If A denotes ÷, B denotes ×, C denotes + and D denotes −, then which of the following statements is true?
11 B 34 A 17 D 8 A 3 = \( \frac{38}{3} \)
6 B 18 D 26 A 13 C 7 = \( \frac{173}{13} \)
32 C 8 A 16 D 4 = −\( \frac{3}{4} \)
9 C 9 A 9 D 9 B 9 = −71
This problem involves substituting given symbols with mathematical operators and then evaluating the expressions using the order of operations (BODMAS/PEMDAS).
First, we need to replace the letters A, B, C, and D with their corresponding mathematical operations:
Then, we evaluate each option one by one following the BODMAS/PEMDAS rule (Brackets, Orders/Exponents, Division/Multiplication, Addition/Subtraction).
The expression is \(11 \text{ B } 34 \text{ A } 17 \text{ D } 8 \text{ A } 3\).
Substitute the operators:
\[ 11 \times 34 \div 17 - 8 \div 3 \]The expression becomes:
\[ 11 \times 2 - \frac{8}{3} \]The expression becomes:
\[ 22 - \frac{8}{3} \]The given result is \(\frac{38}{3}\). Since \[\frac{58}{3} \neq \frac{38}{3}\], Option A is incorrect.
The expression is \(6 \text{ B } 18 \text{ D } 26 \text{ A } 13 \text{ C } 7\).
Substitute the operators:
\[ 6 \times 18 - 26 \div 13 + 7 \]The expression becomes:
\[ 6 \times 18 - 2 + 7 \]The expression becomes:
\[ 108 - 2 + 7 \]The given result is \(\frac{173}{13}\). Since \(113 \neq \frac{173}{13}\), Option B is incorrect.
The expression is \(32 \text{ C } 8 \text{ A } 16 \text{ D } 4\).
Substitute the operators:
\[ 32 + 8 \div 16 - 4 \]The expression becomes:
\[ 32 + \frac{1}{2} - 4 \]The given result is \(-\frac{3}{4}\). Since \[\frac{57}{2} \neq -\frac{3}{4}\], Option C is incorrect.
The expression is \(9 \text{ C } 9 \text{ A } 9 \text{ D } 9 \text{ B } 9\).
Substitute the operators:
\[ 9 + 9 \div 9 - 9 \times 9 \]The expression becomes:
\[ 9 + 1 - 81 \]The given result is \(-71\). Since \(-71 = -71\), Option D is correct.
Correct Option: D) \(9 \text{ C } 9 \text{ A } 9 \text{ D } 9 \text{ B } 9 = -71\)
To calculate the maturity amount for compound interest compounded quarterly, we need to adjust the annual interest rate and the time period. The annual rate is divided by 4, and the number of years is multiplied by 4 to get the number of compounding periods. Then, we use the compound interest formula.
Since the interest is compounded quarterly, the rate per quarter will be the annual rate divided by 4.
\[ \text{Rate per quarter} (r) = \frac{\text{Annual Rate}}{4} = \frac{20\%}{4} = 5\% \]The time period is 9 months. To convert this to quarters, divide by 3 (since there are 3 months in a quarter).
\[ \text{Number of compounding periods} (n) = \frac{\text{Total months}}{\text{Months per quarter}} = \frac{9}{3} = 3 \text{ quarters} \]The formula for the amount (\(A\)) after compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]Substitute \(P = 16000\), \(r = 5\), and \(n = 3\) into the formula:
\[ A = 16000 \left(1 + \frac{5}{100}\right)^3 \]\[ A = 16000 \left(1 + 0.05\right)^3 \]\[ A = 16000 \left(1.05\right)^3 \]\[ A = 16000 \times 1.157625 \]\[ A = 18522 \]Mr. Murthy will get Rs. 18,522 on maturity.
Correct Option: D) Rs. 18,522
The problem asks for the ratio of two selling prices when an article is sold at different profit percentages, given the cash difference between these selling prices. We can assume a cost price (CP) for the article and then calculate the selling prices (SP) for each profit percentage. Finally, we find the ratio of these selling prices.
Let the Cost Price (CP) of the article be \(P\).
When the article is sold at a profit of 4%, the Selling Price (\(SP_1\)) is given by:
\[ SP_1 = CP + 4\% \text{ of } CP = P + \frac{4}{100}P = P \left(1 + \frac{4}{100}\right) = P \left(\frac{104}{100}\right) \]When the article is sold at a profit of 6%, the Selling Price (\(SP_2\)) is given by:
\[ SP_2 = CP + 6\% \text{ of } CP = P + \frac{6}{100}P = P \left(1 + \frac{6}{100}\right) = P \left(\frac{106}{100}\right) \]The cash difference between the two selling prices is given as Rs. 3. So,
\[ SP_2 - SP_1 = 3 \]\[ P \left(\frac{106}{100}\right) - P \left(\frac{104}{100}\right) = 3 \]\[ P \left(\frac{106 - 104}{100}\right) = 3 \]\[ P \left(\frac{2}{100}\right) = 3 \]\[ \frac{2P}{100} = 3 \]\[ 2P = 300 \]\[ P = \frac{300}{2} = 150 \]So, the Cost Price (CP) of the article is Rs. 150.Now, we can find the actual selling prices:
\[ SP_1 = 150 \times \frac{104}{100} = 1.5 \times 104 = 156 \]\[ SP_2 = 150 \times \frac{106}{100} = 1.5 \times 106 = 159 \]The ratio of the two selling prices \(SP_1 : SP_2\) is:
\[ \frac{SP_1}{SP_2} = \frac{156}{159} \]To simplify the ratio, we can divide both numbers by their greatest common divisor. Both 156 and 159 are divisible by 3 (since the sum of digits \(1+5+6=12\) and \(1+5+9=15\) are divisible by 3).\[ \frac{156 \div 3}{159 \div 3} = \frac{52}{53} \]So, the ratio is 52:53.C) 52:53 is the correct ratio of the two selling prices, as calculated in the step-by-step solution.
To find the HCF (Highest Common Factor) of two numbers, we can use the Euclidean Algorithm. This method involves repeatedly dividing the larger number by the smaller number and replacing the larger number with the smaller number and the smaller number with the remainder, until the remainder is zero. The last non-zero remainder is the HCF.
We need to find the HCF of 3341 and 3328. We start by dividing the larger number (3341) by the smaller number (3328).
\[ 3341 = 3328 \times 1 + 13 \]Since the remainder is not zero, we replace the larger number with the smaller number (3328) and the smaller number with the remainder (13). Now we divide 3328 by 13.
\[ 3328 = 13 \times 256 + 0 \]The remainder is now 0. The HCF is the last non-zero remainder, which was 13.
C) 13 is the HCF of 3341 and 3328, as determined by the Euclidean Algorithm.
This problem involves calculating the cost price of an item given its selling price and loss percentage, and then determining a new selling price to achieve a desired profit percentage. We will use the standard formulas for profit and loss percentages.
Therefore, the bus should be sold for Rs. 25,300 to get a profit of 15%.
Correct Option: C) Rs. 25,300
The question asks about the specific Schedule of the Indian Constitution that enumerates the States and Union Territories. To answer this, one needs to recall the contents of the various Schedules of the Constitution.
Correct Option: A) The First Schedule of the Constitution of India lists the names of the States and Union Territories and their territorial extent.
The question asks to identify the Lokayukta of Delhi as of 2017. This requires knowledge of specific appointments to key governmental positions during that period.
Correct Option: B) Justice Reva Khetrapal
Justice Reva Khetrapal was appointed as the Lokayukta of Delhi in October 2015 and served in that capacity, including throughout 2017.
The question asks about the fundamental rule for naming files within the same folder in a Windows-based computer. The core principle is that each file within a given directory must have a unique identifier. This identifier is primarily determined by its name and extension.
document.docx, image.jpg).Correct Option: C) they have the same name, and are of the same file type
report.docx and summary.docx). This is a common scenario and does not prevent them from being in the same folder.document.txt and document.docx). The different extensions make them unique files, allowing them to coexist in the same folder.To find the approximate cost for 4 minutes, we first need to determine the cost per minute. Once the cost per minute is known, we can multiply it by 4 minutes to get the total cost.
Given that the cost for 6 minutes is Rs. 32.
\[ \text{Cost per minute} = \frac{\text{Total Cost}}{\text{Total Minutes}} \]Substitute the given values:
\[ \text{Cost per minute} = \frac{32 \text{ Rs.}}{6 \text{ minutes}} \]Simplify the fraction:
\[ \text{Cost per minute} = \frac{16}{3} \text{ Rs./minute} \]Now, multiply the cost per minute by 4 minutes:
\[ \text{Cost for 4 minutes} = \text{Cost per minute} \times 4 \text{ minutes} \]Substitute the calculated cost per minute:
\[ \text{Cost for 4 minutes} = \frac{16}{3} \text{ Rs./minute} \times 4 \text{ minutes} \]Perform the multiplication:
\[ \text{Cost for 4 minutes} = \frac{16 \times 4}{3} \text{ Rs.} \]\[ \text{Cost for 4 minutes} = \frac{64}{3} \text{ Rs.} \]
Divide 64 by 3:
\[ \frac{64}{3} \approx 21.333... \text{ Rs.} \]Rounding to two decimal places, the approximate cost is Rs. 21.33.
A) 21.30 — The calculated cost is approximately Rs. 21.33. Among the given options, Rs. 21.30 is the closest approximation. It seems the options are rounded to one decimal place or slightly rounded down.
The Gandhara art - a style of Buddhist visual art that developed between 1st century BCE and the 7th century CE, flourished largely during the ___ dynasty.
The question asks about the dynasty during which the Gandhara art style predominantly flourished. This requires knowledge of ancient Indian history, specifically the timeline and characteristics of different art styles and the dynasties associated with them.
Correct Option: A) The Gandhara art style, characterized by its Greco-Buddhist elements and human depiction of Buddha, flourished predominantly during the Kushan dynasty, which ruled from the 1st to the 3rd century CE. This period aligns perfectly with the specified timeline for the development of Gandhara art.