This problem involves substituting given symbols with mathematical operators and then evaluating the expression using the order of operations (BODMAS/PEMDAS).
The value of the expression is 38.
Correct Option: D) 38
To find the percentage profit, we need to calculate the Cost Price (CP), Marked Price (MP), and Selling Price (SP). We are given the CP, the markup percentage, and the discount percentage. We will first calculate the MP, then the SP, and finally the profit percentage.
Given, Cost Price \( = \text{₹}1,300 \).
The article's price was marked up by 35%.
\[ \text{Marked Price (MP)} = \text{CP} \times \left(1 + \frac{\text{Markup Percentage}}{100}\right) \] \[ \text{MP} = 1300 \times \left(1 + \frac{35}{100}\right) = 1300 \times \left(1 + 0.35\right) = 1300 \times 1.35 \] \[ \text{MP} = \text{₹}1,755 \]It was sold at a discount of 20% on the marked price.
\[ \text{Selling Price (SP)} = \text{MP} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right) \] \[ \text{SP} = 1755 \times \left(1 - \frac{20}{100}\right) = 1755 \times \left(1 - 0.20\right) = 1755 \times 0.80 \] \[ \text{SP} = \text{₹}1,404 \]Profit is the difference between Selling Price and Cost Price.
\[ \text{Profit} = \text{SP} - \text{CP} = 1404 - 1300 = \text{₹}104 \]Percentage Profit is calculated on the Cost Price.
\[ \text{Percentage Profit} = \frac{\text{Profit}}{\text{CP}} \times 100 \] \[ \text{Percentage Profit} = \frac{104}{1300} \times 100 = \frac{104}{13} = 8\% \]Correct Option: D) 8%
This problem involves simple interest. We are given that a sum of money doubles itself in 5 years. We need to find the annual rate of interest. When a sum of money doubles, it means the interest earned is equal to the principal amount. We can use the simple interest formula to solve this.
The Simple Interest earned is the difference between the Amount and the Principal:
\[\text{SI} = A - P\] \[\text{SI} = 2P - P\] \[\text{SI} = P\]The formula for Simple Interest is:
\[\text{SI} = \frac{P \times R \times T}{100}\]We know \(\text{SI} = P\), \(T = 5\), and we need to find \(R\).
\[P = \frac{P \times R \times 5}{100}\]Divide both sides by \(P\) (assuming \(P \neq 0\)):
\[1 = \frac{R \times 5}{100}\]Multiply both sides by 100:
\[100 = R \times 5\]Divide by 5:
\[R = \frac{100}{5}\] \[R = 20\]So, the rate of interest is 20% per year.
Correct Option: B) 20%
Simplify:
144 ÷ [\( \frac{8}{4} \) × {7 + 7 − (5 + 8 − (9 + 2))}]
To simplify the given expression, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS (Brackets/Parentheses, Orders/Exponents, Division/Multiplication, Addition/Subtraction). We will start from the innermost brackets and work our way outwards.
First, let's write down the given expression:
\[ 144 \div \left[ \frac{8}{4} \times \left\{ 7 + 7 - (5 + 8 - (9 + 2)) \right\} \right] \]Start with the innermost parenthesis: \((9 + 2)\)
\[ 9 + 2 = 11 \]Substitute this back into the expression:
\[ 144 \div \left[ \frac{8}{4} \times \left\{ 7 + 7 - (5 + 8 - 11) \right\} \right] \]Next, evaluate the parenthesis \((5 + 8 - 11)\):
\[ 5 + 8 - 11 = 13 - 11 = 2 \]Substitute this back into the expression:
\[ 144 \div \left[ \frac{8}{4} \times \left\{ 7 + 7 - 2 \right\} \right] \]Now, evaluate the curly braces \(\{7 + 7 - 2\}\):
\[ 7 + 7 - 2 = 14 - 2 = 12 \]Substitute this back into the expression:
\[ 144 \div \left[ \frac{8}{4} \times 12 \right] \]Next, evaluate the fraction inside the square bracket: \(\frac{8}{4}\)
\[ \frac{8}{4} = 2 \]Substitute this back into the expression:
\[ 144 \div [2 \times 12] \]Evaluate the multiplication inside the square bracket:
\[ 2 \times 12 = 24 \]Finally, perform the division:
\[ 144 \div 24 = 6 \]C) The simplified value of the expression is 6.
The problem presents a series of three-letter codes. We need to identify the pattern in the letters based on their positions in the English alphabet and apply this pattern to find the missing term.
A) IAS — This option correctly follows the established pattern of adding 4 to the alphabetical position of each letter in the sequence.
This is a logical reasoning problem involving scheduling. We need to deduce the exam schedule for each person based on the given clues and then determine the number of people between S and Q.
Correct Option: D) Three
The question asks to classify irrigation projects based on their Cultivable Command Area (CCA) in India. Understanding the standard classification criteria for irrigation projects is key to answering this question.
Correct Option: D) Major Projects — Irrigation projects with a Cultivable Command Area (CCA) of more than 10,000 hectares are officially classified as Major Projects in India.
The problem requires us to apply specific letter transformation rules to a given set of words and then count how many of the resulting letter clusters contain no vowels. The rules are:
We need to process each word individually and then check the transformed word for vowels.
Let's apply these steps to each word:
From the analysis, the clusters "JBF" and "MPS" do not contain any vowels.
Therefore, there are two such letter clusters.
A) Two — As calculated, the words ICE and NOT transform into JBF and MPS respectively, neither of which contains any vowels. Thus, there are two such clusters.
The length of a vertical rod and its shadow are in the ratio of 2 : \(\sqrt{12}\). Find the angle of elevation of the sun.
This problem involves trigonometry, specifically the tangent function, which relates the angle of elevation to the ratio of the opposite side (height of the rod) to the adjacent side (length of the shadow) in a right-angled triangle.
Correct Option: D) 30°
The problem requires us to identify the highest and lowest numbers from a given set of three-digit numbers, then extract specific digits from them, and finally perform a subtraction operation as specified.
Correct Option: D) −7 is the correct resultant when the third digit of the highest number (9) is subtracted from the first digit of the lowest number (2).