Exercise 12.1
1. Given the following values, find the unknown values:
(i) C.P. = Rs 1200, S.P. = Rs 1350 Profit/Loss , ?
(ii) C.P. = Rs 980, S.P. = Rs 940 Profit/Loss = ?
(iii) C.P. = Rs 720, S.P. ?, Profit = Rs 55.50
(iv) C.P. ? S.P. = Rs 1254, Loss = Rs 32
Solution:
(i) CP = Rs. 1200, SP = Rs. 1350
CP < SP. So, profit.
Profit = Rs. (1350 – 1200) = Rs. 150
(ii) CP = Rs. 980, SP = Rs. 940
CP > SP. So, loss.
Loss = Rs. (980 – 940) = Rs. 40
(iii) CP = Rs. 720, SP = ?, profit = Rs. 55.50
Profit = SP – CP
Rs. 55.50 = SP – Rs. 720
SP = Rs. (55.50 + 720) = Rs. 775.50
(iv) CP = ?, SP = Rs. 1254, loss = Rs. 32
Loss = CP – SP
Rs. 32 = CP – Rs. 1254
CP = Rs. (1254 + 32) = Rs. 1286
2. Fill in the blanks in each of the following:
(i) C.P. = Rs 1265, S.P. = Rs 1253, Loss = Rs ______
Solution:
CP = 1265, SP = 1253
Loss = CP – SP
Loss = 1265 – 1253 = Rs. 12
(ii) C.P. = Rs______ , S.P. = Rs 450, Profit = Rs 150
Solution:
SP = Rs. 450, profit = 150
Profit = SP – CP
150 = 450 – CP
CP = 450 – 150
CP = Rs. 300
(iii) C.P. = Rs 3355, S.P. = Rs 7355, profit/loss = Rs______
Solution:
CP = Rs. 3355, SP = 7355,
As, SP > CP. So, there will be profit.
Profit = SP – CP
Profit = 7355 – 3355
Profit = Rs. 4000
(iv) C.P. = Rs _______, S.P. = Rs 2390, Loss = Rs 5.50
Solution:
SP = 2390, loss = 5.50
Loss = CP – SP
Rs. 5.50 = CP – Rs. 2390
CP = 5.50 + 2390
CP = Rs. 2395.50
3. Calculate the profit or loss and profit or loss per cent in each of the following cases:
Solution:
(i) CP = Rs. 4560, SP = Rs. 5000
Here, SP > CP. So, profit.
Profit = SP – CP = Rs. (5000 – 4560)= Rs. 440
Profit % = {(Profit/CP) x 100}% = {(440/4560) x 100}% = {0.0965 x 100}% = 9.65%
(ii) CP = Rs. 2600, SP = Rs. 2470.
Here, CP > SR. So, loss.
Loss = CP – SP = Rs. (2600 – 2470) = Rs. 130 Profit% = {(Profit/CP) x 100}%= {(130/2600) x 100}%
= {0.05 x 100}% = 5%
(iii) CP = Rs. 332, SP= Rs. 350.
Here, SP > CP. So, profit.
Profit = SP – CP = Rs. (350 – 332) = Rs. 18 Profit% = {(Profit/CP) x 100}% = {(18/332) x 100}%
= {0.054 x 100}% = 5.4%
(iv) CP = Rs. 1500, SP = Rs. 1500
SP = CP.
So, neither profit nor loss.
4. Find the gain or loss per cent, when:
(i) C.P. = Rs 4000 and gain = Rs 40.
Solution:
CP = 4000, gain = 40
Gain % = {(Gain/CP) x 100)
Gain % = {(40/4000) x 100}
Gain % = (0.01 x 100)
Gain % = 1%
(ii) S.P. = Rs 1272 and loss = Rs 328
Solution:
SP = Rs. 1272, loss = Rs. 328
Loss = CP – SP
CP = Loss + SP
CP = 328 + 1272
CP = Rs. 1600
Loss % = {(Loss/CP) x 100}
Loss % = {(328/1600) x 100}
Loss % = 20.5%
(iii) S.P. = Rs 1820 and gain = Rs 420.
Solution:
SP = 1820, gain = 420
Gain = SP – CP
CP = SP – Gain
CP = 1820 – 420
CP = Rs. 1400
Gain % = {(Gain/CP) x 100}
Gain % = {(420/1400) x 100
Gain % = 30%
5. Find the gain or loss per cent, when:
(i) C.P. = Rs 2300, Overhead expenses = Rs 300 and gain = Rs 260.
Solution:
C.P = Rs 2300
Over head expenses = Rs 300
Gain = Rs 260
Total = 2300 + over head expenses
= 2600
= 10%
(ii) C.P. = Rs 3500, Overhead expenses = Rs 150 and loss = Rs 146
Solution:
C.P = Rs 3,500
Over head expenses = Rs 150
Loss = 146 Total C.P = 3650
= 4%
6. A grain merchant sold 600 quintals of rice at a profit of 7%. If a quintal of rice cost him Rs 250 and his total overhead charges for transportation, etc. were Rs 1000 find his total profit and the selling price of 600 quintals of rice.
Solution:
Cost of 1 quintal of rice = Rs. 250
Cost of 600 quintals of rice = 600 x 250 = Rs. 150000
Overhead expenses = Rs. 1000
Total CP = Rs. (150000 + 1000) = Rs. 151000
Profit % = (Profit/CP) x 100
7 = (P/151000) x 100
P = 1510 x 7 = Rs. 10570
Profit = Rs. 10570
SP = CP + profit = Rs. (151000 + 10570) = Rs. 161570
7. Naresh bought 4 dozen pencils at Rs 10.80 a dozen and sold them for 80 paise each. Find his gain or loss percent.
Solution:
It is given that the cost of 1 dozen pencils = Rs. 10.80
So, Cost of 4 dozen pencils = 4 x 10.80 = Rs. 43.2
Selling price of each pencil = 80 paise
Total number of pencils = 12 x 4 = 48 [After that,, 1 dozen = 12 pencils]
SP of 48 pencils = 48 x 80
SP of 48 pencils = 3840 paise
SP of 48 pencils = Rs. 38.40 [After that,, 100 Paisa = 1 Rs]
Here, SP < CP. So, there will be loss.
Loss = CP – SP = 43.2 – 38.4 = Rs. 4.8
Loss % = (Loss/CP) x 100
Loss % = (4.8/43.2) x 100
Loss % = 480/43.2
Loss % = 11.11%
8. A vendor buys oranges at Rs 26 per dozen and sells them at 5 for Rs 13. Find his gain percent.
Solution:
CP of 1 dozen oranges = Rs. 26
CP of 1 orange = 26/12 = Rs. 2.16
CP of 5 oranges = 2.16 x 5 = Rs. 10.8
Now, SP of 5 oranges = Rs. 13
Gain = SP – CP = Rs. (13- 10.8) = Rs. 2.2
Gain %= (Gain/CP) x 100 = (2.2/10.8) x 100 = 20.3%
9. Mr Virmani purchased a house for Rs 365000 and spent Rs 135000 on its repairs. If he sold it for Rs 550000, find his gain percent.
Solution:
Amount Mr. Virmani paid to purchase the house = Rs. 365000
Amount he spent on repair = Rs. 135000
Total amount he spent on the house (CP) = Rs. (365000 + 135000) = Rs. 500000
SP of the house = Rs. 550000
Gain = SP – CP = Rs. (550000 – 500000) = Rs. 50000
Gain % = (Gain/CP) x 100= (50000/500000) x 100
= 5000000/500000 = 10%
10. Shikha purchased a wrist watch for Rs 840 and sold it to her friend Vidhi for Rs 910. Find her gain percent.
Solution:
The cost price of the wristwatch, CP = Rs. 840
Selling price of the wristwatch, SP = Rs. 910
CP < SP. So, there will be profit.
Gain = SP – CP = (910 – 840) = Rs. 70
Gain % = (Gain/CP) x 100
Gain % = (70/840) x 100
Gain % = 7000/840
Gain % = 8.3%
11. A business man makes a 10% profit by selling a toy costing him Rs 120. What is the selling price?
Solution:
CP = Rs. 12
Profit % = 10
We now that
SP = {(100 + profit %)/100} x CP = {(100+ 10)/100} x 120
= {(110/100)} x 120 = 1.1 x 120
= Rs. 132
12. Harish purchased 50 dozen bananas for Rs 135. Five dozen bananas could not be sold because they were rotten. At what price per dozen should Harish sell the remaining bananas so that he makes a profit of 20%?
Solution:
Total number of bananas = 50 dozen
No. of Bananas which were rotten = 5 dozen
Bananas left after removing rotten bananas = 50 – 5 = 45 dozens
Cost price of 50 dozens bananas, CP = Rs. 135
Price at which Harish should sell 45 dozen bananas to make a profit of 20%;
Profit % = (Gain/CP) x 100
20 = (Gain/135) x 100
Gain = 270/10 = Rs. 27
We know that;
Gain = SP – CP
27 = SP – 135
SP = 27 + 135
SP = Rs. 162
SP of 45 dozens of bananas = Rs. 162
SP for 1 dozen of bananas = 162/45 = Rs. 3.6
Harish should sell the bananas at Rs. 3.60 a dozen in order to make a profit of 20%.
13. A woman bought 50 dozen eggs at Rs 6.40 a dozen. Out of these 20 eggs were found to be broken. She sold the remaining eggs at 55 paise per egg. Find her gain or loss percent.
Solution:
Cost of one dozen eggs = Rs. 6.40
Cost of 50 dozen eggs = 50 x 6.40 = Rs. 320
Total number of eggs = 50 x 12 = 600
Number of eggs left after removing the broken ones = 600 – 20 = 580
SP of 1 egg = 55 paise
So, SP of 580 eggs = 580 x 55 = 31900 paise = Rs. 31900/100 = Rs. 319
Loss = CP – SP = Rs. (320-319) = Re. 1
Loss % = (Loss/CP) x 100 = (1/320) x 100 = 0.31%
14. Jyotsana bought 400 eggs at Rs 8.40 a dozen. At what price per hundred must she sell them so as to earn a profit of 15%?
Solution:
Cost of 1 dozen of eggs = Rs. 8.40
Cost of 1 egg = 8.40/12 = Rs. 0.7 [After that,, 1 dozen = 12 eggs]
Cost of 400 eggs = 400 x 0.7 = Rs. 280
Price at which Jyotsana should sell the 400 eggs to earn a profit of 15%,
Profit % = (Gain/CP) x 100
15 = (Gain/280) × 100
Gain = (15 × 280)/100
Gain = Rs. 42
We know that, Gain = SP – CP
42 = SP – 280
SP = Rs. 322
The SP of 400 eggs = 322
SP for 100 eggs = (322 × 100)/400 = Rs. 80.50
Therefore, the SP per one hundred eggs is Rs. 80.50.
15.A shopkeeper makes a profit of 15% by selling a book for Rs 230. What is the C.P. and the actual profit ?
Solution:
Given that the SP of a book = Rs. 230
Profit % = 15
After that,
CP = (SP x 100) + (100 + profit %)
CP = (230x 100) + (100 + 15)
CP = 23000 + 115 = Rs. 200
Also, Profit = SP – CP = Rs. (230 – 200) = Rs. 30
Actual profit = Rs. 30
16. A bookseller sells all his books at a profit of 10%. If he buys a book from the distributor at Rs 200, how much does he sell it for ?
Solution:
Given
Profit % = 10% CP = Rs. 200
After that,
SP = {(100 + profit %)/100} x CP = {(100 + 10)/100} x 200
= {110/100} x 200 = Rs. 220
The bookseller sells the book for Rs. 220.
17. A flowerist buys 100 dozen roses at Rs 2 a dozen. By the time the flowers are delivered, 20 dozen roses are mutilated and are thrown away. At what price should he sell the rest if he needs to make a 20% profit on his purchase ?
Solution:
According to question,
cost of 1 dozen roses = Rs. 2
Florist bought 100 dozens of roses.
Thus, cost price of 100 dozen roses = 2 x 100 = Rs. 200
No. of roses thrown away = 20 dozen
Roses left after discarding the mutilated ones = 100 – 20 = 80 dozens
Price at which the florist should sell the 80 dozen roses in order to make a profit of 20%,
Profit % = (Profit/CP) x 100
20 = (Profit/200) x 100
Profit = (20 x 200)/100
Profit = Rs. 40
As we know that; Profit = SP – CP
40 = SP – 200
SP = Rs. 240
Therefore, flowerist should sell the rest of the flowers at Rs. 240 to make 20% profit on his purchase.
18. By selling an article for Rs 240, a man makes a profit of 20%.What is his C.P. ? What would his profit percent be if he sold the article for Rs 275 ?
Solution:
Let CP = Rs. x SP = Rs. 240
Let profit be Rs. P.
Now, profit % = 20%
After that, Profit % = (Profit/CP) x 100
=> 20 = (P/x) x 100
=> P = 20x/100 = x/5
Profit = SP – CP = 240 – x
=> P = 240 – x
=> x/5 = 240 – x
=> 240 = x + x/5
=> 240 = 6×15
=> x = 1200/6
=> 200
So, CP = Rs. 200
New SP = Rs. 275 and CP = Rs. 200
Profit % = {(SP – CP)/CP} x 100
=> {(275 – 200)1200} x 100 = (75/200) x 100
= 7500/200
= 37.5%