In a family, the age of father, mother, son and grandson are A, B, C and D respectively. Given that A - B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years, then B - C is :

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Q: 117 (CAPF/2014)
In a family, the age of father, mother, son and grandson are A, B, C and D respectively. Given that A - B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years, then B - C is :

question_subject: 

Logic/Reasoning

question_exam: 

CAPF

stats: 

0,11,11,2,2,7,11

keywords: 

{'average age': [0, 0, 1, 2], 'age': [2, 1, 1, 2], 'grandson': [0, 0, 1, 1], 'family': [0, 1, 0, 0], 'father': [15, 3, 10, 14], 'years': [1, 0, 0, 2], 'mother': [4, 3, 4, 7]}

To solve this question, let`s break down the information given:

1. A - B = 3: This means that the age of the father (A) is 3 years more than the age of the mother (B).

2. B + C = 78: This tells us that the age of the mother (B) plus the age of the son (C) is equal to 78.

3. C + D = 33: This means that the age of the son (C) plus the age of the grandson (D) is equal to 33.

4. The average age of the family is 34 years: To get the average age, you would add up the ages of all family members and divide by the number of members. Using the given variables, we can express this as: (A + B + C + D)/4 = 34.

Now, let`s solve for B - C:

From equation 1, we know that A - B = 3, which means A = B + 3.

Substituting this into equation 4, we get (B + 3 + B + C + D)/4 = 34.

Combining like terms, we have (2B + C + D