The problem asks us to identify the letter-cluster pair that does not follow the same pattern as the others. We need to find the relationship between the letters within each pair and between the two clusters in each option, based on their positions in the English alphabet.
Correct Option: A) HK - LP
In this option, the difference between H (8) and K (11) is \(11 - 8 = 3\). The difference between L (12) and P (16) is \(16 - 12 = 4\). This pattern (differences of 3 and 4 within clusters) is different from the other options where the difference within each cluster is 1.
Options B, C, and D follow a consistent pattern: both clusters consist of consecutive letters, and the second cluster starts 6 letters before the end of the first cluster. Option A does not follow this pattern.
This problem involves calculating the combined work rate of two pipes, one filling and one emptying. We will determine the individual rates of filling and emptying, then find the net rate when both operate simultaneously. Finally, we will use the net rate to find the total time required to fill the tank.
Correct Option: D) 20
The tank will be filled completely in 20 minutes when both pipes are operated together.
This problem involves substituting given symbols with mathematical operators and then evaluating the expression using the order of operations (BODMAS/PEMDAS).
The given expression is: \(1 \text{ P } 45 \text{ R } 2 \text{ Q } 2 \text{ S } 4 = ?\)
Given substitutions:
Substitute the symbols into the expression:
\[ 1 + 45 \div 2 \times 2 - 4 = ? \]Now, apply the BODMAS/PEMDAS rule:
Step 1: Division
\[ 45 \div 2 = 22.5 \]The expression becomes:
\[ 1 + 22.5 \times 2 - 4 \]Step 2: Multiplication
\[ 22.5 \times 2 = 45 \]The expression becomes:
\[ 1 + 45 - 4 \]Step 3: Addition
\[ 1 + 45 = 46 \]The expression becomes:
\[ 46 - 4 \]Step 4: Subtraction
\[ 46 - 4 = 42 \]Therefore, the value of the expression is 42.
B) 42 — After substituting the operators and following the order of operations (BODMAS/PEMDAS), the expression evaluates to 42.
The question asks for the Infant Mortality Rate (IMR) in India as per the Sample Registration System (SRS) report for the year 2019. This is a factual question requiring knowledge of specific demographic data released by government agencies.
C) 30 per 1000 live births — The Sample Registration System (SRS) 2019 report stated that the Infant Mortality Rate (IMR) in India was 30 per 1000 live births. This figure represents the number of infant deaths (children under one year of age) per 1000 live births.
To solve this problem, we need to find the combined ratio of x, y, and z from the given individual ratios. Once the combined ratio \(x : y : z\) is established, we can distribute the total amount of ₹15,120 according to this ratio.
Combine the ratios:
Given ratios are:
\[ x : y = 2 : 5 \]\[ y : z = 4 : 7 \]To combine these, we need to make the value of \(y\) common in both ratios. The least common multiple (LCM) of 5 and 4 (the values of \(y\)) is 20.
Now, we have a common value for \(y\), so we can write the combined ratio:
\[ x : y : z = 8 : 20 : 35 \]Calculate the sum of the ratio parts:
Sum of the ratio parts \( = 8 + 20 + 35 = 63 \)
Distribute the total amount:
The total amount to be distributed is ₹15,120.
So, the amounts received by x, y, and z are ₹1,920, ₹4,800, and ₹8,400, respectively.
Correct Option: D) 1,920, 4,800 and 8,400
The problem states that Manjit spends 40% of his income and saves ₹18,000. We need to find his total income. We can determine the percentage of income saved and then use this percentage along with the saved amount to calculate the total income.
Let Manjit's total income be \(I\). We can represent the total income as 100%.
Manjit spends 40% of his income. Therefore, the percentage of income he saves is:
\[ \text{Percentage of Savings} = 100\% - \text{Percentage of Spending} \]\[ \text{Percentage of Savings} = 100\% - 40\% = 60\% \]We are given that his savings amount to ₹18,000. This means that 60% of his total income is equal to ₹18,000.
\[ 60\% \text{ of } I = \text{₹}18,000 \]To find the total income \(I\), we can set up the equation:
\[ 0.60 \times I = 18,000 \]Now, solve for \(I\):
\[ I = \frac{18,000}{0.60} \]\[ I = \frac{18,000}{\frac{60}{100}} \]\[ I = \frac{18,000 \times 100}{60} \]\[ I = \frac{1,800,000}{60} \]\[ I = 30,000 \]Thus, Manjit's total income is ₹30,000.
B) 30,000
The problem requires us to modify a given number based on specific rules for its even and odd digits, and then count how many digits appear more than once in the newly formed number.
Correct Option: C) Two
The digits 4 and 8 appear more than once in the new number 8046824. Therefore, two digits appear more than once.
The problem presents an analogy between letter-clusters. We need to find the pattern or relationship between the letters in the given pair (LPR) and apply the same logic to find the missing clusters (# and %). This involves analyzing the positional values of the letters in the English alphabet.
A) # = HNT, % = TUT. This option correctly identifies both missing letter-clusters based on the derived pattern of (+4, +2, -2) between the corresponding letters of the pairs.
The problem presents an analogy between letter-clusters. We need to identify the pattern or relationship between the letters in the given pair (RWX : %) and apply the same logic to find the missing cluster (# : AND). This typically involves analyzing the alphabetical positions of the letters or specific transformations like skipping letters.
C) # = XQB, % = UTZ
As derived in the step-by-step explanation, if we assume the pattern is a letter-wise transformation from the first cluster to the second cluster, then for XQB \(\to\) AND, the shifts are \((+3, -3, +2)\). Applying this same pattern to RWX gives:
Thus, RWX \(\to\) UTZ. This confirms that # = XQB and % = UTZ is the correct pair.