Question

63 cookies are distributed among four children Ram, Arjun, John, and Imran 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 number of cookies that John got. Find the number of cookies that each one received. [4 MARKS]

Answer 1

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

Let the no. of cookies with Ram 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