Logical Deduction

As per the question,

Hence, option (a) is the correct answer.

As per the statement,

Conclusions I. (O) II. (P) III. (P)

Hence, option (c) is the correct answer.

According to the question,

Hence, 'Tinu' is sitting immediate right of 'Vineet'.

According to the statement,

Conclusions I. $ x \quad $ II. $ \checkmark $

Hence, the only Conclusion II follows.

Let's analyze the statement and the conclusions step by step.

Statement:

$\text{“The team manager humiliated Satish in front of his colleagues on a Monday Morning.”}$

Conclusion I:

$\text{“The team manager did not like Satish.”}$

Conclusion II:

$\text{“Satish was not as popular as his other colleagues.”}$

Key Points:

The statement tells us that the manager humiliated Satish publicly.

It does not provide information about the manager's personal feelings toward Satish.

It also does not offer any details about Satish’s popularity compared to his colleagues.

Analysis:

For Conclusion I:

The humiliation could be due to reasons like correcting behavior, maintaining discipline, or even a lapse in judgment.

The statement does not explicitly indicate that the manager "did not like" Satish.

Thus, we cannot conclude that personal dislike is necessarily the reason behind the action.

For Conclusion II:

The statement is silent about Satish’s standing among his colleagues.

Lack of popularity is not mentioned or implied by the fact that he was humiliated.

Therefore, this conclusion also does not follow with certainty.

Since neither conclusion is directly supported by the information given in the statement, the correct answer is:

Option D: Neither conclusion I nor II is true.

Let's denote Bishnu's current age by $B$ and Anil's current age by $A$.

We are given:

The product of their ages is 240:

$A \times B = 240.$

Twice Bishnu's age is 4 years more than Anil's age:

$2B = A + 4.$

Step 1: Express Anil's age in terms of Bishnu's age.

From the second equation,

$A = 2B - 4.$

Step 2: Substitute this expression into the product equation.

Replacing $A$ in $A \times B = 240$ gives:

$ (2B - 4) \times B = 240. $

Step 3: Simplify and solve for $B$.

Multiply out the left side:

$2B^2 - 4B = 240.$

Divide the entire equation by 2:

$B^2 - 2B = 120.$

Rearrange it into standard quadratic form:

$B^2 - 2B - 120 = 0.$

Step 4: Factor the quadratic equation.

We need two numbers that multiply to $-120$ and add to $-2.$ These numbers are $-12$ and $10.$ Hence, we factor:

$(B - 12)(B + 10) = 0.$

Step 5: Solve for $B$.

Set each factor equal to zero:

$B - 12 = 0 \quad \Rightarrow \quad B = 12,$

$B + 10 = 0 \quad \Rightarrow \quad B = -10.$

Since age cannot be negative, we discard $B = -10$ and accept $B = 12.$

Step 6: Find Bishnu's age 2 years ago.

Bishnu's age 2 years ago is:

$12 - 2 = 10.$

Thus, Bishnu's age 2 years ago was 10 years.

The correct answer is Option A: 10 year.

Let's analyze the given information step by step to determine the ages of P, Q, R, S, and T relative to each other:

1. $\mathrm{T}$ is older than $\mathrm{P}$.

This means $\mathrm{T} > \mathrm{P}$.

2. $\mathrm{Q}$ is younger than $\mathrm{T}$.

This means $\mathrm{T} > \mathrm{Q}$.

3. $\mathrm{S}$ is older than $\mathrm{R}$.

This means $\mathrm{S} > \mathrm{R}$.

4. $\mathrm{P}$ is older than $\mathrm{S}$ but younger than $\mathrm{Q}$.

This means $\mathrm{Q} > \mathrm{P} > \mathrm{S}$.

Now let's combine these relationships to form an order:

From (1) and (2), we have: $\mathrm{T} > \mathrm{Q}$.

From (4), we have: $\mathrm{Q} > \mathrm{P} > \mathrm{S}$.

From (3), we have: $\mathrm{S} > \mathrm{R}$.

Combining all the information, we get:

$\mathrm{T} > \mathrm{Q} > \mathrm{P} > \mathrm{S} > \mathrm{R}$.

Therefore, the oldest among all is T.

Correct Answer: Option B - T

To analyze whether the given conclusions follow from the statement, let's carefully examine the statement and each conclusion individually.

Statement: In a one-day cricket match, the total runs made by a team were 200. Out of these, 160 runs were made by spinners.

Conclusion I: $80 \%$ of the team consists of spinners.

This conclusion points out a percentage related to the team composition. However, the statement only talks about the runs made by spinners and does not provide any direct information about what percentage of the team members are spinners. Therefore, we cannot conclusively determine the team composition based only on the runs scored.

Conclusion II: The opening batsmen were spinners.

This conclusion assumes that the opening batsmen were spinners based on the runs scored. The statement, however, does not provide any information about who were the opening batsmen - it only mentions the total and specific runs scored by spinners. Therefore, this conclusion cannot be definitively drawn from the given statement.

We see that neither conclusion I nor conclusion II can be conclusively derived from the given statement.

Answer: Option C: Neither I nor II follows.

To determine which conclusions definitely follow from the given statement, let's analyze each conclusion in detail.

Statement: The old order changed yielding place to new

This statement implies that there is a process where old systems or ideas are being replaced by new ones.

Conclusion I: Change is the law of nature.

This conclusion is a broad generalization stating that change is a fundamental principle of the natural order. The statement supports this idea by illustrating an example of change (the old order making way for new). Thus, Conclusion I follows from the statement.

Conclusion II: Discard old ideas because they are old.

This conclusion implies that ideas should be discarded merely because they are old. The statement does not provide sufficient information to support the notion that "old ideas should be discarded only due to their age." It merely indicates that the old order changes to make way for something new but does not necessarily suggest discarding ideas solely because of their age.

Based on this analysis, it is clear that:

Option A: Only Conclusion I follows.

Let's denote the amounts received by Rajesh, Vivek, and Kripal as $ R $, $ V $, and $ K $ respectively.

According to the problem, Rajesh gets double the amount that Vivek gets, so we have:

$ R = 2V $

Similarly, Kripal gets double the amount that Rajesh gets, so we have:

$ K = 2R $

The total amount to be divided is ₹ 5110. Therefore, we can write the equation:

$ R + V + K = 5110 $

Substitute $ R $ and $ K $ in terms of $ V $ from the above equations:

$ R = 2V $

$ K = 2R = 2(2V) = 4V $

Now substitute these into the total amount equation:

$ 2V + V + 4V = 5110 $

Simplify the equation:

$ 7V = 5110 $

Solve for $ V $:

$ V = \frac{5110}{7} = 730 $

Now, calculate the amounts received by Rajesh and Kripal:

$ R = 2V = 2 \times 730 = 1460 $

$ K = 4V = 4 \times 730 = 2920 $

So, the amount of money Kripal will get is ₹ 2920.

Therefore, the correct option is Option A: ₹ 2920.

According to the question,

Hence, A sits immediate left of E.

To determine who is the tallest among P, Q, T, A, and B, let's break down the given information step by step.

1. T is taller than P and B but shorter than A and Q.

This gives us the following relationships:

$ T > P $

$ T > B $

$ T < A $

$ T < Q $

2. P is not the shortest.

This indicates that there is at least one person shorter than P. Given that T is taller than P and that T is not the shortest either, B must be the shortest because T is also taller than B.

So now we have:

$ B < P $

$ B < T $

Since P is not the shortest and B is the only one left for the shortest position:

$ B < P $

Combining the given information, we can establish the following order from shortest to tallest:

$ B < P < T $

Next, we know that T is taller than P and B, but shorter than A and Q. Therefore, A and Q must be taller than T. The possible orders for A and Q relative to each other are:

Either:

$ A > Q > T > P > B $

or:

$ Q > A > T > P > B $

In either case, the tallest among them is either A or Q.

Therefore, the correct answer is:

Option C: A or Q