This problem involves work and time concepts. We are given the combined filling rate of three flood gates and then how the work progresses when one gate is closed. We need to find the time taken by one specific gate to fill the reservoir alone. We will use the concept that if a gate fills a reservoir in 't' hours, its one-hour work is \(1/t\) of the reservoir.
Let the rates at which flood gates A, B, and C fill the reservoir be \(r_A\), \(r_B\), and \(r_C\) respectively (fraction of reservoir filled per hour).
Given that A, B, and C together can fill the reservoir in 6 hours. So, their combined one-hour work rate is:
\[ r_A + r_B + r_C = \frac{1}{6} \]All three gates work together for 2 hours. The amount of reservoir filled in these 2 hours is:
\[ \text{Work done in 2 hours} = 2 \times (r_A + r_B + r_C) = 2 \times \frac{1}{6} = \frac{1}{3} \]After 2 hours, flood gate C is closed. The remaining part of the reservoir to be filled is:
\[ \text{Remaining work} = 1 - \frac{1}{3} = \frac{2}{3} \]Flood gates A and B fill this remaining \(2/3\) part in 7 hours. So, their combined one-hour work rate is:
\[ r_A + r_B = \frac{\text{Remaining work}}{\text{Time taken}} = \frac{2/3}{7} = \frac{2}{21} \]Now we have two equations:
Substitute the value of \(r_A + r_B\) from equation (b) into equation (a) to find \(r_C\):
\[ \frac{2}{21} + r_C = \frac{1}{6} \]\[ r_C = \frac{1}{6} - \frac{2}{21} \]To subtract the fractions, find a common denominator, which is 42:
\[ r_C = \frac{7}{42} - \frac{4}{42} \]\[ r_C = \frac{3}{42} = \frac{1}{14} \]The rate of flood gate C alone is \(1/14\) of the reservoir per hour. Therefore, the number of hours taken by flood gate C alone to fill the reservoir is the reciprocal of its rate:
\[ \text{Time for C alone} = \frac{1}{r_C} = \frac{1}{1/14} = 14 \text{ hours} \]Correct Option: C) 14
The question asks to identify the Indian cueist who won the 2017 IBSF World Billiards Championship held in Doha. This is a factual question related to sports achievements, requiring knowledge of prominent Indian athletes and their victories.
Correct Option: D) Pankaj Advani is the correct answer. He is a celebrated Indian cueist who has won multiple world championships in both billiards and snooker, including the 2017 IBSF World Billiards Championship in Doha.
The question asks to identify the Chef de Mission of the Indian contingent for the Asian Games 2018. This is a factual question related to sports administration and current affairs at the time of the event. Recalling key appointments for major sporting events is crucial for competitive exams.
Correct Option: C) Brij Bhushan Sharan Singh was appointed as the Chef de Mission of the Indian contingent for the Asian Games 2018.
The question asks about the function of an odometer. We need to identify which physical quantity an odometer is designed to measure.
Correct Option: B) Distance
What is the horizontal mirror image of REST?
To find the horizontal mirror image of the word "REST," we need to visualize how each letter would appear if reflected across a vertical axis.
Looking at the options, Option D matches this transformation.
Correct Option: D) ê€ÆSâŽ
Choose the mirror image for the following figure when the mirror is kept at the MN line.
To find the mirror image of a figure, we need to reflect the elements across the given mirror line. In this case, the mirror is placed along the MN line. The mirror image will have the same shapes and sizes, but their orientation will be reversed horizontally.
After reflecting, the correct orientation matches option B.
Correct Option: B) The mirror image correctly reflects the elements across the MN line.
Find the odd man out:
The task is to identify the figure that does not follow the pattern seen in the other options. We need to analyze the shapes and their properties in each diagram.
Correct Option: B) Option B stands out as the odd one because it has a polygon inside another polygon, unlike the others.
The question asks to identify the enzyme whose action is facilitated by hydrochloric acid (HCl) secreted by the gastric glands. This relates to the process of digestion in the stomach.
D) Pepsin. Hydrochloric acid activates pepsinogen into pepsin, which then begins the digestion of proteins in the stomach.
If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘÷’ means ‘+’ and ‘×’ means ‘÷’, then what is the value of 23 − 4 + 15 × 3 ÷ 10?
This problem involves substituting new meanings for mathematical operators and then evaluating the expression according to the order of operations (BODMAS/PEMDAS).
The original expression is: \(23 - 4 + 15 \times 3 \div 10\)
Applying the changes:
So, the new expression is: \(23 \times 4 - 15 \div 3 + 10\)
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Operations are performed from left to right for Division/Multiplication and Addition/Subtraction.
C) 97 is the correct value of the expression after applying the given operator changes and following the order of operations.
The problem involves decoding a pattern based on a given example. We need to identify the rule used to convert letters into numbers for the word "TEEN" and then apply the same rule to find the code for "ENTER". This is a common type of coding-decoding question where each letter is assigned a numerical value, usually its position in the English alphabet.
The word is TEEN, and its code is 205514.
Comparing the letters with their numerical values, we can see that each letter is represented by its alphabetical position:
So, the rule is to replace each letter with its corresponding position in the English alphabet.
Putting these numbers together in sequence gives the code for ENTER:
5 (for E) + 14 (for N) + 20 (for T) + 5 (for E) + 18 (for R) = 51420518.
Correct Option: A) 51420518