5.4 Blood Relations & Direction Sense

Blood Relations & Direction Sense

Blood Relations and Direction Sense test spatial reasoning, logical mapping, and strict constraint adherence. In SBI PO Prelims, these topics appear as 3-question standalone sets. In Mains, they are combined with seating arrangements or presented as complex coded puzzles. Mastering standardized notation prevents errors under time pressure.

---

Blood Relations: Family Tree Standard Notations

To eliminate ambiguity, construct family tree diagrams using these universal notations:

• Male: Represented by a Square or Plus sign $\square$ / $[+]$.
• Female: Represented by a Circle or Minus sign $\bigcirc$ / $[-]$.
• Married Couple (Spouse): Connected by a double horizontal line ($=$).
• Siblings: Connected by a single horizontal line ($-$).
• Parent-Child Relationship: Connected by a vertical line (|), where parents are placed in the upper generation.

       [ Grandfather (+) ] = [ Grandmother (-) ]   <-- Generation +2
                                |
               +----------------+----------------+
               |                                 |
        [ Father (+) ] = [ Mother (-) ]     [ Uncle (+) ] <-- Generation +1
                         |
         +---------------+---------------+
         |                               |
    [ Self (+) ] = [ Spouse (-) ]   [ Sister (-) ]        <-- Generation 0
         |
    [ Son (+) ]                                          <-- Generation -1

Generation Gap Hierarchy

• Generation +2: Paternal/Maternal Grandfather, Grandmothers.
• Generation +1: Father, Mother, Paternal/Maternal Uncles, Aunts, Father-in-law, Mother-in-law.
• Generation 0: Self, Brother, Sister, Cousin, Brother-in-law, Sister-in-law, Spouse.
• Generation -1: Son, Daughter, Nephew, Niece, Son-in-law, Daughter-in-law.

[!CAUTION] The Gender Assumption Trap: Never assume gender based on names. In a statement like "Rohan is the child of Anita", Rohan could be male or female. Gender can only be fixed if Rohan is explicitly called a "son", or if Rohan is married to a female (making Rohan male).

---

Coded Blood Relations Strategy

In Coded Blood Relations, symbols represent relations (e.g., $A + B \implies A$ is father of $B$). To solve "Find the expression where $X$ is the uncle of $Y$", use Option Elimination:

1. Gender Test: Since $X$ is an uncle, $X$ must be Male ($+$). Eliminate options where $X$ is female or where $X$'s gender cannot be determined (e.g., if $X$ is at the end of an expression without a spouse link).
2. Generation Gap Test: An uncle is in Generation $+1$ relative to $Y$. Calculate the cumulative generation gap for each option ($+1$ for parent, $0$ for sibling, $-1$ for child). Eliminate options that do not sum to $+1$.

---

Direction Sense: 8-Cardinal Grid & Distance Math

Direction questions involve movement across eight cardinal directions: North (N), South (S), East (E), West (W), North-East (NE), North-West (NW), South-East (SE), and South-West (SW).

                      North (N)
                        |    / North-East (NE)
          North-West    |   /
              (NW) \    |  /
                    \   | /
    West (W) --------+-------- East (E)
                    /   | \
              (SW) /    |  \ (SE)
          South-West    |   \ South-East
                        |
                      South (S)

Turn Mechanics

• Right Turn (Clockwise 90°): North $\to$ East $\to$ South $\to$ West $\to$ North.
• Left Turn (Counter-Clockwise 90°): North $\to$ West $\to$ South $\to$ East $\to$ North.

Shortest Distance Formula (Pythagoras Theorem)

To calculate the straight-line displacement ($d$) between starting point $(x_1, y_1)$ and ending point $(x_2, y_2)$: $d = \sqrt{(\Delta x)^2 + (\Delta y)^2}$ where $\Delta x$ is net East-West displacement and $\Delta y$ is net North-South displacement.

---

Shadow Principles

Shadow direction depends entirely on the position of the Sun and the person's facing direction:

---

Step-by-Step Worked Example

Problem: A traveler starts at Point P, walks 12 km North to Point Q, turns Right (East) and walks 9 km to Point R, turns Right (South) and walks 15 km to Point S, turns Right (West) and walks 5 km to Point T, and finally turns Right (North) and walks 3 km to Point U.

Tasks: Determine the shortest distance between Point P and Point U, and the direction of Point U relative to Point P.

Step-by-Step Coordinate Calculation

1. Start at P: $(x_0, y_0) = (0, 0)$.
2. P to Q (12 km North): $(x_1, y_1) = (0, +12)$.
3. Q to R (9 km East): $(x_2, y_2) = (+9, +12)$.
4. R to S (15 km South): $(x_3, y_3) = (+9, 12 - 15) = (+9, -3)$.
5. S to T (5 km West): $(x_4, y_4) = (9 - 5, -3) = (+4, -3)$.
6. T to U (3 km North): $(x_5, y_5) = (+4, -3 + 3) = (+4, 0)$.

Distance and Direction Evaluation

• Net $x$-displacement ($\Delta x$): $+4$ km (East).
• Net $y$-displacement ($\Delta y$): $0$ km.
• Shortest Distance: $d = \sqrt{4^2 + 0^2} = 4$ km.
• Direction of U relative to P: Point U lies exactly East of Point P.

Final Answer: Shortest distance is 4 km; Direction is East.