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This mock test of Olympiad Test: Profit And Loss - 2 for Class 7 helps you for every Class 7 entrance exam.
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QUESTION: 1

What was the percentage of discount given?

I. 23.5% profit was earned by selling an almirah for Rs 12,350.

II. If there were no discount, the earned profit would have been 30%.

III. The cost price of the almirah was Rs 10,000.

Solution:

I. S.P. = Rs 12350, Gain = 23.5%

C.P. = Rs (1 00/123.5) × 12350

= Rs 1 0000

II. M.P. = 130% of C.P. = 130% of

Rs 10,000 = Rs 13,000.

From I and II, discount

= Rs (1 3000 – 12350) = Rs 650

Discount % = (650/13000) × 100% = 5% Thus, I and II give the answer.

II and III cannot give the answer because we require profit percentage with discount and profit percentage without discount.

So II and III are not sufficient.

Since III gives C.P. = Rs 10,000, I and III give the answer.

Therefore, I and II [or] I and III give the answer.

∴ Correct answer is (d).

QUESTION: 2

What is the percent profit earned by the shopkeeper on selling the articles in his shop?

I. Labelled price of the articles sold was 130% of the cost price.

II. Cost price of each article was Rs 550.

III. A discount of 10% on labelled price was offered.

Solution:

I. Let C.P. be Rs x.

Then, M.P. = 130% of x = Rs (13x/10)

II. S.P. = 90% of M.P.

Thus, I and III give S.P. = Rs (90/100) × (13x/10) = Rs (117x/100)

Gain = Rs (117x/100) – x = Rs (17x/100)

Thus, from I and III, gain % can be obtained.

QUESTION: 3

A trader uses 800 gm weight instead of 1 kg. Find his profit %.

Solution:

He is buying 800 gm but selling 1000 gm.

So, C.P. is for 800 gm and S.P. is for 1000 gm.

S.P. /C.P. = 1000/800 = 1.25

Therefore, 25% profit.

QUESTION: 4

A trader uses 1 kg weight for 800 gm and increases the price by 20%. Find his profit/loss %.

Solution:

1 kg weight for 800 gm

Loss (decrease) = 800/1000 = 0.8

20% increase in price = profit (increase) = 1.2

So, net effect = (0.8) × (1.2) = 0.96

Therefore, 4% loss

QUESTION: 5

A milk vendor mixes water to milk such that he gains 25%. Find the percentage of water in the mixture.

Solution:

To gain 25%, the volume has to be increased by 25%.

So, for 1 litre of milk, 0.25 litre of water is added

Total volume = 1.25 litres

% of water = 0.25 / 1.25 × 100 = 20%.

QUESTION: 6

A trader bought an item for Rs 200. If he wants a profit of 22%, at what price must he sell it?

Solution:

C.P. = 200, Profit = 22%.

So, S.P. = 1.22

C.P. = 1.22 × 200 = Rs 244

QUESTION: 7

A person buys an item at Rs 120 and sells to another at a profit of 25%. If the second person sells the item to another at Rs 180, what is the profit % of the second person?

Solution:

S.P. of 1^{st} person = C.P. of 2^{nd} person

= 1.25 × 120 = 150

S.P. of 2^{nd} person = 180

Profit % = S.P. /C.P. = 180/150 = 1.2

Therefore, profit of second person is 20%

QUESTION: 8

A milk vendor mixes water to 20 litres of milk such that the ratio of milk and water is 4:3. He buys the milk at Rs 10 per litre and sells the mixture at Rs 12 per litre. Find the profit % of the vendor.

Solution:

Milk : Water = 4:3

He bought 4 parts (milk) but sold 7 parts (mixture)

C.P. = 10 and S.P. = 12.

So, profit % = (S.P. /C.P.) × (S.P. /C.P.)

= (7/4) × (12/10) = 2.1

Therefore, 110% gain.

QUESTION: 9

A trader buys some apples at a price of 10 apples for Rs 8 and sells them at a price of 8 apples for Rs 10. Find his profit or loss %.

Solution:

He bought 10 apples for Rs 8 and sold 8 apples for Rs 10.Clearly he got profit S.P. > C.P.

(S.P./C.P.) × (S.P. /C.P.)

= (10/8) × (10/8) = 100/64 = 1.5625

Therefore, 56.25 % gain.

QUESTION: 10

A trader allows a discount of 25% on his articles but wants to gain 50% gain. How many times the C.P. should be marked on the items?

Solution:

C.P. applied with profit = M.P. applied with discount = S.P.

1.5 C.P. = 0.75M.P. (Since 50% gain and 25% discount)

Therefore, M.P. = 2 C.P.

QUESTION: 11

By selling an item at a price a trader gains 40%. What is the profit / loss % if the item is sold at half the price?

Solution:

S.P. =1.4 C.P.

(S.P. /2) = 0.7 C.P.

Therefore, 30% loss

QUESTION: 12

A trader gets a profit of 25% on an article. If he buys the article at 10% lesser price and sells it for Rs 2 less, he still gets 25% profit. Find the actual C.P. of the article.

Solution:

25% gain

∴ S.P. = 1.25 C.P......... (i)

Now, C.P. is 10% less

0.9 C.P. and S.P. is Rs 2 less ⇒ (S.P. -2).

Still, profit is 25% ⇒ (S.P. – 2) =1.25

(0.9 C.P.), where S.P. = 1.25 C.P. [From equation (i)]

C.P. = Rs 16.

QUESTION: 13

A trader gets a discount of 20% from the dealer and marks it at 20% more price than the actual MP to the customer. Find his overall gain %.

Solution:

Let M.P. be the price on the item.

Then, C.P. = 0.8M.P. (20% discount) and S.P. = 1.2M.P.

So, gain = S.P./ C.P. = 1.2/0.8 = 1.5 Therefore, gain = 50%.

QUESTION: 14

If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?

Solution:

Let the cost price of 1 article be Rs1.

Therefore, cost price of 20 articles = 20 × 1 = Rs 20

The selling price of 25 articles = cost price of 20 articles = Rs 20.

Now, we know the selling price of 25 articles. Let us find the cost price of 25 articles.

Cost price of 25 articles = 25 × 1 = Rs 25

Therefore, profit made on sale of 25 articles = Selling price of 25 articles – cost price of 25 articles = 20 – 25 = – Rs 5

As the profit is in the negative, the merchant has made a loss of Rs 5.

Therefore, % loss = (Loss/Cost price) x 100 % loss = (–5/25) × 100 = 20% loss.

QUESTION: 15

Sam buys 10 apples for Rs 1. At what price should he sell a dozen apples if he wishes to make a profit of 25%?

Solution:

The cost price of 1 apple = 1/10th of a dollar or Rs 0.10.

As Sam wishes to make a profit of 25%, his selling price per apple will be 0.10 + 25% of 0.10 = Rs 0.125

If the selling price of 1 apple is Rs 0.125, then the selling price of a dozen apples

= 12 × 0.125

= Rs 1.5

QUESTION: 16

By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What will be the percent profit made by the merchant if he sells the article at 95% of its marked price?

Solution:

Let the marked price be S and the cost price of the article be C.

When the merchant sells at 80% of marked price, he sells at 0.8S This results in a loss of 12%.

Loss is always computed as a percentage of cost price.

Therefore, the loss incurred by the merchant = 0.12C

Hence, he will be selling the article at C – 0.12C = 0.88C when he sells at 80% of his marked price.

Equating the two sides of the relation, we get 0.8S = 0.88C S = 1.1C

Now, if the merchant sells at 95% of the marked price, he will be selling at 95% of 1.1C = 1.045C

Hence, the merchant will make a profit of 4.5%.

QUESTION: 17

What is the maximum percentage discount that a merchant can offer on her Marked Price so that she ends up selling at no profit or loss, if she had initially marked her goods up by 50%?

Solution:

The merchant had initially marked her goods up by 50%.

Let us assume that her cost price of the goods to be Rs100.

Therefore, a 50% mark up would have resulted in her marked price being Rs 100 + 50% of Rs 100 = Rs 100 + Rs 50 = Rs 150

The question states that she finally sells the product at no profit or loss.

This essentially means that she sells the product at cost price, which in this case would be Rs 100.

Therefore, she had offered a discount of ` 50 on her marked price of Rs 150.

Hence, the % discount offered by her

= (50/100 × 100) % = 33.33%.

QUESTION: 18

A merchant who marked his goods up by 50% subsequently offered a discount of 20%. What is the percentage profit that the merchant make after offering the discount?

Solution:

To make calculations easy, let us assume that the cost price = Rs 100 The merchant marks his goods up by 50%.

Therefore, his quoted price = cost price + mark up = Rs 100 + 50% of Rs 100 = 100 + 50 = Rs 1 50

Now, the merchant offers a discount of 20% on his quoted price Therefore, amount of discount = 20% of Rs 150 = 20% of 150 = Rs 30

Therefore, he finally sells it for Rs 150 – Rs 30 = Rs 120.

We assumed his cost to be Rs 100 and he sold it finally for Rs 120.

Therefore, his net profit = Rs 20 on his cost of Rs 100

Hence, his % profit = (20/100 × 100) % = 20%

QUESTION: 19

If oranges are bought at the rate of 30 for a rupee, how many oranges must be sold for a rupee in order to gain 25%?

Solution:

He must sell less than 30 oranges in order to gain.

Hence, required number of oranges

= 30[(100)/ (100 + 25)] = 24

QUESTION: 20

Satish marks his goods 25% above cost price but allows 12.5% discount for cash payment. If he sells the article for Rs 875, find his cost price.

Solution:

Marked price = Rs 875[100/(100 – 12.5)]

= Rs 875(100/87.5)

Cost price = Rs 875(100/87.5)

(100/100+25) = Rs 800

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