This problem involves the concept of boats and streams. We are given the speed of the boat in the direction of the stream (downstream) and against the direction of the stream (upstream). We need to find the speed of the current. We can use the standard formulas relating these speeds to the speed of the boat in still water and the speed of the current.
Let the speed of the boat in still water be \(V_b\) km/hr.
Let the speed of the current be \(V_c\) km/hr.
When the boat goes in the direction of the stream (downstream), the speeds add up. So, the downstream speed is given by:
\[ V_d = V_b + V_c \]From the problem, the boat goes 46 km/hr in the direction of the stream. So,
\[ V_b + V_c = 46 \quad \text{(Equation 1)} \]When the boat goes against the direction of the stream (upstream), the speed of the current opposes the boat's speed. So, the upstream speed is given by:
\[ V_u = V_b - V_c \]From the problem, the boat goes 36 km/hr against the direction of the stream. So,
\[ V_b - V_c = 36 \quad \text{(Equation 2)} \]We have a system of two linear equations:
Equation 1: \(V_b + V_c = 46\)
Equation 2: \(V_b - V_c = 36\)
To find the speed of the current (\(V_c\)), we can subtract Equation 2 from Equation 1:
\[ (V_b + V_c) - (V_b - V_c) = 46 - 36 \]\[ V_b + V_c - V_b + V_c = 10 \]\[ 2V_c = 10 \]Now, solve for \(V_c\):
\[ V_c = \frac{10}{2} \]\[ V_c = 5 \text{ km/hr} \]A) 5 km/hr is the correct speed of the current, as calculated by subtracting the upstream speed from the downstream speed and dividing by 2.
Pipe A can fill an empty cistern alone in 26 hours and pipe B can fill the same cistern alone in 36 hours. The time taken by them to fill half of the cistern by operating together will be:
15 \( \frac{17}{31} \) hours
11 \( \frac{17}{31} \) hours
7 \( \frac{17}{31} \) hours
16 \( \frac{17}{31} \) hours
To solve this problem, we first determine the individual work rates of Pipe A and Pipe B. Then, we find their combined work rate when operating together. Finally, we calculate the time taken to fill half of the cistern using their combined work rate.
Pipe A can fill the cistern in 26 hours. So, in 1 hour, Pipe A fills:
\[ \text{Work rate of A} = \frac{1}{26} \text{ of the cistern per hour} \]Pipe B can fill the cistern in 36 hours. So, in 1 hour, Pipe B fills:
\[ \text{Work rate of B} = \frac{1}{36} \text{ of the cistern per hour} \]When both pipes operate together, their work rates add up:
\[ \text{Combined work rate} = \text{Work rate of A} + \text{Work rate of B} \\ = \frac{1}{26} + \frac{1}{36} \]To add these fractions, find a common denominator, which is the Least Common Multiple (LCM) of 26 and 36. \(26 = 2 \times 13\) \(36 = 2^2 \times 3^2\) LCM(26, 36) = \(2^2 \times 3^2 \times 13 = 4 \times 9 \times 13 = 36 \times 13 = 468\).
\[ \text{Combined work rate} = \frac{1 \times 18}{26 \times 18} + \frac{1 \times 13}{36 \times 13} \\ = \frac{18}{468} + \frac{13}{468} \\ = \frac{18 + 13}{468} = \frac{31}{468} \text{ of the cistern per hour} \]If they fill \(\frac{31}{468}\) of the cistern in 1 hour, then the time taken to fill the entire cistern (1 unit) is the reciprocal of their combined work rate:
\[ \text{Time to fill full cistern} = \frac{1}{\text{Combined work rate}} = \frac{468}{31} \text{ hours} \]We need to find the time taken to fill half of the cistern, which is \(\frac{1}{2}\) of the total time:
\[ \text{Time to fill half cistern} = \frac{1}{2} \times \frac{468}{31} \\ = \frac{234}{31} \text{ hours} \]Divide 234 by 31:
\(234 \div 31\) \(31 \times 7 = 217\) \(234 - 217 = 17\)
So, \[\frac{234}{31} = 7 \frac{17}{31}\] hours.
Correct Option: C) 7 \( \frac{17}{31} \) hours
The question asks for the first experimental initiative that marked the beginning of India's Green Revolution. To answer this, recall the key programs launched in the early phases of agricultural development in India, particularly those focused on increasing food production.
A) Intensive Agricultural District Programme (IADP) was launched in 1960-61 and is widely recognized as the first major experimental initiative that paved the way for the Green Revolution in India. It focused on providing a comprehensive package of inputs and services to farmers in selected districts to boost agricultural production.
In this question, a group of number/symbol is coded using letter codes as per the codes given below and the conditions which follow. The correct combination of codes following the conditions is your answer.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Number/ symbol | 8 | 6 | * | % | 9 | & | 3 | + | @ | 5 | $ | 7 | 4 |
| Code | W | C | E | J | F | A | D | Q | G | P | R | B | U |
Conditions:
(I) If the first element is a number and the last a symbol, the codes for these two (the first and the last elements) are to be interchanged.
(II) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©.
(III) If the third element is a perfect cube, the second element is to be coded as the code for the third element.
What will %987 be coded as?
To solve this problem, we need to track Vinay's movements step-by-step on a 2D plane. We can represent his starting point as the origin (0,0) and then calculate his final position by adding and subtracting distances along the North-South and East-West axes. Once we have his final position (Point P), we can determine the shortest distance and direction required to return to Point A.
C) 4 km to the East. Based on our step-by-step tracking, Vinay ends up 4 km to the West of his starting point A. To return to A, he must travel 4 km in the East direction.
To find the mode of a dataset, we need to identify the value that appears most frequently. This involves counting the occurrences of each unique number in the given data.
A) 49 — The number 49 appears 4 times in the data, which is the highest frequency among all the numbers. Therefore, 49 is the mode.
The question asks about the types of cases that can be settled in a Lok Adalat. Lok Adalats are alternative dispute resolution mechanisms in India, designed to provide a speedy and amicable settlement of disputes. Understanding their jurisdiction is key to answering this question.
C) Compoundable offences. Lok Adalats are empowered to settle both civil and criminal cases, provided the criminal cases are compoundable under the law. This means that the offense can be compromised between the parties without the full trial process, leading to a quicker resolution.
The question asks to identify a position that is NOT universally found in every Gram Panchayat in India. This requires knowledge of the typical structure and functionaries of Gram Panchayats as mandated by the 73rd Constitutional Amendment Act and subsequent state legislations.
In a Gram Panchayat, there is no specific position of an "Elected Treasurer." Financial matters are typically handled by the Panchayat Secretary (a government-appointed official) in coordination with the Sarpanch and the Gram Panchayat members. While there are financial responsibilities, a separate, directly elected treasurer position is not a standard feature of the Gram Panchayat structure across all states in India.
To solve this series, we need to find the pattern in the differences between consecutive numbers. Often, in such series, the differences themselves form a recognizable pattern (e.g., arithmetic progression, geometric progression, or a series of squares/cubes).
The first differences are: 6, 9, 15, 24.
The second differences are: 3, 6, 9.
Thus, the missing number is 94.
Correct Option: A) 94
The question asks to identify the host country for the 2025 FIFA Club World Cup. This requires knowledge of recent FIFA announcements regarding major tournament venues.
Correct Option: C) United States