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Question

‘A # B’ means ‘A is the sister of B’;

‘A $ B’ means ‘A is the father of B’.

‘A @ B’ means ‘A is the wife of B’.

‘A % B’ means ‘A is the brother of B’.

Which of the following options means ‘J is the father of R’?

This question was previously asked in
SSC CGL 2020 (Tier-2) Statistics Previous Year Paper 3 (28-Jan-2022)
The correct answer is

C @ J $ K % M # R

Solving Blood Relation Code Problems

This question asks us to decode relationships given by symbols and find which expression means 'J is the father of R'. We are given the following code meanings:

  • ‘A # B’ means ‘A is the sister of B’
  • ‘A $ B’ means ‘A is the father of B’
  • ‘A @ B’ means ‘A is the wife of B’
  • ‘A % B’ means ‘A is the brother of B’

We need to analyze each option to determine the relationship between J and R. Let's examine the structure of the relationships in each option.

Analyzing the Options for J and R Relationship

Let's break down the relationship in each expression:

Option 1: C @ J % K $ M # R

  • C @ J: C is the wife of J. (J is the husband of C)
  • J % K: J is the brother of K.
  • K $ M: K is the father of M.
  • M # R: M is the sister of R.

In this option, J is the brother of K, and K is the father of M and R (since M and R are siblings). So, J is the uncle of R. This does not match the requirement that J is the father of R.

Option 2: C @ J $ K % M # R

  • C @ J: C is the wife of J. (J is the husband of C)
  • J $ K: J is the father of K.
  • K % M: K is the brother of M.
  • M # R: M is the sister of R.

Let's trace the relationship between J and R:

  • J is the father of K.
  • K is the brother of M. This means K and M are children of J (and C, J's wife).
  • M is the sister of R. This means M and R are siblings. Since M is a child of J, R must also be a child of J.

Therefore, J is the father of R in this option. This matches the requirement.

Option 3: J @ C $ K % M # R

  • J @ C: J is the wife of C. (C is the husband of J)
  • C $ K: C is the father of K.
  • K % M: K is the brother of M.
  • M # R: M is the sister of R.

In this option, J is the wife of C, and C is the father of K, M, and R. J is the mother of R. This does not match the requirement that J is the father of R.

Option 4: C @ R $ K % M # J

  • C @ R: C is the wife of R. (R is the husband of C)
  • R $ K: R is the father of K.
  • K % M: K is the brother of M.
  • M # J: M is the sister of J.

In this option, R is the father of K and M. M is the sister of J, which means J is also a child of R (or R's spouse). So R is the father of J. This means J is the child of R, not the other way around. This does not match the requirement that J is the father of R.

Based on the analysis, only Option 2 results in J being the father of R.

Step-by-Step Derivation for Option 2

Let's meticulously follow the relations in 'C @ J $ K % M # R':

  1. C @ J: C is the wife of J. This establishes J as the husband and C as the wife.
  2. J $ K: J is the father of K. K is the child of J.
  3. K % M: K is the brother of M. This establishes K and M as siblings. Since J is the father of K, J is also the father of M.
  4. M # R: M is the sister of R. This establishes M and R as siblings. Since J is the father of M, J is also the father of R.

Therefore, the expression 'C @ J $ K % M # R' clearly indicates that J is the father of R.

Relationship Summary per Option (J to R)
Option Expression Relationship of J to R Matches 'J is father of R'?
1 C @ J % K $ M # R Uncle No
2 C @ J $ K % M # R Father Yes
3 J @ C $ K % M # R Mother No
4 C @ R $ K % M # J Child (R is father of J) No

The analysis confirms that Option 2 correctly represents the relationship 'J is the father of R'.

Revision Table: Key Concepts

Concept Description Application in Problem
Coded Relations Representing family relationships using symbols or codes. Used to translate expressions like 'A $ B' into relationships like 'A is the father of B'.
Tracing Relationships Following the chain of relationships from one person to another in an expression. Crucial for determining the final relationship between J and R by evaluating the links between them in the expression.
Siblings Persons sharing one or both parents (Brother, Sister). Understanding sibling relationships (like K % M and M # R) helps deduce common parentage.

Additional Information: Blood Relation Logic

Blood relation questions test your ability to understand and interpret family relationships based on given information. When dealing with coded relations:

  • Process the expression from left to right, identifying the relationship between adjacent pairs of letters using the given codes.
  • Build a mental or written family tree or diagram as you decode the relationships. This helps visualize the connections.
  • Pay close attention to the gender indicated by the relationship (e.g., father is male, sister is female).
  • The gender of a person might be specified by their role (father, wife, brother) or sometimes needs to be inferred from multiple relationships.
  • Work backwards if necessary, or trace forward, depending on how the question is phrased. In this case, tracing forward from J towards R was effective.
  • Practice is key to quickly decoding complex expressions and identifying the desired relationship.
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Similar Questions

  1. If X × Y means that X is the mother of Y, X – Y means that X is the father of Y, X ÷ Y means that X is the sister of Y, then which of the following expression shows that P is the paternal grandfather of R?

  2. ‘A # B’ means ‘A is the father of B’.

    ‘A % B’ means ‘A is the mother of B’.

    ‘A @ B’ means ‘A is the sister of B’.

    ‘A & B’ means ‘A is the son of B’.

    If ‘G # M # T % S @ H & R & W @ U’, then which of the following statements is NOT correct?

  3. A + B means ‘B is the brother of A’;

    A - B means ‘A is the mother of B’;

    A × B means ‘A is the father of B’;

    A ÷ B means ‘ A is the son of B’.

    If, P + R × T - Q ÷ s + U, then how is S related to R?
  4. A + B means ‘A is the mother of B’;

    A - B means ‘A is the husband of B’;

    A × B means ‘A is son of B’;

    A ÷ B means ‘A is the daughter of B’.

    If W × Z + Y ÷ X, then how is X related to Z?
  5. ‘A +B’ means ‘A is the sister of B’

    ‘A - B’ means ‘A is the daughter of B’

    ‘A × B’ means ‘A is the brother of B’

    ‘A B’ means ‘A is the husband of B’

    IfV + U × Q – T + R + P × S, then how is P related to V?
  6. A + B means ‘B is the daughter of A’;

    A - B means ‘B is the sister of A’;

    A × B means ‘B is the husband of A’;

    A ÷ B means ‘A is the father of B’

    If, P ÷ R × T + Q - S × U + Z, Then how is R related to Z?
  7. A + B means ‘A is the husband of B’;

    A - B means ‘A is the wife of B’;

    A × B means ‘A is the mother of B’;

    A ÷ B means ‘A is the son of B’

    If, W × R × J – S ÷ V + L, Then which of the following statements is NOT correct?
  8. A + B means ‘A is the sister of B’;

    A - B means ‘A is the father of B’;

    A × B means ‘A is the son of B’;

    A ÷ B means ‘A is the Wife of B’

    If, E ÷ F - H + J ÷ G × D, then how is E related to G?
  9. ‘A + B’ means ‘A is the daughter of B’.

    ‘A $ B’ means ‘A is the husband of B’.

    ‘A @ B’ means ‘A is the brother of B’.

    ‘A & B’ means ‘A is the mother of B’.

    ‘A % B’ means ‘A is the son of B’.

    If ‘W @ S % K $ G & U & T @ R + C’, then which of the following statements is correct?

  10. A + B means ‘A is the mother of B’;

    A – B means ‘A is the brother of B’;

    A × B means ‘A is the father of B’;

    A ÷ B means ‘A is the daughter of B’;

    If P – K × Y – J ÷ S + R, then which of the following statements is NOT correct?

Important Questions from Coded Blood Relation Problems

  1. If A @ B means A is the son of B, A # B means A is the husband of B and A * B means A is the daughter of B, then what does P @ Q * R # S mean? 

  2. If P $ Q means P is the husband of Q; P ! Q means P is the mother Q and P * Q means P is the daughter of Q, which of the following shows that Z is brother of W's wife, if Z is male?

  3. If P $ Q means P is the brother of Q; P ! Q means P is the mother Q and P * Q means P is the son of Q, which of the following shows that W is brother of Z?

  4. If ‘A + B’ means ‘A is the mother of B’, ‘A - B’ means ‘A is the father of B’, ‘A × B’ means ‘A is the brother of B’, ‘A & B’ means ‘A is the son of B’, then how is M related to K in the expression ‘N − M + T × L & G & K’?

  5. A # B means ‘A is the father of B’.

    A @ B means ‘A is the son of B’.

    A & B means ‘A is the sister of B’.

    A % B means ‘A is the wife of B’.

    If W # Q @ T & Y @ M % K, then how is K related to W?

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