Unit6 - Subjective Questions

Difference between Simple Interest (SI) and Compound Interest (CI):

1. Basis of Calculation:

   • Simple Interest: Interest is calculated only on the original principal amount () throughout the loan period.
   • Compound Interest: Interest is calculated on the principal amount plus the accumulated interest from previous periods. It is "interest on interest".

2. Growth of Principal:

   • SI: The principal remains constant.
   • CI: The principal increases periodically as interest is added to it.

3. Magnitude:

   • For the first year (or first conversion period), SI and CI are equal. For subsequent years, CI is always greater than SI.

4. Formulas:

   • Simple Interest:
   • Compound Interest:

   Where = Principal, = Rate per annum, = Time in years.

Given:

• Principal () =
• Rate () =
• Time () = $2$ years

1. Calculate Simple Interest (SI):

2. Calculate Compound Interest (CI):

3. Difference:

Alternative Method (Short Trick for 2 years):

Answer: Rs. 50

Concept of Depreciation:
Depreciation refers to the decrease in the value of an asset (like machinery, vehicles, buildings, etc.) over time due to wear and tear, usage, or obsolescence. Unlike compound interest where value grows, depreciation works on the principle of compound decrease.

Formula:
If the present value of a machine is and it depreciates at a rate of per annum, then the value of the machine after years () is given by:

• : Original Value / Present Value
• : Rate of depreciation
• : Number of years
• : Depreciated Value (Scrap Value)

Given:

• Present Population () = $160,000$
• Growth Rate () = per annum
• Time () = $2$ years

Formula for Growth:

Calculation:

Answer: The population after 2 years will be 176,400.

Let the Principal be , Rate of Interest be per annum, and Time be $2$ years.

1. Simple Interest () for 2 years:

2. Compound Interest () for 2 years:

Using :

3. Difference () between and :

The term cancels out.

Conclusion: The formula for the difference for 2 years is .

Given:

• Initial Value () =
• Depreciation Rate () =
• Time () = $3$ years

Formula:

Calculation:

Answer: The value of the scooter after 3 years will be Rs. 29,160.

In analytical reasoning regarding blood relations, diagrams are essential. The standard conventions are:

1. Gender Representation:

   • Male: Represented by a Square ( ) or a Plus sign ( ).
   • Female: Represented by a Circle ( ) or a Minus sign ( ).

2. Relationships:

   • Married Couple (Spouse): Connected by a Double horizontal line ( ) or a double-headed arrow (). E.g., .
   • Siblings (Brother/Sister): Connected by a Single horizontal line ( ). E.g., .

3. Generations:

   • Generation Gap: Represented by a Vertical line ( ).
   • Parents are placed above the vertical line, and children are placed below it.

Example Structure:

• Father () --- Mother () (Double line)
• |
• Son () --- Daughter () (Single line)

Analysis:

1. Speaker: A man.
2. Constraint: "I have no brother or sister." -> This means the speaker is the only child of his parents.
3. Phrase breakdown: "...my father's son."
   • Since the speaker has no siblings, "my father's son" refers to the speaker himself.
4. Substitution: Replace "my father's son" with "me" (the speaker) in the original sentence.
   • Modified Sentence: "That man's father is me (the speaker)."

Deduction:
If the speaker is the father of the person in the photograph ("that man"), then the person in the photograph must be the speaker's son.

Answer: It was the photograph of his son.

Step-by-Step Movement:

1. Start Point (A): The man starts at A.
2. Move 1: Walks 5 km South to point B.
   • Current Position: South of Start.
3. Move 2: Turns Right from South. (Note: When facing South, a right turn is towards the West). Walks 3 km to point C.
   • Current Position: South-West of Start.
4. Move 3: Turns Left from West. (Note: When facing West, a left turn is towards the South). Walks 5 km to point D.

Final Analysis:

• The man is now significantly South of the starting point (5km + 5km = 10km South total).
• He is also West of the starting vertical line (3km West).
• Combining these vectors: He is in the South-West direction relative to the starting point.

Answer: South-West.

Given:

• years

Step 1: Find the Principal () using the CI formula.

Step 2: Calculate Simple Interest ().

Answer: The Simple Interest is Rs. 400.

Shadow Rules rely on the position of the sun relative to the cardinal directions.

1. At Sunrise (Morning):

• The Sun is in the East.
• Shadows fall towards the West.
• Rules:
  • If a person faces North, their shadow falls to their Left.
  • If a person faces South, their shadow falls to their Right.
  • If a person faces East, their shadow falls Behind them.
  • If a person faces West, their shadow falls in Front of them.

2. At Sunset (Evening):

• The Sun is in the West.
• Shadows fall towards the East.
• Rules:
  • If a person faces North, their shadow falls to their Right.
  • If a person faces South, their shadow falls to their Left.
  • If a person faces East, their shadow falls in Front of them.
  • If a person faces West, their shadow falls Behind them.

Note: At 12:00 Noon, the sun is vertically overhead, so there is no shadow (or it is vertically below the object).

Goal: Find the expression where C is the son of M.

• For C to be a son, C must be Male.
• M must be a parent (Mother or Father) of C.

Let's analyze standard patterns (assuming options were M - N x C + F or similar structure):
To show C is the son of M, the relationship chain must establish:

1. M is a parent.
2. C is the child.
3. C is male.

Example Construction:
Consider the expression: M N + C (Wait, this makes M father of N, N brother of C. So M is father of C. Is C male?)
In many coded inequality problems, the gender of the last person is often unknown unless defined by a spouse relation.

Let's construct the correct specific chain: or .

However, usually, the question is provided with options. Since this is subjective, let's create the valid expression.
We need: Parent of (Male).

Expression:

• : M is father of N.
• : N is sister of C. (So M is father of C).
• : C is brother of D. (This confirms C is Male).

Conclusion: In the expression , M is the father of N, N is the sister of C, so M is the father of C. Since C is the brother of D, C is a male. Thus, C is the son of M.

Concept: In Compound Interest, if a sum becomes times in years, it remains in a geometric progression.

Given:

• Sum becomes 2 times (Doubles) in 15 years.

Logic:

• Let Principal = .
• After 15 years Amount = .
• After next 15 years Amount = .
• After next 15 years Amount = .

Mathematical Approach:

Answer: It takes 45 years to become eight times itself.

Concept: Compound interest depends on the frequency at which the interest is added back to the principal.

1. Annually: Interest is calculated once a year. Rate = , Time = .
2. Half-yearly: Interest is calculated every 6 months (2 times a year). The rate is halved () and time periods double ().
3. Quarterly: Interest is calculated every 3 months (4 times a year). The rate is divided by 4 () and time periods quadruple ().

Effect:

• As the frequency of compounding increases, the interest is added to the principal more often.
• This leads to "interest on interest" being generated earlier and more frequently.
• Conclusion: For the same nominal rate and time period, Quarterly CI > Half-yearly CI > Annual CI. The Effective Annual Rate (EAR) increases with the frequency of compounding.

Visualizing the Path:

1. Start (Home - Origin): Let Home be at .
2. Move 1 (NW): She moves 30m North-West. Let's call this point A.
3. Move 2 (SW): From A, she moves 30m South-West. This is perpendicular to the first move (90 degrees left). She reaches point B.
   • Geometrically, she has moved Left relative to the previous path.
4. Move 3 (SE): From B, she moves 30m South-East. This is parallel to the first leg but in the opposite direction (or 90 degrees left from SW). She reaches point C.

Shape Analysis:

• The path forms three sides of a Rhombus (or Square, since angles are 90 degrees and sides are equal).
• Start NW SW SE.
• Point C is exactly North-East of the Home (Origin) if she were to close the loop, but actually, based on vector addition:
  • Vector 1 (NW) cancels partially with Vector 3 (SE). Actually, visually, she traces a square path.
  • Home A (NW)
  • A B (SW) (Left of NW is SW)
  • B C (SE) (Left of SW is SE)
  • C is located North-East of the Home.

Final Move:

• She turns towards her house.
• She is currently at C (North-East of Home).
• To go back to Home, she must travel in the opposite direction of where she is.
• Opposite of North-East is North-East.

Wait, let's re-verify: Start NW SW (Result is due West of start) SE (Result is South of West point).
Actually, simpler logic: The path is a square tilted by 45 degrees.
Move 1: NW. Move 2: SW. Move 3: SE.
The 4th closing side of the square would be North-East to return to start.

Answer: She is moving in the North-East direction.

Constructing the Family Tree:

1. Q is brother of R: Q (Male) -- R (Gender unknown).
2. P is sister of Q: P (Female) -- Q (Male) -- R. (P, Q, R are siblings).
3. S is daughter of R: R is the parent of S (Female).
4. T is brother of S: T (Male) -- S (Female). (T and S are children of R).

Analyzing Relationship with Q:

• Q is the brother of R.
• T and S are children of R.
• Therefore, Q is the Uncle of T and S.

Identifying Cousins:

• The question asks "Who are the cousins of Q?".
• Cousins belong to the same generation.
• We have info on P, Q, R (Siblings) and T, S (Nieces/Nephews).
• We do not have information about the children of P or Q, nor do we have information about the parents' siblings of Q.

Conclusion: Based strictly on the provided data, Q has no cousins mentioned in the group. T and S are his nephews/niece.

However, if the question meant "Who are the cousins of T?", the answer requires children of P or Q. If the question implies relationships:
Correction: Perhaps the question implies calculating the relationship of T and S.
Since the question asks "Who are the cousins of Q?", and no other family branches are defined, the answer is None or Data Inadequate.

(Standard interpretation in such exams: If no data exists, state relationships defined. Here, T and S are nephew/niece).

Detailed Answer: The data provided establishes Q as the uncle of T and S. No individuals in Q's generation (other than siblings P and R) are mentioned. Thus, no cousins can be identified.

Understanding the Directions:

1. North-East (NE): Located exactly between North () and East (). Angle = from North.
2. South-South-West (SSW): This is midway between South () and South-West ().
   • South is .
   • South-West is .
   • SSW = from North.

Calculating the Angle:

• Angle = Position of SSW - Position of NE
• Angle =
• Angle = .

Alternative Geometric Visualization:

• NE is clockwise from North.
• SW is directly opposite NE ( away).
• SSW is (half of $45$) counter-clockwise from South towards West.
• Angle NE to South = .
• South to SSW = .
• Total Angle = .

Answer: $157.5$ degrees.

Methodology: We must calculate interest for each year, deduct tax, and add the remaining interest to the principal for the next year.

Year 1:

• Tax = of
• Net Interest =
• Amount after Y1 () =

Year 2:

• Tax = of
• Net Interest =
• Amount after Y2 () =

Year 3:

• Tax = of
• Net Interest =
• Final Amount =

Answer: Rs. 5,624.32

Statement: "A's mother is the only daughter of B's father."

Breaking it down:

1. "B's father": The father of B.
2. "Only daughter of B's father":
   • B has a father.
   • Since B is specified as Male, B is the son.
   • The "only daughter" must be B's sister.
3. Substitution:
   • "A's mother is [B's sister]."

Relationship:

• Since B's sister is A's mother, B is the brother of A's mother.
• Mother's brother is called Maternal Uncle.

Answer: B is the Maternal Uncle of A (and A is the Nephew/Niece of B).

Coordinates Calculation (Start at 0,0):

1. East 10m:
2. Right Turn (South) 10m:
3. Left Turn (East) 10m:
4. Left Turn (North) 40m:

Final Coordinates:
Start Coordinates:

Shortest Distance (Hypotenuse):
Using Pythagoras Theorem ():

Answer: meters (approx 36.05m).