To find Tanya's original salary, we need to understand that her enhanced salary is her original salary plus a 15% increment. We can set up an equation where the original salary is represented by a variable, and then solve for it.
Let Tanya's original salary be \(S\).
The increment is 15% of her original salary, which can be written as \(0.15 \times S\).
Her enhanced salary is her original salary plus the increment:
\[ \text{Enhanced Salary} = \text{Original Salary} + \text{Increment} \] \[ 14,030 = S + 0.15S \]Combine the terms involving \(S\):
\[ 14,030 = (1 + 0.15)S \] \[ 14,030 = 1.15S \]To find \(S\), divide the enhanced salary by 1.15:
\[ S = \frac{14,030}{1.15} \]Perform the division:
\[ S = 12,200 \]So, Tanya's original salary was ₹12,200.
Correct Option: C) ₹12,200
This is a blood relations question. We need to deduce the relationship between Mr. X and Ms. Y based on the given information. We will break down the statements to identify the family members and their connections.
Correct Option: C) Father
This problem involves calculating the time taken to cover a certain distance at different speeds and then determining the required speed to reach on time. We will use the formula \(\text{Distance} = \text{Speed} \times \text{Time}\) and set up equations based on the given conditions to find the distance and the correct time.
Let the distance to the station be \(D\) km. Let the correct time to reach the station be \(T\) hours.
Condition 1: Man travels at 4 kmph and misses the train by 1 hour.
The time taken is \(\frac{D}{4}\) hours. Since he misses the train by 1 hour, this time is 1 hour more than the correct time \(T\).
\[ \frac{D}{4} = T + 1 \quad \text{(Equation 1)} \]Condition 2: Man increases speed to 5 kmph and misses the train by 24 minutes.
First, convert 24 minutes to hours:
\[ 24 \text{ minutes} = \frac{24}{60} \text{ hours} = \frac{2}{5} \text{ hours} \]The time taken is \(\frac{D}{5}\) hours. Since he still misses the train by 24 minutes, this time is \(\frac{2}{5}\) hours more than the correct time \(T\).
\[ \frac{D}{5} = T + \frac{2}{5} \quad \text{(Equation 2)} \]Now we have a system of two linear equations with two variables \(D\) and \(T\). We can solve for \(D\) and \(T\).
From Equation 1, we can express \(T\) as:
\[ T = \frac{D}{4} - 1 \]Substitute this expression for \(T\) into Equation 2:
\[ \frac{D}{5} = \left(\frac{D}{4} - 1\right) + \frac{2}{5} \]\[ \frac{D}{5} = \frac{D}{4} - 1 + \frac{2}{5} \]Rearrange the terms to solve for \(D\):
\[ \frac{D}{4} - \frac{D}{5} = 1 - \frac{2}{5} \]\[ \frac{5D - 4D}{20} = \frac{5 - 2}{5} \]\[ \frac{D}{20} = \frac{3}{5} \]\[ D = \frac{3}{5} \times 20 \]\[ D = 3 \times 4 \]\[ D = 12 \text{ km} \]Now that we have the distance \(D = 12\) km, we can find the correct time \(T\) using Equation 1:
\[ T = \frac{D}{4} - 1 \]\[ T = \frac{12}{4} - 1 \]\[ T = 3 - 1 \]\[ T = 2 \text{ hours} \]Finally, we need to find the speed at which he should have travelled to reach the station exactly on time. Let this speed be \(S\) kmph.
Using the formula \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\):
\[ S = \frac{D}{T} \]\[ S = \frac{12 \text{ km}}{2 \text{ hours}} \]\[ S = 6 \text{ kmph} \]Correct Option: D) 6 kmph
To determine the face value of 'x' in the number x4562, we will use the divisibility rule for 9. A number is divisible by 9 if the sum of its digits is divisible by 9.
Identify the given number: The number is x4562.
Apply the divisibility rule for 9: According to the rule, if a number is divisible by 9, then the sum of its digits must be divisible by 9.
Calculate the sum of the digits: The digits are x, 4, 5, 6, and 2.
Sum of digits \( = x + 4 + 5 + 6 + 2 \)
Sum of digits \( = x + 17 \)
Find the possible value(s) of x: For the number to be divisible by 9, \( (x + 17) \) must be a multiple of 9.
Since 'x' is a single digit (it's the first digit of a number, so it cannot be 0, but in this context, it's a placeholder for a digit, so it can be 0-9; however, as the leading digit, it's usually 1-9. Let's consider the smallest multiple of 9 greater than 17).
The multiples of 9 are 9, 18, 27, 36, ...
Therefore, the only possible single-digit value for 'x' that makes the sum divisible by 9 is 1.
Determine the face value of x: The face value of x is 1.
D) 1 — The sum of the digits \( x + 4 + 5 + 6 + 2 = x + 17 \). For this sum to be divisible by 9, \( x + 17 \) must be a multiple of 9. The smallest multiple of 9 greater than 17 is 18. So, \( x + 17 = 18 \), which gives \( x = 1 \). This is a valid single digit.
The question asks to identify the Indian-origin administrator of the Center for Medicare & Medicaid Services (CMS) in the USA under the Trump administration, specifically as of 2018. This requires knowledge of key appointments in the US federal government during that period.
Correct Option: A) Seema Verma was indeed the administrator of the Centers for Medicare & Medicaid Services (CMS) under President Donald Trump. She was nominated by Trump in November 2016 and confirmed by the Senate in March 2017, serving until January 2021. Her role as an Indian-American in a high-profile federal agency during the Trump regime makes her the correct answer for the period mentioned (2018).
To determine which metal displaces iron from iron chloride, we need to refer to the reactivity series of metals. A more reactive metal can displace a less reactive metal from its salt solution.
\[ \text{Zn(s)} + \text{FeCl}_2\text{(aq)} \rightarrow \text{ZnCl}_2\text{(aq)} + \text{Fe(s)} \]
A) Zinc is more reactive than iron. Thus, it can displace iron from iron chloride solution.
To find the square root of 5184, we can use either the prime factorization method or the long division method. Alternatively, since options are provided, we can test each option by squaring it and checking if it equals 5184. We can also use the unit digit to narrow down the options.
B) 72 — As calculated, \(72 \times 72 = 5184\).
This question tests knowledge about the persistence of hearing, a physiological phenomenon related to how the human ear and brain process sound. The persistence of hearing refers to the duration for which the sensation of a sound remains in our brain after the sound stimulus has ceased.
Correct Option: B) 0.1 sec
The question asks to identify the Chairman of Tata Sons as of February 2018, who previously served as the CEO of Tata Consultancy Services (TCS). This requires knowledge of prominent business leaders and their roles within major Indian conglomerates.
Correct Option: A) N Chandrasekaran
N Chandrasekaran was appointed Chairman of Tata Sons in January 2017 and assumed office in February 2017. Prior to this, he was the Chief Executive Officer (CEO) and Managing Director of Tata Consultancy Services (TCS) from 2009. This perfectly matches the description in the question.
15 small rods, each of length 23 \( \frac{2}{7} \) m are joined to make a big rod. What then is the length of the big rod?
349 \( \frac{1}{7} \) m
349 \( \frac{5}{7} \) m
349 \( \frac{2}{7} \) m
349 \( \frac{3}{7} \) m
To find the total length of the big rod, we need to multiply the number of small rods by the length of each small rod. The length of each small rod is given as a mixed fraction, which should first be converted into an improper fraction for easier calculation.
The length of one small rod is given as \(23 \frac{2}{7}\) m.
\[ 23 \frac{2}{7} = \frac{(23 \times 7) + 2}{7} = \frac{161 + 2}{7} = \frac{163}{7} \text{ m} \]There are 15 small rods. To find the total length, multiply the number of rods by the length of one rod.
\[ \text{Total length} = 15 \times \frac{163}{7} \]\[ \text{Total length} = \frac{15 \times 163}{7} \]\[ \text{Total length} = \frac{2445}{7} \text{ m} \]To express the total length in the format of the options, divide 2445 by 7.
\[ 2445 \div 7 \]\[ 2445 = 7 \times 349 + 2 \]\[ \text{Total length} = 349 \frac{2}{7} \text{ m} \]C) The calculated total length is \(349 \frac{2}{7}\) m, which matches option C.