his percentage Loss?

Solution:
CP = #450.00
SP = #12 x 30 = #360.00

PL = (450 – 360)/450 x 100

= 90/450 x 100 = 20%

Q12: By selling 20 oranges for #1.35, a trader makes a profit of 8%. What is his percentage gain or loss if he sells the same 20 oranges for #1.10?

Solution:
CP = ?
SP = #1.35
PG = 8%

(1.35 – CP)/CP = 8/100

100(1.35 – CP) = 8 x CP
135 – 100CP = 8CP
-108CP = -135
CP = #1.25

If he had sold the same 20 oranges for #1.10, it will be a loss for him because the cost price is greater than the selling price.

PL = (1.25 – 1.1)/1.25 x 100

= 0.15/1.25 x 100
= 12%

Q13: A trader bought 100 Oranges at 5 for #1.20. 20 Oranges got spoilt and the remaining were sold at 4 for #1.50. Find the percentage gain or loss.

Solution:
Total CP = (100/5) x #1.20
= #24.00

20 oranges got spoilt.
Remaining = 100 – 20 = 80 oranges.

SP = (80/4) x #1.50
= #30.00
Since the selling price is greater than the CP, it is a gain.

PG = (30 – 24)/24 x 100 = 25%

Q14: Audu bought an article for #50,000 and sold it to Femi at a loss of x%. Femi later sold the article to Oche at a profit of 40%. If Femi made a profit of #10,000. Find the value of x.

Solution:
Audu’s SP = Femi’s CP

Let Femi’s CP = y
40/100 x y = 10000
2y/5 = 10000
y = #25,000 = CP

Femi’s
CP = #25,000
SP = #25,000 + #10,000
SP = #35,000

Remember that Audu’s SP = Femi’s CP

Audu’s
SP = #25,000
CP = #50,000
PL = x%

x = (50000 – 25000)/50000 x 100

x = 50%

Q15: A car dealer bought a second hand car for #250,000.00 and spent #70,000.00 refurbishing it. He then sold the car car for #400,000.00. What is the percentage gain?

Solution:
CP = #250,000 + #70,000
= #320,000

SP = #400,000
PG = ?

PG = (400000 – 320000)/320000 x 100

= 80000/320000 x 100 = 8/32 x 100
= 25%

Q16: A man bought a wrist watch for #150 but was only able to sell it for #120. Find the loss percent on the transaction.

Solution:
CP = #150
SP = #120
PL = ?

PL = (150 – 120)/150 x 100

= 30/150 x 100
= 100/5 = 20%

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