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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 2^{nd} 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 :**

1^{st} discount = 40%

2^{nd} discount = 20%

Therefore the single discount

= (40 + 20) – 40 × 20/100

= 60 – 8

= 52

**∴** Single discount 52

**Question no – (11)**

**Solution :**

1^{st} discount (x_{1}) = 20%

2^{nd} discount (x_{2}) = 5%

**∴** Marked price = Rs 35600

**∴** Payment received in each by the shopkeeper for the AC

= (1 – x_{1}/100) (1 – x_{2}/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 1^{st} 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

2^{nd} store allows 35% discount then

SP = (100 – 100 × 35/100) Rs

= 100 – 35

= Rs 75

**∴** 1^{st} 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.

**Previous Chapter Solution : **