Unit2 - Subjective Questions
PEA305 • Practice Questions with Detailed Answers
Explain the concept of Percentage-to-Fraction conversion. Convert the following percentages into their simplest fractional forms:\n1. \n2. \n3.
Concept:
Percentage to fraction conversion involves dividing the percentage value by 100 and simplifying the resulting fraction. Mastering these standard conversions aids in quick mental calculations.
Conversions:
-
: This is equivalent to .
-
: This is equivalent to . Since :
-
: This can be seen as .
If the price of petrol increases by , by what percentage must a car owner reduce his consumption so as not to increase his expenditure on petrol?
To keep expenditure constant when price increases, consumption must decrease.
Formula:
If price increases by , the reduction in consumption is given by:
Calculation:
Here, .
Conclusion:
The consumption must be reduced by .
Define Successive Percentage Change and derive the formula for the net percentage change when a number is changed by and then by .
Definition:
Successive percentage change refers to the change in a value relative to its new value after a previous percentage change, rather than the original value.
Derivation:
Let the initial value be 100.
- First change of :
- Second change of on :
- Final Value:
- Net Change from 100:
Result:
Net Percentage Change =
A student multiplied a number by instead of . Calculate the percentage error in the calculation.
To find the percentage error, we compare the difference (error) to the true value.
Step 1: Assume a number.
Let the number be the LCM of the denominators (3 and 5), i.e., 15.
Step 2: Calculate True Value and Erroneous Value.
- True Value:
- Erroneous Value:
Step 3: Calculate Error.
Step 4: Calculate Percentage Error.
Answer: The percentage error is .
In an election between two candidates, one got of the total valid votes, and of the votes were invalid. If the total number of votes was 7500, find the number of valid votes that the other candidate got.
Step 1: Calculate Total Valid Votes.
Total votes = 7500.
Invalid votes = . Therefore, Valid votes = .
Step 2: Analyze Candidate Shares.
- The winner got of valid votes.
- Therefore, the other candidate (loser) got of valid votes.
Step 3: Calculate Other Candidate's Votes.
Answer: The other candidate received 2700 votes.
A candidate who gets marks in an examination fails by 30 marks. Another candidate who gets marks gets 42 marks more than the passing marks. Find the percentage of marks required to pass.
Step 1: Set up the equation.
Let the total marks be .
- Passing marks according to Candidate 1:
- Passing marks according to Candidate 2:
Step 2: Equate and Solve for .
Step 3: Calculate Passing Marks.
Step 4: Calculate Passing Percentage.
Answer: The passing percentage is .
Distinguish between Cost Price (CP), Selling Price (SP), and Marked Price (MP). How are they related in the context of Profit and Discount?
- Cost Price (CP): The price at which goods are purchased or manufactured. This is the base value for calculating profit or loss percentage.
- Selling Price (SP): The price at which goods are sold to the customer.
- Marked Price (MP): The price listed on the label of the article (also called List Price). Discounts are calculated on this price.
Relationships:
- Profit/Loss Context:
(or ) - Discount Context:
- Combined Relation:
A dishonest dealer professes to sell his goods at cost price but uses a weight of 960 grams for a kg weight. Find his gain percentage.
Concept:
When a dealer sells at Cost Price but uses false weight, the gain is derived purely from the quantity saved.
Formula:
OR
Calculation:
- True Weight = 1000g
- False Weight (Actually Used) = 960g
- Difference (Error) =
Answer: His gain percentage is .
If the Cost Price of 15 articles is equal to the Selling Price of 10 articles, calculate the Profit percentage.
Given:
Method:
Let the price of 1 article be . Or, simply assume the LCM of quantities as the total value. Let (LCM of 15 and 10).
- Find CP per article:
- Find SP per article:
- Calculate Profit:
- Calculate Profit %:
Answer: The profit is .
Two articles are sold at the same price of Rs 990 each. On one, the seller gains and on the other, he loses . Find the overall gain or loss percentage.
Concept:
When two articles are sold at the same Selling Price, and one is sold at profit and the other at loss, the net result is always a loss.
Formula:
Calculation:
Here, .
(Alternatively, calculating manually):
- SP1 = 990, Profit = 10% CP1 = .
- SP2 = 990, Loss = 10% CP2 = .
- Total SP = 1980. Total CP = 2000.
- Loss = 20. Loss % = .
Answer: Overall Loss.
Calculate the single discount equivalent to three successive discounts of , , and .
Method 1: Using Base 100
Let the Marked Price (MP) be 100.
- After discount:
- After discount on 80:
- After discount on 72:
Calculate Total Discount:
Answer: The single equivalent discount is .
A shopkeeper marks his goods above the cost price. He then allows a discount of on the marked price. What is his actual profit percentage?
Assumption:
Let the Cost Price (CP) be Rs 100.
Step 1: Determine Marked Price (MP).
MP is above CP.
Step 2: Apply Discount.
Discount is on MP.
Step 3: Determine Selling Price (SP).
Step 4: Calculate Profit %.
Answer: The actual profit is .
Derive the relationship between Cost Price (CP) and Marked Price (MP) in terms of Profit percentage () and Discount percentage ().
We can equate the Selling Price (SP) calculated from both the Cost Price perspective and the Marked Price perspective.
1. From Cost Price:
When there is a profit of :
2. From Marked Price:
When there is a discount of :
3. Equating both SPs:
Canceling the denominator (100) from both sides:
Final Relationship:
A reduction of in the price of sugar enables a housewife to purchase 6 kg more for Rs 240. Find the original price per kg of sugar.
Logic:
The reduction in price creates a monetary saving. This saved money is used to buy the extra quantity.
Step 1: Calculate Saving.
Total amount = Rs 240.
Reduction = .
Step 2: Find Reduced Price.
With this saved Rs 48, she can buy 6 kg more.
Step 3: Find Original Price.
Let Original Price be .
Reduced Price is of Original Price ().
Answer: The original price was Rs 10 per kg.
A shopkeeper sells sugar in such a way that the selling price of 950g is the same as the cost price of 1kg. Find his gain or loss percent.
Analysis:
- He sells 950g but recovers the cost of 1000g.
- This means he is selling less quantity for the same price, which implies a Loss.
- Wait, let's re-read carefully: SP of 950g = CP of 1000g.
- Since SP > CP (he gets the money for 1kg by only giving 950g), this is a Gain.
Calculation:
- Qty Sold (for which money is received) = 950g (physically parted with)
- Difference =
Answer: The gain is .
The population of a town increases by annually. If its present population is 80,000, what will it be after 2 years?
Formula for Compound Growth:
Where is present population, is rate, is time.
Calculation:
Answer: The population after 2 years will be 88,200.
A trader offers a "Buy 4, Get 1 Free" scheme. What is the effective discount percentage?
Concept:
The discount percentage in a "Buy Get Free" scheme is calculated based on the total articles received by the customer.
Formula:
Calculation:
- Free Items = 1
- Paid Items = 4
- Total Items (Marked Price basis) =
Answer: The effective discount is .
By selling an article for Rs 720, a man loses . At what price should he sell it to gain ?
Step 1: Find Cost Price (CP).
SP = 720, Loss = .
Step 2: Find New SP for 5% Gain.
New Profit = .
Answer: He should sell it for Rs 840.
A manufacturer sells a product to a wholesaler at a profit of . The wholesaler sells it to a retailer at a profit of . The retailer sells it to a customer for Rs 3,960 at a profit of . Find the Cost Price for the manufacturer.
Chain Rule Method:
Let the Manufacturer's CP be .
- Manufacturer sells to Wholesaler at of .
- Wholesaler sells to Retailer at of previous price.
- Retailer sells to Customer at of previous price.
Equation:
Solve for :
Answer: The Cost Price for the manufacturer is Rs 2,500.
Explain the concept of Common Selling Price in profit and loss. If a person sells two items at the same price, gaining on one and losing on the other, explain why we cannot simply add or subtract the percentages to find the net outcome.
Concept of Common Selling Price:
This scenario arises when two different articles are sold for the exact same monetary value (SP1 = SP2). However, their Cost Prices (CP) are usually different because the profit/loss percentages applied to them are different.
Why percentages cannot be added:
Profit and Loss percentages are calculated on the Cost Price, not the Selling Price.
- For Item 1: .
- For Item 2: .
Since is the same, if $P
eq LCP_1CP_2CP_1CP_2+P\%-L\%$ to find the net result. We must calculate the Total SP and Total CP individually to find the true net profit/loss percent.