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Joy of Mathematics Class 8 Solutions Chapter 9 Profit Loss and Discount
Welcome to NCTB Solution. Here with this post we are going to help 8th class students for the Solutions of Joy of Mathematics Class 8 Book, Chapter 9 Profit, Loss and Discount. Here students can easily find step by step solutions of all the problems for Profit, Loss and Discount. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily. Here students will find solutions for Exercise 9.1 and 9.2
Profit, Loss and Discount Exercise 8 Solution
Question no – (1)
Solution :
(a) CP = Rs 800, SP = Rs 896
=> CP = 800
SP = 896
Profit = 896 – 800
= 96
∴ Profit percentage
= Profit/CP × 100
= 96/800 × 100
= 12%
Therefore, profit percentage 12%
(b) Here,
C.P. = 1200
S.P. = 1308
Profit = 1308 – 1200
= 1008
∴ Profit percentage
= 1008/1200 × 100
∴ Profit percentage 84%
(c) Here,
C.P. = 500, SP = 475
Loss = C.P. – S.P.
= 500 – 475
= 25
∴ Loss percentage
= 25/500 × 100
= 5%
(d) Here,
C.P. = 425, SP = 459
Profit = 459 – 425
= 34
∴ Profit percentage
= 34/425 × 100
= 8%
∴ Profit percentage = 8%
Question no – (2)
Solution :
(a) Here,
S.P. = 720
Profit = 12 1/2%
= 25/25 %
Now, C.P. = 100/100 + profit% × S.P.
= 100/100 + 25/2 × 720
= 100/200 + 25/2 × 720
= 100 × 2/225 × 720
= 8 × 80
= 640
Hence, CP = Rs 640
(b) Here, SP = 999, Profit = 11%
∴ CP = 100/100 + profit% × SP
= 100/100 + 11 × 999
= 100/111 × 999
= 900
Therefore C.P. = Rs900
(c) Here, S.P. = Rs 4600, Loss = 8%
∴ C.P. = 100/100 – loss% × SP
= 100/100 – 8 × 4600
= 100/92 × 4600
= 5000
Therefore C.P. = Rs 5000
(d) Here, S.P. = Rs 9000, Loss = 10%
C.P. = 100/100 – loss% × S.P.
= 100/100 – 10 × 9000
= 100/90 × 9000
= 10000
Therefore C.P. = Rs 10000
Question no – (3)
Solution :
(a) Here, CP = Rs 400
Overhead expense = Rs 100
New CP = (400 + 100) = 500
SP = Rs 450
∴ Loss% = Loss%/CP × 100
= 50/500 × 100
= 10
Therefore loss = 10%
(b) Here,
CP = Rs 500
Overhead expense = Rs 80
New CP = (500 + 80) = Rs 580
SP = Rs 609
Profit = SP – CP = 609 – 580
= 29
∴ Profit percentage = profit/CP × 100
= 29/580 × 100
= 5
∴ Profit percentage 5%
(c) Here, CP = Rs 350
Overhead expense = Rs 80
Gain = Rs 43
New CP = (350 + 80) = 430
∴ Gain percentage = 43/430 × 100
= 10
∴ Gain percentage 10%
(d) Here,
CP = 250
Overhead expense = 50
New CP = (250 + 50) = 300
Loss = 60
∴ Loss percentage = 60/300 × 100
= 20%
Therefore loss percentage 20%
Question no – (4)
Solution :
S.P. = 4998
Profit = 5%
C.P = 100/100 + profit% × S.P
= 100/400 + profit% × 4998
= 100/105 × 4998
= 499800/105
= 4760
Therefore the cost price of the almirah 4760.
Question no – (5)
Solution :
Here, Sofa’s SP = Rs 3560
Loss = 11%
cost price of the sofa = 100/100 – loss% × SP
= 100/100 – 11 × 3560
= 100/89 × 3560
Now, cost price of the sofa = 4000
Gain = 12%
SP = 100 + gain%/100 × CP
= 100 + 12/100 × 4000
= 112/100 × 4000
= 448
Therefore the selling price of the Sofa is Rs 448.
Question no – (6)
Solution :
Here,
Amount paid of the car = Rs 45.500
Repair expense = Rs 4500
∴ Actual CP of the car
= (45,500 + 4500)
= 50,000
∴ SP of the car = 53, 550
Profit = SP – CP
= 53,550 – 50,000
= 3,550
∴ Profit percentage,
= 3550/50,000 × 100
= 71/10
= 7.1%
∴ Profit percentage 7.1%
Question no – (7)
Solution :
Amount paid of the 2nd hand
Refrigerator = 4000
Painted expense = 350
Now, Actual CP
= (4000 + 350)
= Rs 4350
Profit% = 8%
Now, SP = 100 + profit%/100 × CP
= 100 + 8/100 × 4350
= 108/100 × 4350
= 4,698
Therefore the selling price of the refrigerator Rs 4698.
Question no – (8)
Solution :
Cost of each item = Rs 600
∴ At 10% loss the item selling cost
= 600 – 600 × 10/100
= 600 – 60
= 540
Cost of whole item
= 3 × 600
= 1800
∴ At 20% gain cost of all items
= 1800 + 1800 × 20/100
= 1800 + 360
= Rs 2160
∴ Required price for selling the other two items
= 2160 – 540
= 1620
So, cost of selling of each item
= 1620/2
= Rs 810
Question no – (9)
Solution :
Here,
Selling price = 54,720
Losses = 5%
Cost price = 100/100 – loss% × SP
= 100/100 – 5 × 54720
= 100/95 × 54720
= 57,600
∴ CP = 57,600
Profit = 10%
∴ Selling price = 100 + profit/100 × CP
= 100 + 10/100 × 57600
= 110/100 × 57600
= 63,360
∴ Selling price of the article 63,360/-.
Question no – (10)
Solution :
Selling price of each cars = 99000
At 10% gains cost price of the car
= 100/100 + gains% × SP
= 100/100 + 10 × 99000
= 100/110 × 99000
= 90000
Again,
At 10% losses cost price of the car
= 100/100 – loss% × SP
= 100/100 – 10 × 99000
= 100/90 × 99000
= 110000
∴ Total selling price of the cars
= 2 × 99000
= 198000
∴ Total cost price of the cars,
= 90000 + 110000
= 200,000
∴ Loss = CP – SP
= 200000 – 198000
= 2000
∴ Loss percentage
= 2000/200000 × 100
= 1
Therefore, the loss percentage 1%
Question no – (11)
Solution :
Let, the S.P of both the fans are x
∴ At 10% profit,
C.P = 100/100 + profit% × S.P
= 100/100 + 10 × x
= 100/110 × x
= 10x/11
Again, 10% loss
C.P = 100/100 – loss% × SP
= 100/100 – 10 × x
= 100x/90
= 10x/9
Ratio of cost price of the two fans are
= 10x/11 : 10x/9
= 1/11 : 1/9
= 1/11 × 99 : 1/9 × 99
= 9 : 11
The cost price of both the fans are = 5000
∴ C.P of one fans
= 5000 × 9/20
= 2250
∴ C.P of another fans
= (5000 – 2250)
= Rs 2750
Question no – (12)
Solution :
Amount of 60kg butter at the rate of Rs 150 per kg
= 60 × 150
= 9000/-
∴ Sold 1/3 of it at a loss of 6%
= 1/3 × 60kg
= 20kg
∴ Cost price of 20kg butter
= 20 × 150
= 3000
At 6% loss SP = 100 – loss%/100 × CP
= 100 – 6/100 × 3000
= 94/100 × 3000
= 2820
At 10% gain or the whole deal = 100 + gain%/100 × CP
= 100 + 10/100 × 9000
= 110 × 90
= 9900
∴ Required price
= 9900 – 2820
= 7080
∴ Selling price remaining per kg
= 7080/40
= 177 Rs
Question no – (13)
Solution :
Let the cost price of a chair = 100
At 10% profit selling price
= 100 + 10
= 110
At 15% profit selling price
= 100 + 15
= 115
∴ Difference of selling price
= 115 – 110
= 5
According to the question,
5 → 75
1 → 75/5
= 15
Therefore the cost price of a chair
= 15 × 100
= Rs 1500
Question no – (14)
Solution :
Let, the cost price of an article is = 100
At, 15% profit selling price
= 100 + 15
= 115
Again, at 18% gained selling price
= 100 + 18
= 118
∴ Difference of selling price
= 118 – 115
= 3
According to the question,
3 → 21
1 → 21/3 = 7
∴ Therefore the cost price of an article
= 7 × 100
= Rs 700
Question no – (15)
Solution :
Let, the cost price of one orange = Rs x
According to the question,
SP of 9 orange = CP of 10 orange
= 10x
∴ SP of 1 orange = 10x/9
S.P > C.P, therefore there is profit
∴ Profit in selling one orange = SP – CP
= 10x/9 – x
= 10x – 9x/9
= x/9
∴ Profit = x/9/x × 100
= x/9 × x × 100
= 100/9
Therefore, profit percentage 11 1/9%
Question no – (16)
Solution :
Let, the cost price of an article = x
According to the question,
SP of 5 article = CP of 4 articles
= 4x
SP of 1 article = 4x/5
Hence, CP > SP therefore there is loss
∴ Loss = CP – SP
= x – 4x/5
= 5x – 4x/5
= x/5
∴ Loss% = x/5/x × 100
= x × 100/5 × x
= 20%
Therefore, loss percentage 20%
Question no – (17)
Solution :
Let, the cost price of an article is = 100
∴ At 20% profit SP
= (100 + 20)
= 120
∴ Total profit
= (120 – 100)
= 20
According to the question,
20 → 60
1 → 60/20
= 3
∴ The CP of an article
= 3 × 100
= Rs 300
∴ The SP of an article
= 300 + 300 × 20/100
= 300 + 60
= Rs 360
Question no – (18)
Solution :
Let, the cost price of the article is = 100
At 10% profit SP = 100 + 10
= 110
Now, He bought it 20% less then
Now, CP = (100 – 100 × 20/100)
= 80
Profit = 40%
SP = 80 + 80 × 40/100
= 80 + 32
= 112
Difference of SP = 112 – 110
= 2
According to the question,
2 → 10
1 → 10/2 = 5
Therefore the cost price of an article = Rs 500
Question no – (19)
Solution :
Let, CP of a tablet computer = x
∴ SP of a tablet computer = x × 3/4
= 3x/4
Hence, C.P > S.P therefore there is loss
∴ Loss = C.P – S.P
= x – 3x/4
= 4x – 3x/4
= x/4
∴ loss% = x/4/x × 100
= x/4 × x × 100
= 25%
Therefore the loss percentage 25%
Profit, Loss and Discount Exercise 9.2 Solution :
Question no – (1)
Solution :
(a) Here,
MP = Rs 20
Discount = 20%
∴ SP = 20 – 20 × 20/100
= 20 – 4
= 16
∴ The required SP = Rs 16
(b) Here,
MP = Rs 400
Discount =12 1/2% = 25/2%
∴ SP = 400 – 400 × 25/2 × 100
= 400 – 50
= Rs 350
∴ The required SP = Rs 350
(c) Here,
MP = Rs 750
Discount = 12%
∴ SP = 750 – 750 × 12/100
= 750 – 90
= Rs 660
∴ The required SP = Rs 660
(d) Here,
MP = Rs 425
Discount = 8%
SP = 425 – 425 × 8/100
= 425 – 34
= Rs 391
∴ The required SP = Rs 391
Question no – (2)
Solution :
(a) Here,
SP = 666
Discount = 7 1/2% = 15/2%
∴ MRP = SP × 100/100 – discount
= 666 × 100/100 – 15/2
= 66600/200 – 15/2
= 66600 × 2/185
= Rs 720
Therefore the required MRP = 720
(b) Here,
SP = Rs 391
Discount = 80%
∴ MRP = SP × 100/100 – discount
= 391 × 100/100 – 80
= 391 × 100/20
= Rs 1945
∴ Therefore the required MRP = 1945
(c) Here,
SP = 8514
Discount = 12%
∴ MRP = SP × 100/100 – discount
= 8514 × 100/100 – 12
= 8514 × 100/88
= Rs 9675
∴ Therefore the required MRP = 9675
(d) Here,
SP = Rs 11932
Discount = 5%
∴ MRP = SP × 100/100 – discount
= 11932 × 100/100 – 5
= 11932 × 100/95
= 12,560
Therefore the required MRP = 12560
Question no – (3)
Solution :
(a) Here,
MP = 5000
SP = 4500
∴ Discount = 5000 – 4500
= 500
∴ Discount percentage
= 500/5000 × 100
= 10
Therefore the discount percentage 10%
(b) Here,
M.P = Rs 975
S.P = Rs 897
∴ Discount= 975 – 897
= 78
∴ Discount percentage = Discount/MRP × 100
= 78/975 × 100
= 8
Therefore the required discount percentage 8%
(c) Here,
M.P = Rs 900
S.P = Rs 801
∴ Discount
= 900 – 801
= 99
∴ Discount percentage
= 99/900 × 100
= 11%
Therefore, the required discount percentage 11%
(d) Here,
M.P = Rs 720
S.P = Rs 684
∴ Discount = 720 – 684
= 36
∴ Discount percentage
= 36/720 × 100
= 5%
Therefore, the required discount percentage 5%
Question no – (4)
Solution :
M.P of a Sari = Rs 4510
M.P of two Jeans = 2 × 1920
= Rs 3840
∴ Total MP = (4510 + 3840)
= 8350
At 25% discount on all the items then,
the outlay = 8350 – 8350 × 25/100
= 8350 – 2087.5
= Rs 6262.5
Therefore the outlay Rs 6262.5
Question no – (5)
Solution :
Let, the cost price = 100
∴ Marks his book 40% above, the cost price.
Therefore M.P = 100 + 100 × 40/100
= Rs 140
Now, At discount 25%
S.P = 140 – 140 × 25/100
= 140 – 35
= 105
∴ SP > MP, therefore there is gain.
∴ Gain = 105 – 100 = Rs 5
∴ Gain percentage
= 5/100 × 100
= 5%
Therefore, the gain percentage 5%
Question no – (6)
Solution :
Here, cost price = Rs 4550
Gains% = 20%
∴ Selling price
= 4550 + 4550 × 20/100
= 4550 + 910
= Rs 5460
∴ (a) its selling price 5460/-
∴ (b) SP = Rs 5460
Discount = 25%
M.P = SP × 100/100 – discount
= 5460 × 100/100 – 25
= 546000/75
= Rs 7280
Hence, its marked price 7280/-
Question no – (7)
Solution :
Here,
Cost price of gas burner = Rs 3750
(a) Marked price
= 3750 + 3750 × 40/100
= 3750 + 1500
= Rs 5250
(b) Discount = 10%
then, selling price = 5254 – 5254 × 10/100
= 5254 – 525
= Rs 4725
(c) Here,
C.P = 3750
S.P = 4725
∴ Profit% = 4725 – 3750/3750 × 100
= 975/3750 × 100
= 26
Therefore, profit percentage 26%
Question no – (8)
Solution :
Here,
Marked price of a shirt = Rs 1500
∴ At 20% discount
∴ Selling price
= 1500 – 1500 × 20/100
= 1500 – 300
= 1200
Now, profit = 20%
∴ Cost price of a shirt
= 100/100 + profit% × SP
= 100/100 + 20 × 1200
= 100/120 × 1200
= Rs 1000
∴ Cost price the shirt Rs 1000
Question no – (9)
Solution :
Here,
S.P = 1100
Discount = 12%
(a) Marked price of the article
= S.P × 100/100 – discount
= 1100 × 100/100 – 12
= 110000/88
= Rs 1250
(b) Here,
S.P = 1100
Gains = 10%
∴ The cost price in the transaction
= 100/100 + gains% × SP
= 100/100 + 10 × 1100
= 100/110 × 110
= Rs 1000
Therefore, the cost price 1000 Rs
Question no – (10)
Solution :
1st discount = 40%
2nd discount = 20%
Therefore the single discount
= (40 + 20) – 40 × 20/100
= 60 – 8
= 52
∴ Single discount 52
Question no – (11)
Solution :
1st discount (x1) = 20%
2nd discount (x2) = 5%
∴ Marked price = Rs 35600
∴ Payment received in each by the shopkeeper for the AC
= (1 – x1/100) (1 – x2/100) × MP
= (1 – 20/100) (1 – 5/100) × 35600
= (100 – 20/100) (100 – 5/100) × 35600
= 80/100 × 95/100 × 35600
= Rs 27056
Therefore the selling price 27056/-
Question no – (12)
Solution :
Let, the marked price of an article
= 100 in two different store
∴ The 1st store allows two successive discount 23% and 28% then,
SP = (1 – 23/100) (1 – 28/100) × 100
= (100 – 23/100) (100 – 28/100) × 100
= 77/100 × 72/100 × 100
= Rs 55.44
2nd store allows 35% discount then
SP = (100 – 100 × 35/100) Rs
= 100 – 35
= Rs 75
∴ 1st store is better offer.
Question no – (13)
Solution :
Marked price of a smart phone = Rs 25000
Discount = 20% of 25000
= 20/100 × 25000
= 5000
∴ Amount of discount
= (25000 – 5000)
= 20000
∴ GST charged
= 12% of 20000
= 12/100 × 20000
= 2400
∴ Net amount payment,
= (20000 + 2400)
= Rs 22400
Thus, customer has to pay Rs 22400 for the smart phone.
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