If Sohan, while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other.
UPSC-2014
has makes no profit and no loss.
he makes a profit of 1%.
he suffers a loss of 1%.
he suffers a loss of 2%.
This problem involves calculating profit and loss percentages when two items are sold at the same price, but one incurs a profit and the other a loss. A common misconception is that a 10% profit and a 10% loss cancel each other out. However, since the profit and loss are calculated on different cost prices, there will always be an overall loss in such scenarios.
If there is a 10% profit, it means the selling price is 110% of the cost price.
\[ \text{SP}_1 = \text{CP}_1 + 0.10 \times \text{CP}_1 = 1.10 \times \text{CP}_1 \]\[ 100 = 1.10 \times \text{CP}_1 \]\[ \text{CP}_1 = \frac{100}{1.10} = \frac{1000}{11} \]If there is a 10% loss, it means the selling price is 90% of the cost price.
\[ \text{SP}_2 = \text{CP}_2 - 0.10 \times \text{CP}_2 = 0.90 \times \text{CP}_2 \]\[ 100 = 0.90 \times \text{CP}_2 \]\[ \text{CP}_2 = \frac{100}{0.90} = \frac{1000}{9} \]As established in step 1, Total SP = \(₹200\).
Since Total CP \( = \frac{20000}{99} \approx 202.02 \) and Total SP \( = 200 \), Total CP > Total SP, which means there is a loss.
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = \frac{20000}{99} - 200 \]\[ \text{Loss} = \frac{20000 - (200 \times 99)}{99} = \frac{20000 - 19800}{99} = \frac{200}{99} \]Alternative Formula: When two articles are sold at the same selling price, and there is a profit of \(x\%\) on one and a loss of \(x\%\) on the other, there is always a loss. The loss percentage is given by the formula:
\[ \text{Loss Percentage} = \left( \frac{x}{10} \right)^2 \% \]In this case, \(x = 10\).\[ \text{Loss Percentage} = \left( \frac{10}{10} \right)^2 \% = (1)^2 \% = 1\% \]A and B decide to travel from place X to place Y by bus. A has ₹ 10 with him and he finds that it is 80% of the bus fare for two persons. B finds that he has ₹ 3 with him and hands it over to A. In this context, which one of the following statements is correct?
UPSC-2014
Now the money A has is just enough to buy two tickets.
A still needs ₹ 2 for buying the tickets.
After buying the two tickets A will be left with 50 paise.
The money A now has is still not sufficient to buy two tickets.
The problem involves calculating the total bus fare for two persons and then determining if the combined money A and B have is sufficient, and if so, how much change is left.
A has ₹ 10, which is 80% of the bus fare for two persons.
Let the total bus fare for two persons be \(F\).
\[ 80\% \text{ of } F = \text{₹ } 10 \] \[ 0.80 \times F = 10 \] \[ F = \frac{10}{0.80} \] \[ F = \frac{100}{8} \] \[ F = \text{₹ } 12.50 \]So, the total bus fare for two persons is ₹ 12.50.
Initially, A has ₹ 10.
B has ₹ 3 and hands it over to A.
Total money A has now \( = \text{₹ } 10 + \text{₹ } 3 = \text{₹ } 13 \).
Money A has \( = \text{₹ } 13 \).
Bus fare for two persons \( = \text{₹ } 12.50 \).
Amount left with A \( = \text{Total money} - \text{Bus fare} \)
\[ \text{Amount left} = \text{₹ } 13.00 - \text{₹ } 12.50 \] \[ \text{Amount left} = \text{₹ } 0.50 \]₹ 0.50 is equivalent to 50 paise.
Correct Option: C) After buying the two tickets A will be left with 50 paise.
As per agreement with a bank, a businessman had to refund a loan in some equal instalments without interest. After paying 18 instalments he found that 60 percent of his loan was refunded. How many instalments werethere in the agreement?
UPSC-2014
This problem involves understanding percentages and direct proportionality. We are given the number of instalments paid and the percentage of the loan refunded. We need to find the total number of instalments agreed upon.
C) 30 — As calculated, 18 instalments represent 60% of the loan, so 100% of the loan corresponds to 30 instalments.
When 70% of a number x is added to another number y, the sum becomes 165% of the value of y When 60% of the number x is added to another number z, then the sum becomes 165% of the value of Z. Which one of the following is correct?
UPSC-2022
We need to establish the relationship between the three numbers x, y, and z based on the given conditions. We will translate the word problems into algebraic equations and then solve for the ratios or relationships between the variables.
Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list?
UPSC-2022
The problem involves calculating the total number of voters based on the percentage of votes cast, the percentage of votes received by one candidate, and the winning margin. We will work backward from the votes cast to the total voters on the list.
Thus, the total number of voters in the voters list is 15000.
A) 15000 is the correct answer, as derived from the step-by-step calculation.
The increase in the price of a certain item was 25%. Then the price was decreased by 20% and then again increased by 10%. What is the resultant increase in the price?
UPSC-2022
To find the resultant increase in price, we can assume an initial price and then apply the given percentage changes sequentially. Alternatively, we can use a direct formula for successive percentage changes.
Correct Option: B) 10%
