Explanation : 
Let’s break down the given information and solve the problem step by step:

The man started from home at 14:30 hours and arrived at the village when the village clock indicated 15:15 hours.

He stayed in the village for 25 minutes.
He drove back home by a different route, which was 1.25 times the first route, and at a rate twice as fast as the first route.
He reached home at 16:00 hours.
First, we need to calculate the time taken for each part of the trip:

Total time taken by the man to come back home: 16:00 – 14:30 = 1.5 hours = 90 minutes
Out of which he stayed in the village for 25 minutes.
So, his total traveling time = 90 – 25 = 65 minutes

Let’s denote the time taken for the first route as 100 units. Since the return route was 1.25 times the initial route, the time taken would have increased by 25%. So, the time taken for the second route would be 125 units.

But it is also given that while returning he drove twice as fast, which means the time taken must have been halved. So, the time taken while returning is 62.5 units.

Therefore, the total traveling time can be represented as:

100 units (first route) + 62.5 units (second route) = 65 minutes
162.5 units = 65 minutes

Now, we can find out the actual time taken for the first route:
100 units = (65/162.5) × 100 = 40 minutes

So, the man took 40 minutes to reach the village. The actual time at that moment was:
14:30 (start time) + 40 minutes (travel time) = 15:10 hours
Comparing the village clock with the actual time:
15:15 (village clock) – 15:10 (actual time) = 5 minutes

Hence, the village clock is 5 minutes fast. The correct answer is: d. 5 minutes fast

Explanation : 
Statement 1: A 20 × 8 sheet can be precisely divided into four square sheets, including two 4×4 squares and two 8×8 squares.

Statement 2: A 20 × 8 sheet can be segmented into 10 triangular sheets, each with an equal area of 16 square units.

Therefore, the correct answer is option (3), which states that both statements 1 and 2 are accurate.

Explanation : 

24 men and 12 women

The answer to this question is d. Data is inadequate to draw any conclusion.

This is because the information given in the question does not specify whether men and women have the same efficiency in doing the work or if their efficiencies are different. Without this information, it’s not possible to determine how long it would take for 12 men and 24 women to do the same piece of work.

Explanation : 

To determine which lecture is in the third period, we will analyze the given statements:

Statement-1: Lecture F is preceded by A and followed by C.
From this statement, we know the order of three lectures: A -> F -> C. However, it does not provide any information about the exact time or period of these lectures, so we cannot determine which lecture is in the third period using this statement alone.

Statement-2: There is no lecture after lecture B.
This statement tells us that lecture B is the last lecture, scheduled at 1:00 p.m. However, it does not provide any information about the other lectures, so we cannot determine which lecture is in the third period using this statement alone.

Now, let’s see if we can answer the question by combining both statements:

From Statement-1, we know that A -> F -> C is a sequence of lectures. And from Statement-2, we know that B is the last lecture. So, we can create two possible scenarios:

Scenario 1:
A -> F -> C -> D -> E -> B

Scenario 2:
D -> A -> F -> C -> E -> B

In both scenarios, we cannot determine which lecture is in the third period, as it can be either C (Scenario 1) or F (Scenario 2). Even E position is also not fixed.

Thus, the correct answer is d. Both Statement-1 and Statement-2 are not sufficient to answer the question.

Explanation : 

To determine the age of Manisha, we need to analyze both statements together.

Statement-1: Manisha is 24 years younger than her mother.
Let Manisha’s age be M and her mother’s age be X. So, X = M + 24.

Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3:5.
In 5 years, Manisha’s age will be M + 5 and her mother’s age will be X + 5. The ratio of their ages at that time will be 3:5.
(M + 5) / (X + 5) = 3 / 5

Now, we have two equations with two variables:

X = M + 24
(M + 5) / (X + 5) = 3 / 5
Substitute the value of X from the first equation into the second equation:
(M + 5) / (M + 24 + 5) = 3 / 5

Solve for M:
5(M + 5) = 3(M + 29)
5M + 25 = 3M + 87
2M = 62
M = 31

Manisha’s age is 31. Therefore, both Statement-1 and Statement-2 are sufficient to answer the question. The correct answer is:

c. Both Statement-1 and Statement-2 are sufficient to answer the Question

Explanation : 
Q1: Correct Answer – a.    1 and 2 only
Explanation – The correct answer is a. 1 and 2 only. The unsustainability in production pattern is due to heavy dependence on fossil fuels and limited availability of resources. Expansion of recycling is a measure taken by some developed countries to alleviate the worst effects of unsustainable production patterns, but it is not a cause of unsustainability in production patterns.

Q2: Correct Answer – d.   1, 2 and 3
Explanation – The correct answer is d. 1, 2 and 3. All three statements are correct ways in which developed countries can support developing countries’ transition to sustainable human development. Developed countries can make clean energy sources available at low cost, provide loans for improving public transport at nominal interest rates and encourage developing countries to change their production and consumption patterns.

Explanation : 
Q1: Correct Answer – d.   It is based on the proposition of poverty as meagre income or buying capacity.

Explanation – The methodology adopted in India to count the “poor” is debatable because it exclusively relies on the notion of poverty as insufficient income or insufficient purchasing power. This can be better categorized as income poverty [d].
The passage does not provide information about options a, b and c. However, it is possible that there may be confusion regarding what should constitute the ‘poverty line’ [a], wide diversities in the condition of the rural and urban poor [b], and no uniform global standard for measuring income poverty [c]. These factors could also contribute to making the methodology adopted in India to count the “poor” debatable.

Q2: Correct Answer – c.    there are no evidences to refute it

Explanation – Income poverty is only one measure of counting the ‘poor’ because it only talks about one kind of deprivation while ignoring all others. Poverty ultimately affects human well-being and if it’s about deprivations affecting human well-being, then income poverty is only one aspect of it [a].
The passage does not provide information about options b, c and d. However, it is possible that other deprivations in a human life may have nothing to do with lack of purchasing power [b], income poverty may not be a permanent condition and could change from time to time [c], and income poverty may restrict human choices only at a point of time [d]. These factors could also contribute to making income poverty only one measure of counting the ‘poor’.

Q3: Correct Answer – a.    1 only

Explanation – By “poverty of a life,” the author means all deprivations in a human life which stem not only from lack of income but also from lack of real opportunities given by social constraints as well as personal circumstances—to choose other types of living [a].
The passage does not provide information about options b, c and d. However, it is possible that poverty of a life could also refer to the impoverished state of poor people in rural and urban areas [b], missed opportunities in diverse personal circumstances [c], and material as well as non-material deprivations in a human life which restrict human choices permanently [d].

Explanation : 
Q1: Correct Answer – b.   Politicians should be selected from those trained in administration.

Explanation – The author of the passage is making a comparison between how we approach selecting someone for a specific task in our personal lives versus how we approach selecting someone to administer a state. The author argues that just as we look for specific qualifications and expertise when choosing a physician or a shoemaker, we should also look for the same when choosing someone to administer a state. The statement that best reflects the message of the author is (b) Politicians should be selected from those trained in administration.

Explanation : 
Q1: Correct Answer – d.   Water management practices in India need to change dramatically in the coining years.
Explanation – The passage discusses the increase in the number of Indian middle-class families and how this has led to changes in dietary patterns and energy consumption levels. The passage mentions that people have moved to a higher protein-based diet and that the use of electronic machines and motor vehicles has increased. Both of these changes require more water for production. Based on this information, it seems that option d – “Water management practices in India need to change dramatically in the coming years” – best reflects the crux of the passage.

Explanation : 

There are two containers X and Y

X contains 100 ml of milk. Y containes 100 ml of water.
20 ml of milk from X is transferred to Y.
Now, we get,
X → Milk = 80 ml
Y → Milk = 20 ml and Water = 100 ml
Total mixture in Y is 120 ml in which ratio of Milk and Water is 1 :5 respectively.

After that 20 ml of the mixture of Y is transferred to X,

Mixture to be transferred from Y = Y → Milk = 20/6, Water = (20/6) × 5 = 100/6
Remaining mixture in Y = Y → Milk = 20 – (20/6) = 100/6, Water = 100 – (100/6) = 500/6

New Mixture in X = X → Milk = 80 + (20/6) = 500/6, Water = 100/6

It is given that m denotes the proportion of milk in X i.e. 500/6
It is given that n denotes the proportion of water in Y i.e. 500/6

It means m = n.