Question

In a family, the father took $\frac{1}{4}$ of the cake and he had $3$ times as much as each of the other members had. The total number of family members is ___________.

• A. $3$
• B. $7$
• C. $10$
• D. $12$

Answer 1

Answer: (C)

$10$

Let the number of family members $=x$

fraction of cake the father took $=\frac{1}{4}$

fraction of cake other members had $=\frac{3}{4}$

fraction of cake EACH other members had $=\frac{3}{4(x-1)}$

given that :

fraction of cake the father took was 3 times as much as each of the other members had.

$\Rightarrow \frac{1}{4}=3\times \frac{3}{4(x-1)}$

$\Rightarrow x-1=9$

$\Rightarrow x=10$

the number of family members are $=10$