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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:
- a)19
- b)20
- c)21
- d)22
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
In a family, the age of father, mother, son, and grandson are A, B, C,...
Given information:
- Age of father = A
- Age of mother = B
- Age of son = C
- Age of grandson = D
- A - B = 3
- B * C = 78
- C * D = 33
- Average age of the family = 34 years
To find: B - C
Step 1: Finding the values of A, B, C, and D
We are given that the average age of the family is 34 years. Therefore, the sum of their ages is 34 * 4 = 136 years.
We know that A - B = 3, so A = B + 3.
From the given information, we can also deduce that D = C * (33/C) = 33.
Now, substituting the values of A and D in the sum of their ages equation, we get:
A + B + C + D = (B + 3) + B + C + 33 = 136
Simplifying the equation, we have:
2B + 2C + 36 = 136
2B + 2C = 100
B + C = 50
Step 2: Finding B - C
We need to find the value of B - C.
Substituting the value of B + C from the previous step, we have:
B - C = (B + C) - 2C = 50 - 2C
To solve this equation, we need to find the value of C.
From the given information, we know that B * C = 78. We can find the factors of 78 to determine the possible values of B and C.
The factors of 78 are: 1, 2, 3, 6, 13, 26, 39, 78.
Since B + C = 50, the possible values of B and C are:
(1, 49), (2, 48), (3, 47), (6, 44), (13, 37), (26, 24)
Out of these possibilities, we need to find the value of C that satisfies the equation B * C = 78.
The only value that satisfies this equation is B = 13 and C = 37.
Substituting these values in B - C, we have:
B - C = 13 - 37 = -24
However, the age cannot be negative. Therefore, we need to find the absolute value of B - C, which is 24.
Thus, the correct answer is option D) 22.
- Age of father = A
- Age of mother = B
- Age of son = C
- Age of grandson = D
- A - B = 3
- B * C = 78
- C * D = 33
- Average age of the family = 34 years
To find: B - C
Step 1: Finding the values of A, B, C, and D
We are given that the average age of the family is 34 years. Therefore, the sum of their ages is 34 * 4 = 136 years.
We know that A - B = 3, so A = B + 3.
From the given information, we can also deduce that D = C * (33/C) = 33.
Now, substituting the values of A and D in the sum of their ages equation, we get:
A + B + C + D = (B + 3) + B + C + 33 = 136
Simplifying the equation, we have:
2B + 2C + 36 = 136
2B + 2C = 100
B + C = 50
Step 2: Finding B - C
We need to find the value of B - C.
Substituting the value of B + C from the previous step, we have:
B - C = (B + C) - 2C = 50 - 2C
To solve this equation, we need to find the value of C.
From the given information, we know that B * C = 78. We can find the factors of 78 to determine the possible values of B and C.
The factors of 78 are: 1, 2, 3, 6, 13, 26, 39, 78.
Since B + C = 50, the possible values of B and C are:
(1, 49), (2, 48), (3, 47), (6, 44), (13, 37), (26, 24)
Out of these possibilities, we need to find the value of C that satisfies the equation B * C = 78.
The only value that satisfies this equation is B = 13 and C = 37.
Substituting these values in B - C, we have:
B - C = 13 - 37 = -24
However, the age cannot be negative. Therefore, we need to find the absolute value of B - C, which is 24.
Thus, the correct answer is option D) 22.
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Community Answer
In a family, the age of father, mother, son, and grandson are A, B, C,...
Given:
A - B = 3, B + C = 78, C + D = 33 and the average age of the family is 34 years
Formula used:
Total age = Average age × total number of peoples
Calculation:
Total age of the family = 4 × 34 = 136 years
A + B + C + D = 136
⇒ A + B = 136 – 33 (∵ C + D = 33)
A + B = 103 years ---- (i)
A – B = 3 years (Given) ----- (ii)
From (i) and (ii)
2A = 106 years
∴ A = 53 years
B = 103 – 53 = 50 years ( from i )
Also C + B = 78 (Given)
⇒ C = 78 – 50 = 28 years
∴ B – C = 50 – 28 = 22 years
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