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Olympiad Test: Profit And Loss - 2 - Class 7 MCQ


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20 Questions MCQ Test Mathematics Olympiad Class 7 - Olympiad Test: Profit And Loss - 2

Olympiad Test: Profit And Loss - 2 for Class 7 2024 is part of Mathematics Olympiad Class 7 preparation. The Olympiad Test: Profit And Loss - 2 questions and answers have been prepared according to the Class 7 exam syllabus.The Olympiad Test: Profit And Loss - 2 MCQs are made for Class 7 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Olympiad Test: Profit And Loss - 2 below.
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Olympiad Test: Profit And Loss - 2 - 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.

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 1

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).

Olympiad Test: Profit And Loss - 2 - 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.

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 2

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.

Olympiad Test: Profit And Loss - 2 - Question 3

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

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 3

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.

Olympiad Test: Profit And Loss - 2 - Question 4

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

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 4

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

Olympiad Test: Profit And Loss - 2 - Question 5

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

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 5

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%.

Olympiad Test: Profit And Loss - 2 - Question 6

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

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 6

C.P. = 200, Profit = 22%.
So, S.P. = 1.22
C.P. = 1.22 × 200 = Rs 244

Olympiad Test: Profit And Loss - 2 - 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?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 7

S.P. of 1st person = C.P. of 2nd person
= 1.25 × 120 = 150
S.P. of 2nd person = 180
Profit % = S.P. /C.P. = 180/150 = 1.2
Therefore, profit of second person is 20%

Olympiad Test: Profit And Loss - 2 - 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.

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 8

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.

Olympiad Test: Profit And Loss - 2 - 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 %.

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 9

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.

Olympiad Test: Profit And Loss - 2 - 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?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 10

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.

Olympiad Test: Profit And Loss - 2 - 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?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 11

S.P. =1.4 C.P.
(S.P. /2) = 0.7 C.P.
Therefore, 30% loss

Olympiad Test: Profit And Loss - 2 - 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.

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 12

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.

Olympiad Test: Profit And Loss - 2 - 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 %.

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 13

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%.

Olympiad Test: Profit And Loss - 2 - 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?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 14

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.

Olympiad Test: Profit And Loss - 2 - 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%?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 15

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

Olympiad Test: Profit And Loss - 2 - 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?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 16

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%.

Olympiad Test: Profit And Loss - 2 - 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%?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 17

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%.

Olympiad Test: Profit And Loss - 2 - 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?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 18

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% 

Olympiad Test: Profit And Loss - 2 - 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%?

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 19

He must sell less than 30 oranges in order to gain.
Hence, required number of oranges
= 30[(100)/ (100 + 25)] = 24

Olympiad Test: Profit And Loss - 2 - 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.

Detailed Solution for Olympiad Test: Profit And Loss - 2 - Question 20

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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