To find the number of prime numbers between 476 and 485 (inclusive), we need to list all integers in this range and then check each integer for primality. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Therefore, there is only 1 prime number between 476 and 485 (inclusive).
Correct Option: B) 1
To find the trade discount amount, we first need to calculate the total list price of the units purchased. Then, we apply the given trade discount percentage to this total list price.
The shopkeeper purchases 100 units, and each unit is priced at ₹50.
\[ \text{Total List Price} = \text{Number of Units} \times \text{Price per Unit} \]\[ \text{Total List Price} = 100 \times \text{₹}50 = \text{₹}5000 \]A trade discount of 10% is given on the total list price.
\[ \text{Trade Discount Amount} = \text{Trade Discount Percentage} \times \text{Total List Price} \]\[ \text{Trade Discount Amount} = 10\% \times \text{₹}5000 \]\[ \text{Trade Discount Amount} = \frac{10}{100} \times \text{₹}5000 \]\[ \text{Trade Discount Amount} = \text{₹}500 \]The 5% scheme discount (free units) is a separate type of discount and does not affect the calculation of the trade discount amount, which is always calculated on the list price.
A) ₹500 is the correct trade discount amount calculated from the total list price.
To solve this problem, we need to determine the individual work rates of men and women and then combine them to find the total work rate of 3 men and 3 women. Finally, we can calculate the number of days required to complete the work.
Calculate the work done by 1 man in 1 day:
Given that 5 men can complete a piece of work in 18 days.
Total work done by 5 men in 1 day is \(\frac{1}{18}\) of the work.
So, work done by 1 man in 1 day is \[\frac{1}{18 \times 5} = \frac{1}{90}\] of the work.
Calculate the work done by 1 woman in 1 day:
Given that 9 women can complete the same work in 5 days.
Total work done by 9 women in 1 day is \(\frac{1}{5}\) of the work.
So, work done by 1 woman in 1 day is \[\frac{1}{5 \times 9} = \frac{1}{45}\] of the work.
Calculate the work done by 3 men and 3 women in 1 day:
Work done by 3 men in 1 day is \[3 \times \frac{1}{90} = \frac{3}{90} = \frac{1}{30}\] of the work.
Work done by 3 women in 1 day is \[3 \times \frac{1}{45} = \frac{3}{45} = \frac{1}{15}\] of the work.
Total work done by (3 men + 3 women) in 1 day is:
\[ \frac{1}{30} + \frac{1}{15} = \frac{1 + 2}{30} = \frac{3}{30} = \frac{1}{10} \]Calculate the number of days to complete the work:
If 3 men and 3 women can complete \(\frac{1}{10}\) of the work in 1 day, then they can complete the entire work in 10 days.
B) 10 days
By how much is 65% of 65 greater than \( \frac{4}{5} \) of 15?
To solve this problem, we need to calculate two values: first, 65% of 65, and second, \( \frac{4}{5} \) of 15. Then, we will find the difference between the first value and the second value.
Calculate 65% of 65:
To find a percentage of a number, convert the percentage to a decimal or fraction and multiply it by the number.
\[ 65\% \text{ of } 65 = \frac{65}{100} \times 65 \]\[ = 0.65 \times 65 \]\[ = 42.25 \]Calculate \( \frac{4}{5} \) of 15:
To find a fraction of a number, multiply the fraction by the number.
\[ \frac{4}{5} \text{ of } 15 = \frac{4}{5} \times 15 \]\[ = 4 \times \frac{15}{5} \]\[ = 4 \times 3 \]\[ = 12 \]Find the difference:
The question asks by how much the first value is greater than the second value. So, we subtract the second value from the first value.
\[ \text{Difference} = 42.25 - 12 \]\[ = 30.25 \]D) 30.25 is the correct answer. The difference between 65% of 65 (which is 42.25) and \( \frac{4}{5} \) of 15 (which is 12) is 30.25.
The problem involves calculating the marked price of an article given its selling price and the discount percentage. We will use the formula relating selling price, marked price, and discount percentage.
When a discount is allowed on the marked price, the selling price is calculated as:
\[ \text{SP} = \text{MP} - (\text{Discount Percentage} \times \text{MP}) \]The selling price is the marked price minus the discount. If the discount is \(13\%\), then the article is sold for \(100\% - 13\% = 87\%\) of its marked price.
\[ \text{SP} = \text{MP} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right) \]Let MP be \(x\).
\[ 348 = x \times \left(1 - \frac{13}{100}\right) \]\[ 348 = x \times \left(\frac{100 - 13}{100}\right) \]\[ 348 = x \times \left(\frac{87}{100}\right) \]To find \(x\), rearrange the equation:
\[ x = 348 \times \frac{100}{87} \]We can simplify the fraction. Notice that \(348\) is divisible by \(87\).
\[ 348 \div 87 = 4 \]\[ x = 4 \times 100 \]\[ x = 400 \]The marked price of the article is ₹\(400\).
D) ₹400 is the correct marked price. This is calculated by understanding that a 13% discount means the selling price is 87% of the marked price, and then solving for the marked price.
The problem asks for the ratio of two numbers given a relationship between their percentages and fractions. We will represent the two numbers with variables, set up an equation based on the given information, and then solve for the ratio of the first number to the second number.
Let the first number be \(A\) and the second number be \(B\).
The problem states that 36% of the first number is equal to four-sevenths of the second number. We can write this as an equation:
\[ 36\% \text{ of } A = \frac{4}{7} \text{ of } B \]Convert the percentage to a fraction or decimal:
\[ 36\% = \frac{36}{100} \]Substitute this into the equation:
\[ \frac{36}{100} \times A = \frac{4}{7} \times B \]Simplify the fraction \(\frac{36}{100}\) by dividing both numerator and denominator by their greatest common divisor, which is 4:
\[ \frac{36 \div 4}{100 \div 4} = \frac{9}{25} \]Now the equation becomes:
\[ \frac{9}{25} A = \frac{4}{7} B \]We need to find the ratio of the first number to the second number, which is \(\frac{A}{B}\). To do this, we can rearrange the equation:
Divide both sides by \(B\):
\[ \frac{9}{25} \frac{A}{B} = \frac{4}{7} \]Multiply both sides by \(\frac{25}{9}\) to isolate \(\frac{A}{B}\):
\[ \frac{A}{B} = \frac{4}{7} \times \frac{25}{9} \]Perform the multiplication:
\[ \frac{A}{B} = \frac{4 \times 25}{7 \times 9} = \frac{100}{63} \]The ratio of the first number to the second number is \(100 : 63\).
Correct Option: B) 100 : 63
In a partnership business, the profit is distributed among partners in proportion to their investments. We will first find the ratio of Brijesh's profit share to the total profit to determine his share of the total investment. Then, we can calculate each person's investment and find the difference.
The total profit was ₹12,000, and Brijesh's share was ₹5,700. So, Kushal's share can be found by subtracting Brijesh's share from the total profit.
\[ \text{Kushal's Profit Share} = \text{Total Profit} - \text{Brijesh's Profit Share} \\ \text{Kushal's Profit Share} = \text{₹}12,000 - \text{₹}5,700 \\ \text{Kushal's Profit Share} = \text{₹}6,300 \]The ratio of their profit shares is equal to the ratio of their investments.
\[ \text{Kushal's Profit} : \text{Brijesh's Profit} = 6300 : 5700 \\ \text{Kushal's Profit} : \text{Brijesh's Profit} = 63 : 57 \\ \text{Kushal's Profit} : \text{Brijesh's Profit} = 21 : 19 \]Let the total investment be \(I_{\text{total}}\) and the ratio of investments be \(I_K : I_B = 21 : 19\). The total investment is ₹37,100.
Kushal's Investment:
\[ I_K = \frac{21}{21 + 19} \times I_{\text{total}} \\ I_K = \frac{21}{40} \times 37,100 \\ I_K = 21 \times 927.5 \\ I_K = \text{₹}19,477.5 \]Brijesh's Investment:
\[ I_B = \frac{19}{21 + 19} \times I_{\text{total}} \\ I_B = \frac{19}{40} \times 37,100 \\ I_B = 19 \times 927.5 \\ I_B = \text{₹}17,622.5 \]A) ₹1,855 is the correct difference between Kushal's and Brijesh's investments.
This problem involves calculating the total profit percentage when a trader makes a profit on the selling price and also uses a faulty weight. We need to combine the profit from the marked-up price and the profit from the dishonest weighing to find the overall profit.
Profit from selling price:
The trader claims a profit of 29%. This means if the cost price (CP) is \(C\), the selling price (SP) is \(C \times (1 + 0.29) = 1.29C\).
Profit from dishonest weight:
The trader uses a weight which is 13% less than what is mentioned. This means for every 100 units of weight mentioned, the trader actually sells \(100 - 13 = 87\) units.
The profit from dishonest weighing can be calculated as:
\[ \text{Profit from weight} = \frac{\text{Error}}{\text{True value} - \text{Error}} \times 100 \% \]Here, the error is 13 units, and the true value delivered is 87 units. So, the profit percentage from weight is:
\[ \frac{13}{87} \times 100 \% \]Calculate the overall profit factor:
Let's assume the Cost Price (CP) of 1 unit of grain is Rs. 1.
When the trader sells 87 units of grain, the actual cost to the trader is Rs. 87.
However, the trader charges for 100 units of grain, and on these 100 units, he claims a 29% profit. So, the selling price for 100 units would be:
\[ \text{SP for 100 units} = 100 \times (1 + 0.29) = 129 \]So, the trader sells grain that cost him Rs. 87 for Rs. 129.
The total profit is:
\[ \text{Total Profit} = \text{Selling Price} - \text{Cost Price} = 129 - 87 = 42 \]The total profit percentage is:
\[ \text{Total Profit Percentage} = \frac{\text{Total Profit}}{\text{Cost Price}} \times 100 \% \]\[ \text{Total Profit Percentage} = \frac{42}{87} \times 100 \% \]\[ \text{Total Profit Percentage} \approx 48.275 \% \]Round off the answer:
Rounding off 48.275% to the nearest whole number gives 48%.
C) 48% is the total profit percentage earned by the trader after rounding to the nearest whole number.
The problem asks us to find the greater of two consecutive natural numbers whose product is 6. We can solve this by setting up an algebraic equation or by testing the given options.
C) 3 — The two consecutive natural numbers whose product is 6 are 2 and 3. The greater of these is 3.
This problem asks for the average of the first 152 odd natural numbers. We can solve this by understanding the properties of arithmetic progressions or by recalling a specific formula for the average of the first 'n' odd natural numbers.
Both methods yield the same result.
Correct Option: C) 152