The DAV Class 8 Maths Book Solutions Pdf and **DAV Class 8 Maths Chapter 5 Worksheet 1** Solutions of Profit, Loss and Discount offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 5 WS 1 Solutions

Question 1.

By selling a bedsheet for ₹ 640, a shopkeeper earns a profit of 28%. How much did it cost the shopkeeper?

Solution:

S.P. = ₹ 640

Profit = 28%

C.P. = ?

S.P. = C.P. (1 + \(\frac{\text { Profit }}{100}\))

⇒ 640 = C.P. (1 + \(\frac{28}{100}\))

⇒ 640 = C.P. × \(\frac{128}{100}\)

⇒ C.P. = \(\frac{640 \times 100}{128}\) = ₹ 500

Hence, the required cost price is ₹ 500.

Question 2.

Rajan purchased 250 packets of blades at the rate of ₹ 8 per packet. He sold 70% of the packets at the rate of ₹ 11 per packet and the remaining packets at the rate of ₹ 9 per packet. Find the gain percent.

Solution:

Cost price of 250 packets = 250 × 8 = ₹ 2000

70 % of 250, i.e. 175 packets are sold for ₹ 11 per packet

∴ S.P. of 175 packets = 11 × 175 = ₹ 1925

The remaining packets are 250 – 175 = 75

∴ S.P. of 75 packets = 75 × 9 = ₹ 675

∴ Total S.P. = ₹ 1925 + ₹ 675 = ₹ 2600

∴ Gain = S.P. – C.P. = 2600 – 2000 = ₹ 600

∴ Gain % = \(\frac{\text { Gain }}{\text { C.P. }}\) × 100

= \(\frac{600}{2000}\) × 100 = 30%

Hence, the gain % is 30%.

Question 3.

Ankit sold two jeans for ₹ 990 each. On one, he gains 10% and on the other he lost 10%. Find his gain or loss per cent in the whole transaction.

Solution:

S.P. of two jeans = 2 × 990 = ₹ 1980

Now for 1st jeans,

S.P. = C.P. (1 + \(\frac{\text { Gain }}{100}\))

⇒ 990 = C.P. (1 + \(\frac{10}{100}\))

⇒ 990 = C.P. × \(\frac{110}{100}\)

⇒ C.P. = \(\frac{990 \times 100}{110}\) = ₹ 900

For 2nd jeans,

S.P. = C.P. (1 – \(\frac{\text { Loss }}{100}\))

990 = C.P. (1 – \(\frac{10}{100}\))

990 = C.P. × \(\frac{90}{100}\)

C.P. = \(\frac{990 \times 100}{90}\) = 1100.

∴ Total C.P. = ₹ 900 + ₹ 1100 = ₹ 2000

Now C.P. > S.P.

∴ Loss = ₹ 2000 – ₹ 1980 = ₹ 20

∴ Loss % = \(\frac{\text { Loss }}{\text { C.P. }}\) × 100

= \(\frac{20}{2000}\) × 100 = 1 %.

Hence the loss = 1 %.

Question 4.

Nidhi purchased two sarees for ₹ 2150 each. She sold one saree at a loss of 8% and the other at a gain. If she had a gain of ₹ 1230 on the whole transaction, find the selling price of the second saree.

Solution:

C.P. for one saree = ₹ 2150

Loss = 8%

∴ S.P. = C.P. [1 – \(\frac{\text { Loss }}{100}\)]

= 2150 [1 – \(\frac{8}{100}\)]

= 2150 × \(\frac{92}{100}\) = 1978

Let gain on the other saree be ₹ x.

∴ S.P. for other saree = (₹ 2150 + ₹ x)

∴ Total S.P. for 2 sarees = ₹ 1978 + ₹ 2150 + ₹ x = ₹ (4128 + x)

Total C.P. for 2 sarees = 2 × 2150 = ₹ 4300

∴ Total gain on the whole transaction = S.P. – C.P.

= ₹ (4128 + x) – ₹ 4300 = ₹ (x – 172)

∴ x – 172 = 1230

⇒ x = 1230 + 172 = 1402

∴ S.P. for second saree = C.P. + Gain

= ₹ 2150 + ₹ 1402 = ₹ 3552.

Question 5.

By selling 35 greeting cards, a shopkeeper loses an amount equal to the selling price of 5 greeting cards. Find his loss per cent.

Solution:

Let S.P. for one greeting card be ₹ x.

∴ S.P. for 35 greeting cards = ₹ 35x

and Loss = ₹ 5x

∴ C.P. = S.P. + Loss

= ₹ 35x + ₹ 5x = ₹ 40x

∴ Loss % = \(\frac{\text { Loss }}{\text { C.P. }}\) x 100

= \(\frac{5 x}{40 x}\) x 100

= \(\frac{25}{2}\)

= 12 \(\frac{1}{2}\)%

Hence, the loss = 12\(\frac{1}{2}\)%.

Question 6.

A man bought bananas at the rate of 10 for ₹ 15 and sold at the rate of one dozen bananas for ₹ 15. Find his gain or loss per cent.

Solution:

C.P. for 10 bananas = ₹ 15

∴ C.P. for 1 banana = ₹ \(\frac{15}{10}\) = ₹ 1.50

S.P. for 12 bananas = ₹ 15

∴ S.P. for 1 banana = ₹ \(\frac{15}{12}\) = ₹ 1.25

Here C.P. > S.P.

∴ Loss = C.P. – S.P

= 1.50 – 1.25 = ₹ 0.25

∴ Loss percent = \(\frac{\text { Loss } \times 100}{\text { C.P. }}\)

= \(\frac{0.25 \times 100}{1.50}\)

= \(\frac{50}{3}\)

= \(16 \frac{2}{3}\) %

Hence, the loss per cent is 16 \(\frac{2}{3}\) %.

### DAV Class 8 Maths Chapter 5 Worksheet 1 Notes

Cost price (C.P) :

The price at which an article is purchased or manufactured is called its cost price (C.P.).

Selling price (S.P):

The price at which an article is sold is called its selling price (S.P.).

Profit = S.P. – C.P.

Profit % = \(\frac{\text { Profit }}{\text { C.P. }}\) × 100

Loss = C.P. – S.P.

Loss % = \(\frac{\text { Loss }}{\text { C.P. }}\) × 100

[Note: Profit and Loss are always calculated on the cost price of the article]

Direct formulae

(i) S.P. = C.P. (1 + \(\frac{\text { Profit }}{100}\))

(ii) S.P. = C.P. (1 – \(\frac{\text { Loss }}{100}\))

Market Price:

The price written on the article or tagged with a card is called its Market value.

Discount:

It is a certain percentage of rebate on the market price offered by the shopkeeper.

Discount = M.P. – S.P.

Discount % = \(\frac{\text { Discount }}{\text { M.P. }}\) × 100

Value Added Tax (VAT):

It is a new method of realising tax by the Government at every sale/purchase right from the manufacturer to the retailer. It is not in addition to the existing sales tax, but is the replacement of Sales Tax.

Example 1.

Find the profit or loss per cent, if

(i) C.P. = ₹ 55 and S.P. = ₹ 72.60

(ii) C.P. = ₹ 112, overheads = ₹ 14 and S.F. = ₹ 49.50.

Solution:

(i) Here S.P. > C.P.

∴ Profit = S.P. – C.P.

= 72.60 – 55

= ₹ 17.60

∴ Profit % = \(\frac{\text { Profit }}{\text { C.P. }}\) × 100

=\(\frac{17.60}{55}\) × 100 = 32%.

(ii) C.P. = ₹ 112 and overheads = ₹ 14

∴ Net C.P. = 112 + 14 = 126

S.P. = ₹ 49.50

Here C.P. > S.P.

∴ Loss = C.P. – S.P.

= ₹ 126 – ₹ 94.50

= ₹ 31.50

∴ Loss % = \(\frac{\text { Loss } \times 100}{\text { C.P. }}\)

= \(\frac{31.50 \times 100}{126}\)

= 25%.

Example 2.

Find C.P. when a bicycle is sold for ₹ 1485 at a profit of 8%.

Solution:

Here S.P. = ₹ 1485;

Profit = 8%;

C.P. = ?

S.P. = C.P. [1 + \(\frac{\text { Profit }}{100}\)]

⇒ 1485 = C.P. [1 + \(\frac{8}{100}\)]

⇒ 1485 = C.P. × \(\frac{108}{100}\)

⇒ C.P. = \(\frac{1485 \times 100}{108}\) = ₹ 1375.

Example 3.

If oranges are bought at 11 for ₹ 30 and sold 10 for 31. Find the loss or gain per cent.

Solution:

C.P. for 11 oranges = ₹ 30

∴ C.P. for 1 orange = ₹ \(\frac{30}{11}\)

SP. for 10 oranges = ₹ 31

S.P. for 1 orange = ₹ \(\frac{31}{10}\)

Here S.P. > C.P.

∴ Gain = S.P. – C.P.

= ₹ \(\frac{31}{10}\) – ₹ \(\frac{30}{11}\)

= ₹ \(\frac{41}{110}\)

∴ Gain % = \(\frac{\text { Gain }}{\text { C.P. }}\) × 100

= \(\frac{\frac{41}{110}}{\frac{30}{11}}\) × 100

= \(\frac{41}{3} \%=13 \frac{2}{3} \%\).

Example 4.

By selling a book for ₹ 115.20, a man loses 10%. At what price should he il it to gain 5%?

Solution:

S.P. = ₹ 115.20;

Loss = 10%

C.P. =?

∴ S.P. = C.P. (1 – \(\frac{\text { Loss }}{100}\))

115.20 = C.P. (1 – \(\frac{10}{100}\))

115.20 = C.P. × \(\frac{90}{100}\)

C.P. = \(\frac{115.20 \times 100}{90}\) = ₹ 128

Now C.P. = 128;

Gain = 5%;

S.P. = ?

∴ S.P. = C.P. (1 + \(\frac{\text { Gain }}{100}\))

= 128 (1 + \(\frac{5}{100}\))

= \(\frac{128 \times 105}{100}\)

= ₹ 134.40

Example 5.

Find the rate of discount being given on a sweater whose price has been slahed down from ₹ 975 to ₹ 760.50.

Solution:

Discount = ₹ 975 – ₹ 760.50 = ₹ 214.50

Rate of discount = \(\frac{\text { Discount }}{\text { M.P. }}\) × 100

= \(\frac{214.50}{975}\) × 100 = 22%

Hence, the rate of discount given = 22%.

Example 6.

A shopkeeper fixed the market price of an item 35% above its cost price. Find the discount per cent so a to gain 8%.

Solution:

Let C.P. be ₹ x.

∴ M.P. = x + \(\frac{35}{100}\) x

= ₹ \(\frac{27}{20}\) x

S.P. = C.P. (1 + \(\frac{\text { Gain }}{100}\))

= x (1 + \(\frac{8}{100}\))

= ₹ \(\frac{27}{25}\) x

Discount = M.P. – S.P.

= \(\frac{27}{20}\) x – \(\frac{27}{25}\) x

= ₹ \(\frac{27 x}{100}\)

Discount % = \(\frac{\text { Discount }}{\text { M.P. }}\) × 100

= \(\frac{\frac{27 x}{100}}{\frac{27 x}{20}}\) × 100

= 20%

Hence, the discount is 20%.

Example 7.

A shopkeeper bought a TV at a discount of 30% of the list price of ₹ 24000. He offers a discount of 10% of the listed price to his customer. If the VAT is 10%, find:

(i) The amount paid by the customer.

(ii) The VAT to be paid by the shopkeeper.

Solution:

List price = ₹ 24000

Discount = 30%

Selling price = 24000 – \(\frac{30}{100}\) × 24000

= ₹ 24000 – ₹ 7200

= ₹ 16800

Tax = \(\frac{10}{100}\) × 16800 = ₹ 1680

New S.P. to customer = 24000 – 24000 × \(\frac{10}{100}\)

= ₹ 24000 – ₹ 2400 = ₹ 21600

(i) Amount paid by customer = ₹ 21600 + ₹ 2160 = ₹ 23760

(ii) Total VAT to be paid by the shopkeeper = ₹ 2160 – ₹ 1680 = ₹ 480.