Question

There are 63 cookies distributed among four children Ram, Arjun, John and Imran. Cookies are divided in such a way that Arjun gets twice the number of cookies than Ram. John gets half of the sum of cookies that Arjun and Ram got. Imran gets half of the cookies that John got. Find the number of cookies each one received.
[4 MARKS]

Answer 1

Visualizing the equation : 1 Mark
Steps : 2 Marks
Result : 1 Mark

Let the no. of cookies Ram has be y

According to question, no. of cookies Arjun has = 2 times Ram = $2y$

No. of cookies John has = Half of sum of Ram and Arjun. = $\frac{y+2y}{2}$

And, the number of cookies Imran has $=\frac{John}{2}$

Since, total number of cookies = 63

$y+2y+\left(\frac{y+2y}{2}\right)+\left(\frac{\left(\frac{y+2y}{2}\right)}{2}\right)=63$

$\Rightarrow 3y+\frac{3y}{2}+\frac{3y}{4}=63$

$\Rightarrow \frac{12y+6y+3y}{4}=63$

$\Rightarrow 21y=63\times 4$

$\Rightarrow y=12$

So, No. of cookies Ram got $y=12$

No. of cookies Arjun got $2y=24$

No. of cookies John got $\frac{y+2y}{2}=18$

No. of cookies Imran got = 9