
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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