Question

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) 2
B) 3
C) 4
D) 5

Answer 1

Hint - Convert each of the sentences into equations using variables. Transform one equation such that one variable is in terms of the other. Substitute one variable in the other equation. Obtain the value of the variable and substitute for the other.

Complete step by step answer:
Let d represent the number of daughters and let s represent the number of sons.
Given, each daughter has the same number of brothers as she has sisters
Then, we have
d - 1 = s - Equation (1)
Because the daughter cannot consider herself as one of the sisters hence d-1.
Each son has twice as many sisters as he has brothers
Then, we have
   2 (s - 1) = d -- Equation (2)
Because the son cannot consider himself as one of the brothers hence s-1.
Equation (1) can be manipulated and written as
d = s+1 -- Equation (3)
Substitute d in equation (2)
⟹2 (s - 1) = d
⟹2 (s - 1) = s+1
⟹2s – 2 = s+1
⟹s = 3
Substitute s in equation (3) to get the value of d
⟹d = s+1
⟹d = 3+1
⟹d = 4
Hence, d = 4 and s = 3.
The numbers of sons in the family are 3. Hence Option B is the correct answer.

Note – Converting the sentences into equations is the crucial step in such problems. You can clearly see that this is a clear case of 2 equations and 2 variables after conversion. Upon solving we obtain the values of both the variables. The key is to transform one of the equations such that we have one variable in terms of another. Then the other equation reduces into a single variable equation and becomes easier to solve. On finding the value of one variable the other can be found simply by substituting.