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In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
In a family, each daughter has the same number of brothers as she has ...
Let d and s represent the number of daughters and sons respectively.
Then, we have :
d - 1 = s and 2 (s - 1) = d.
Solving these two equations, we get: d = 4, s = 3.
Most Upvoted Answer
In a family, each daughter has the same number of brothers as she has ...
To solve this problem, let's break it down step by step:
Given information:
- Each daughter has the same number of brothers as she has sisters.
- Each son has twice as many sisters as he has brothers.
First, let's assume the number of daughters in the family is D and the number of sons is S.
Each daughter has the same number of brothers as she has sisters:
- Since there are D daughters in the family, each daughter has D-1 sisters (excluding herself).
- Each daughter also has D-1 brothers (excluding herself).
- So, each daughter has D-1 brothers and D-1 sisters.
Each son has twice as many sisters as he has brothers:
- Since there are S sons in the family, each son has S-1 brothers (excluding himself).
- Each son also has 2(S-1) sisters.
Now, let's equate the number of brothers and sisters for each daughter and son:
For daughters:
- Each daughter has D-1 brothers and D-1 sisters.
- So, D-1 = D-1.
For sons:
- Each son has S-1 brothers and 2(S-1) sisters.
- So, S-1 = 2(S-1).
Solving the equations:
- For daughters: D-1 = D-1 simplifies to 0 = 0, which is always true.
- For sons: S-1 = 2(S-1) simplifies to S-1 = 2S-2, which further simplifies to S = 1.
Therefore, there is only 1 son in the family.
So, the correct answer is (a) 1 son.
Given information:
- Each daughter has the same number of brothers as she has sisters.
- Each son has twice as many sisters as he has brothers.
First, let's assume the number of daughters in the family is D and the number of sons is S.
Each daughter has the same number of brothers as she has sisters:
- Since there are D daughters in the family, each daughter has D-1 sisters (excluding herself).
- Each daughter also has D-1 brothers (excluding herself).
- So, each daughter has D-1 brothers and D-1 sisters.
Each son has twice as many sisters as he has brothers:
- Since there are S sons in the family, each son has S-1 brothers (excluding himself).
- Each son also has 2(S-1) sisters.
Now, let's equate the number of brothers and sisters for each daughter and son:
For daughters:
- Each daughter has D-1 brothers and D-1 sisters.
- So, D-1 = D-1.
For sons:
- Each son has S-1 brothers and 2(S-1) sisters.
- So, S-1 = 2(S-1).
Solving the equations:
- For daughters: D-1 = D-1 simplifies to 0 = 0, which is always true.
- For sons: S-1 = 2(S-1) simplifies to S-1 = 2S-2, which further simplifies to S = 1.
Therefore, there is only 1 son in the family.
So, the correct answer is (a) 1 son.
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In a family, each daughter has the same number of brothers as she has sisters and each son has twice as many sisters as he has brothers. How many sons are there in the family?a)1b)2c)3d)4Correct answer is option 'C'. Can you explain this answer?
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