All questions of Profit & Loss for SSC CGL Exam

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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
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.

To find the additional discount that must be offered to the customer to bring the net price to 108/-, we can follow these steps:

Step 1: Calculate the original price of the fan
The fan is listed at 150/- with a discount of 20%. To find the original price, we need to calculate the price before the discount.
Let's assume the original price is x.
According to the given information, the discount is 20%.
Therefore, the discounted price is (100% - 20%) * x = 80/100 * x = 0.8x.
We know that the discounted price is 150/-.
So, 0.8x = 150.
Dividing both sides by 0.8, we get:
x = 150 / 0.8 = 187.5/-.
Therefore, the original price of the fan is 187.5/-.

Step 2: Calculate the additional discount
Now, we need to find the additional discount that must be offered to bring the net price to 108/-.
Let's assume the additional discount is y%.
The net price after the additional discount can be calculated as:
(100% - y%) * original price = (100% - y%) * 187.5/-.
According to the given information, the net price is 108/-.
So, (100% - y%) * 187.5/- = 108.
Dividing both sides by 187.5/-, we get:
100% - y% = 108 / 187.5.
Simplifying, we get:
100% - y% = 0.576.
Subtracting 100% from both sides, we get:
-y% = -0.424.
Dividing both sides by -1, we get:
y% = 0.424.

Step 3: Calculate the percentage value of y
To find the additional discount as a percentage, we need to multiply y% by 100.
y% * 100 = 0.424 * 100 = 42.4%.
Therefore, the additional discount that must be offered to the customer to bring the net price to 108/- is 42.4%.

Hence, the correct answer is option C) 10%.

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.

Understanding the Problem
A man sells a fan for 1900 with a loss of 5%. We need to determine the selling price to achieve a gain of 20%.
Step 1: Calculate the Cost Price (CP)
- A loss of 5% indicates that the selling price (SP) is 95% of the cost price (CP).
- Using the formula:
SP = CP × (1 - Loss%)
1900 = CP × (1 - 0.05)
1900 = CP × 0.95
- To find CP, rearrange the equation:
CP = 1900 / 0.95
CP = 2000
Step 2: Calculate the Selling Price for a 20% Gain
- To find the selling price for a gain of 20%, the formula is:
SP = CP × (1 + Gain%)
SP = 2000 × (1 + 0.20)
SP = 2000 × 1.20
SP = 2400
Conclusion
- The required selling price to achieve a 20% gain on the fan is 2400.
- Therefore, the correct answer is option B.

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%.

Let's solve this problem step by step:
1. Let the cost price of the article be x.
2. Selling price when sold at 5% above the cost price = 1.05x
3. Buying price at 5% less than what he paid for it = x - 0.05x = 0.95x
4. Selling price when sold at 2 less than the buying price = 0.95x - 2
Now, we are given that if he had bought it at 0.95x and sold it for 0.95x - 2, he would have gained 10%.
This can be written as:
0.95x - (0.95x - 2) = 0.1(0.95x)
2 = 0.1(0.95x)
2 = 0.095x
x = 200
Therefore, the cost price of the article is 200.
So, the correct answer is option B) 400.

Understanding Successive Discounts
When applying successive discounts, the total discount is not simply the sum of the individual discounts. Instead, each discount is applied sequentially on the reduced price after the previous discount. Let's break down how to calculate the equivalent single discount for the successive discounts of 15%, 20%, and 25%.
Step-by-Step Calculation
1. Initial Price: Assume the original price of the article is 100 units for simplicity.
2. First Discount (15%):
- Discount Amount = 15% of 100 = 15
- Price after 1st Discount = 100 - 15 = 85
3. Second Discount (20%):
- Discount Amount = 20% of 85 = 17
- Price after 2nd Discount = 85 - 17 = 68
4. Third Discount (25%):
- Discount Amount = 25% of 68 = 17
- Price after 3rd Discount = 68 - 17 = 51
Calculating Total Discount
- The final price after all discounts is 51.
- Therefore, the total discount = Original Price - Final Price = 100 - 51 = 49.
Calculating Equivalent Single Discount Percentage
- Equivalent Single Discount Percentage = (Total Discount / Original Price) * 100
= (49 / 100) * 100 = 49%
Conclusion
Thus, the equivalent single discount for the successive discounts of 15%, 20%, and 25% is 49%. Hence, the correct answer is option 'C'.

Understanding the Problem:
We are given that the price of sugar has decreased by 10% and as a result, a man is able to buy 1 kg more sugar for 270 rupees. We need to find the original price of sugar per kilogram.

Solution:
Let's assume that the original price of sugar per kilogram is 'x' rupees.

Step 1: Calculate the new price of sugar per kilogram:
Since the price of sugar has decreased by 10%, the new price of sugar per kilogram would be (100% - 10%) = 90% of the original price.

So, the new price of sugar per kilogram is (90/100) * x = 0.9x rupees.

Step 2: Calculate the quantity of sugar purchased:
We are given that with the decrease in price, the man is able to buy 1 kg more sugar for 270 rupees.

Let's assume that the original quantity of sugar purchased was 'y' kilograms.

So, the original cost of y kilograms of sugar at the original price (x rupees per kilogram) would be xy rupees.

With the decrease in price, the man is able to buy (y + 1) kilograms of sugar for 270 rupees.

Therefore, we can write the equation:

0.9x * (y + 1) = 270

Simplifying the equation, we get:

0.9xy + 0.9x = 270

Step 3: Solve the equation:
To solve the equation, we need to find the values of 'x' and 'y'.

From the equation, we can see that 'x' is a common term in both terms. So, we can factor out 'x' to simplify the equation:

x(0.9y + 0.9) = 270

Divide both sides of the equation by 0.9 to isolate 'x':

x = 270 / (0.9y + 0.9)

Step 4: Substitute the value of y:
To find the original price of sugar per kilogram (x), we need to substitute the value of 'y'.

We are given that the man could buy 1 kg more sugar, which means the new quantity of sugar purchased (y + 1) is greater than the original quantity of sugar purchased (y) by 1 kg.

Therefore, y + 1 = y + 1 kg

Substituting this value in the equation:

x = 270 / (0.9(y + 1) + 0.9)

Simplifying further:

x = 270 / (0.9y + 0.9 + 0.9)

x = 270 / (0.9y + 1.8)

Step 5: Substitute the value of x:
We need to find the original price of sugar per kilogram (x). Let's substitute the value of x in terms of y:

x = 270 / (0.9y + 1.8)

Since we are looking for the original price of sugar per kilogram, we need to find the value of x when y = 1 (as the man is able to buy 1 kg more sugar).

Let's solve the problem step by step:

Given information:
- Two articles are sold for 962 each.
- On one article, the seller gains 30%.
- On the other article, the seller loses 26%.

To find the overall gain or loss percentage, we need to calculate the total cost price and the total selling price.

Let's assume the cost price of the first article is C1 and the cost price of the second article is C2.

Calculating the selling price:
- The selling price of the first article is C1 + 30% of C1 = C1 + 0.3C1 = 1.3C1.
- The selling price of the second article is C2 - 26% of C2 = C2 - 0.26C2 = 0.74C2.

According to the given information, both articles are sold for 962 each. So we can write the following equations:

1.3C1 = 962 ...(1)
0.74C2 = 962 ...(2)

Solving equations (1) and (2) will give us the values of C1 and C2.

From equation (1):
C1 = 962/1.3 = 740

From equation (2):
C2 = 962/0.74 = 1300

Calculating the total cost price and total selling price:
Total cost price = C1 + C2 = 740 + 1300 = 2040
Total selling price = 962 + 962 = 1924

Calculating the overall gain or loss percentage:
Gain or Loss = (Total Selling Price - Total Cost Price) / Total Cost Price * 100
= (1924 - 2040) / 2040 * 100
= -116 / 2040 * 100
≈ -5.68627

Therefore, the overall gain or loss percentage, rounded to one decimal place, is approximately 5.7% loss (option B).

Understanding the Marked Price and Discount
The marked price (MP) of the article is given as 736. The shopkeeper offers a discount of 25%, which means the selling price (SP) can be calculated as follows:
- Discount Amount = 25% of MP
- Discount Amount = 0.25 * 736 = 184
Now, we can find the selling price:
- Selling Price (SP) = Marked Price - Discount Amount
- Selling Price (SP) = 736 - 184 = 552
Calculating the Cost Price
The shopkeeper makes a profit of 20% on the cost price (CP). Therefore, we can express the relationship between SP, CP, and the profit percentage:
- Selling Price (SP) = Cost Price (CP) + Profit
- Profit = 20% of CP = 0.20 * CP
This can be rearranged to find the cost price:
- SP = CP + 0.20 * CP
- SP = 1.20 * CP
Now substituting the SP value:
- 552 = 1.20 * CP
To find CP, we rearrange the equation:
- CP = 552 / 1.20
Calculating this gives:
- CP = 460
Conclusion
Thus, the cost price of the article is:
- Cost Price (CP) = 460
The correct answer is option 'A'.