Question

Ravi distributed the chocolates with him equally between Rajesh and Suresh. He was left with a chocolate. Rajesh distributed his share equally among three of his friends and was also left with a chocolate. One of the three distributed his share equally among four of his friends and was left with no chocolate. Which of the following could be the number of chocolates that Rajesh received?

• A. $22$
• B. $34$
• C. $49$
• D. $64$

Answer 1

The correct option is C $49$

Let the no. of chocolates Rajesh got be $x$

$\therefore$ Total no. of chocolates $=2x+1$

Rajesh distributed his share equally among three of his friends and was also left with a chocolate.

$\therefore (x-1)$ can be divided into $3$ equal parts (assumed $p$)

$\therefore x=3p+1$ ....... $\left(i\right)$

As it is given that, one of the three distributed his share equally among four of his friends and was left with no chocolate.

$\therefore p$ can be divided into $4$ equal parts (assumed $a$)

$\therefore p=4a$

Substituting the value of p in eq $\left(i\right)$, we get

$x=3\times 4a+1$

$\Rightarrow x=12a+1$

$\Rightarrow (x-1)=12a$ ......... $\left(ii\right)$

$\therefore (x-1)$ can be divided into $12$ equal parts.

Therefore, $49$ is the only value of x among given options which clearly defines equation $\left(ii\right)$

Hence, $49$ is the correct answer.