Profit & Loss MCQs for SSC CGL Exam

Understanding the Problem
To find the marked price of the instrument, we need to analyze the given information regarding the discounts and profits.
Given Data
- Discount = 20% on the marked price (MP)
- Profit = 25%
- Gain from the sale = 150
Calculating the Selling Price (SP)
1. Let the marked price be MP.
2. The selling price after a 20% discount is:
- SP = MP - (20% of MP) = 0.8 * MP
Relating Cost Price (CP) and Profit
3. Profit of 25% means:
- SP = CP + (25% of CP) = 1.25 * CP
4. Given that the gain over the sale is 150, we find:
- Gain = SP - CP = 150
Setting Up Equations
5. Substitute SP in the gain equation:
- 0.8 * MP - CP = 150
- Rearranging gives us: CP = 0.8 * MP - 150
6. Now, substitute CP in the profit equation:
- 1.25 * CP = 0.8 * MP
- Replacing CP with the previous equation:
- 1.25 * (0.8 * MP - 150) = 0.8 * MP
Simplifying the Equation
7. Expanding gives:
- 1.0 * MP - 187.5 = 0.8 * MP
8. Rearranging yields:
- 1.0 * MP - 0.8 * MP = 187.5
- 0.2 * MP = 187.5
9. Solving for MP:
- MP = 187.5 / 0.2 = 937.5
10. Correcting for rounding gives us:
- MP = 937.50 (Option D)
Conclusion
The marked price of the instrument is 937.50, which confirms option D as the correct answer.

Given:
- Trader bought two horses for 19,500.
- One horse was sold at a loss of 20%.
- The other horse was sold at a profit of 15%.
- The selling price of each horse is the same.

To find:
The cost prices of the horses.

Solution:

Let's assume the cost price of the first horse is "x" and the cost price of the second horse is "y".

Step 1: Formulate equations based on the given information.

- The sum of the cost prices of the two horses is 19,500.
x + y = 19,500 --(1)

- The selling price of each horse is the same.
Selling price of first horse = Selling price of second horse

- Selling price = Cost price + Profit
(x - 20% of x) = (y + 15% of y)

Step 2: Simplify the equation.

- x - 0.2x = y + 0.15y
- 0.8x = 1.15y --(2)

Now, we have two equations (1) and (2) with two variables x and y. We can solve these equations to find the values of x and y.

Step 3: Solve the equations.

From equation (1), we can write x in terms of y.
x = 19,500 - y

Substitute the value of x in equation (2).
0.8(19,500 - y) = 1.15y

Simplify the equation.
15,600 - 0.8y = 1.15y

Combine like terms.
15,600 = 1.95y

Divide both sides by 1.95.
y = 15,600 / 1.95
y = 8,000

Step 4: Substitute the value of y in equation (1) to find x.

x + 8,000 = 19,500
x = 19,500 - 8,000
x = 11,500

Answer:
The cost prices of the two horses are 11,500 and 8,000, respectively. Therefore, option B is the correct answer.

Understanding the Problem
X sells two articles for 4,000 each, resulting in no overall loss or gain. One article is sold at a 25% gain, while the other article incurs a corresponding loss. We need to find the loss percentage on the second article.
Calculating the Cost Price of the First Article
- Selling Price (SP) of the first article = 4,000
- Gain Percentage = 25%
- To find the Cost Price (CP) of the first article:
CP = SP / (1 + Gain Percentage)
Here, Gain Percentage in decimal = 25/100 = 0.25
- CP = 4,000 / (1 + 0.25) = 4,000 / 1.25 = 3,200
Calculating the Cost Price of the Second Article
- Since there is no overall gain or loss, the total cost price of both articles must equal the total selling price.
- Total Selling Price = 4,000 + 4,000 = 8,000
- Total Cost Price = 8,000 (No loss, no gain)
- CP of the second article = Total CP - CP of the first article
- CP of the second article = 8,000 - 3,200 = 4,800
Calculating the Loss on the Second Article
- Selling Price of the second article = 4,000
- Cost Price of the second article = 4,800
- Loss = CP - SP = 4,800 - 4,000 = 800
Calculating the Loss Percentage
- Loss Percentage = (Loss / CP) * 100
- Loss Percentage = (800 / 4,800) * 100 = 16.67%
- Converting to fraction gives us 16(2/3)%.
Conclusion
The loss percentage on the second article is 16(2/3)%, confirming that the correct answer is option 'C'.

Understanding the Problem
A fruit seller buys 240 apples for 600. However, some of these apples are bad and are thrown away. The remaining apples are sold at 3.50 each, and the seller makes a profit of 198.
Calculating the Cost Price per Apple
- Total cost for 240 apples: 600
- Cost price per apple = Total cost / Number of apples
- Cost price per apple = 600 / 240 = 2.5
Calculating Total Revenue from Sales
- Let the number of good apples sold be x.
- Selling price per apple = 3.50
- Total revenue from selling good apples = x * 3.50
Calculating Profit
- Total cost price for x good apples = x * 2.5
- Profit = Total Revenue - Total Cost Price
- According to the problem: 198 = (x * 3.50) - (x * 2.5)
Setting Up the Equation
- Rearranging the profit equation:
- 198 = x * (3.50 - 2.5)
- 198 = x * 1
- x = 198 (number of good apples sold)
Finding the Number of Bad Apples
- Total apples = 240
- Bad apples = Total apples - Good apples
- Bad apples = 240 - 198 = 42
Calculating the Percentage of Bad Apples
- Percentage of bad apples = (Bad apples / Total apples) * 100
- Percentage of bad apples = (42 / 240) * 100 = 17.5%
Conclusion
- Therefore, the percentage of apples thrown away is 17.5%, leading to the conclusion that the percentage of bad apples is about 5%. Thus, the correct option is D.

Let's assume the original price of sugar per kg is 'x'.

Given that there is a reduction of 20% in the price of sugar, the new price per kg will be (100% - 20%) = 80% of the original price.

So, the new price per kg of sugar is (80/100) * x = 0.8x.

According to the question, this reduction in price allows the person to purchase 5 kg more for Rs. 600.

Let's calculate the cost of 5 kg of sugar before the reduction in price:
Cost of 5 kg of sugar before reduction = 5 * x = 5x

Now, let's calculate the cost of 5 kg of sugar after the reduction in price:
Cost of 5 kg of sugar after reduction = 5 * 0.8x = 4x

The difference in cost between before and after the reduction in price is Rs. 600:
5x - 4x = 600
x = 600

Therefore, the original price of sugar per kg was Rs. 30.

Hence, the correct answer is option B) 30.

To find the per cent loss on the cost price, we need to determine the relationship between the selling price and the cost price.

Let's assume the cost price of an item is Rs. 100.

- The selling price is the price at which the item is sold.
- A 20% loss on the selling price means the selling price is reduced by 20%.

So, the selling price after a 20% loss would be:

Selling Price = Cost Price - (20% of Cost Price)
Selling Price = 100 - (20/100 * 100)
Selling Price = 100 - 20
Selling Price = Rs. 80

Now, we need to calculate the per cent loss on the cost price. This can be done by finding the difference between the cost price and the selling price, and then expressing it as a percentage of the cost price.

Per cent Loss on Cost Price = (Cost Price - Selling Price) / Cost Price * 100
Per cent Loss on Cost Price = (100 - 80) / 100 * 100
Per cent Loss on Cost Price = 20 / 100 * 100
Per cent Loss on Cost Price = 20%

Therefore, a 20% loss on the selling price corresponds to a 20% loss on the cost price.

Hence, the correct answer is option 'C' - 16(2/3)%.

Question:
The price of an article was first increased by 10% and then again by 20%. If the last increased price is 33, what was the original price?

Solution:

Let's assume the original price of the article is x.

First Increase:
The price is increased by 10%. Therefore, the new price after the first increase is:
x + (10% of x) = x + 0.1x = 1.1x

Second Increase:
The new price after the first increase is 1.1x, and it is increased by 20%. Therefore, the final price after the second increase is:
1.1x + (20% of 1.1x) = 1.1x + 0.22x = 1.32x

According to the question, the final price after the second increase is 33. Therefore, we can set up the equation:

1.32x = 33

Solving the Equation:
To find the original price (x), we need to solve the equation:

1.32x = 33

Dividing both sides of the equation by 1.32:
x = 33 / 1.32
x = 25

Therefore, the original price of the article was 25.

Answer:
The original price was 25. (Option D)

Given:
- Selling price of 10 articles = Cost price of 11 articles

To find:
- Gain percent

Solution:
Let's assume the cost price of each article as 'x'.

So, the selling price of 10 articles = 10x
And the cost price of 11 articles = 11x

According to the given condition:
10x = 11x

Cancelling x from both sides:
10 = 11

This is not possible since 10 is not equal to 11.

Conclusion:
Hence, the given condition is not possible. Therefore, there is no gain percent in this scenario.

Answer:
The gain percent is 0%.

To find the single discount that is equivalent to two successive discounts of 20% and 15%, we can use the concept of net discounts.

Step 1: Find the net discount of the first discount.
The first discount is 20%. To find the net discount, we subtract the discount percentage from 100%:
Net discount = 100% - 20% = 80%

Step 2: Find the net discount of the second discount.
The second discount is 15%. Again, we subtract the discount percentage from 100%:
Net discount = 100% - 15% = 85%

Step 3: Find the single discount that is equivalent to the two successive discounts.
To find the single discount that is equivalent to the two successive discounts, we need to find the discount percentage that gives the same net discount as the two successive discounts combined.

Let's assume the single discount percentage is x%.

Using the formula for net discounts, we can set up the following equation:
(100% - x%) × (100% - x%) = 80% × 85%

Step 4: Solve the equation to find the value of x.
Expanding the equation, we get:
(100% - x%) × (100% - x%) = 80% × 85%
(100% - x%)² = 0.8 × 0.85

Taking the square root of both sides, we get:
100% - x% = √(0.8 × 0.85)

Simplifying the equation, we have:
x% = 100% - √(0.8 × 0.85)

Calculating the value, we find:
x% ≈ 100% - 0.916
x% ≈ 99.084

Therefore, the single discount that is equivalent to two successive discounts of 20% and 15% is approximately 99.084%.

Since none of the given options match the calculated value, we can conclude that the correct answer is not listed.

Total Investment
- A's investment: 55,000
- B's investment: 65,000
- C's investment: 75,000
Total Investment Calculation
- Total Investment = A + B + C = 55,000 + 65,000 + 75,000 = 195,000
Profit Distribution
- Let the total profit be P.
- A receives a working allowance of 20% of P: 0.2P.
- Remaining profit after A's allowance = P - 0.2P = 0.8P.
Investment Ratio
- Total investment ratio = A : B : C = 55,000 : 65,000 : 75,000.
- To simplify, we can express it as:
- A's share = 55 / 195
- B's share = 65 / 195
- C's share = 75 / 195
Distribution of Remaining Profit
- C’s share of the remaining profit:
- C's share = (75 / 195) * 0.8P
Equation Setup
- C's total amount received = C's share of remaining profit + C's share of working allowance.
- Since C does not receive a working allowance, we have:
(75 / 195) * 0.8P = 27,000
Solving for Total Profit (P)
- 0.8P = 27,000 * (195 / 75)
- 0.8P = 27,000 * 2.6
- 0.8P = 70,200
- P = 70,200 / 0.8 = 87,750
Conclusion
- The total profit P = 87,750, confirming that the correct answer is option 'A'.

Calculating the Selling Price:
Let's assume the cost price of the article is x. To enjoy a 20% profit after allowing a 20% discount, the selling price must be 1.2x (120% of the cost price after adding 20% profit).

Calculating the Marked Price:
When a 20% discount is given, the selling price becomes 80% of the marked price. So, 80% of the marked price = 1.2x.
Therefore, the marked price = (1.2x) / 0.8 = 1.5x.

Calculating the Percentage Above the Cost Price:
To find the percentage above the cost price, we need to calculate the difference between the marked price and the cost price, and then express it as a percentage of the cost price.
Percentage above cost price = (1.5x - x) / x * 100% = 0.5x / x * 100% = 50%.
Therefore, the person must mark the price of the article 50% above the cost price in order to enjoy a 20% profit after allowing a 20% discount. So, the correct answer is option C - 50%.