Grade 6 can even do it :D how about you ?

A, B and C are winers of a raffle draw for a pile of sweets, which they are to divide in the ratio 3:2:1, respectively. However, due to confusion they come at different time to claim their prize. If each takes what they believe to be their correct share of sweets, what fraction of sweets will go unclaimed?


The answer is 0.277777.

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1 solution

Chew-Seong Cheong
Nov 30, 2014

When the winners claim their prizes at different times, each of them the other two are yet to claim their prizes.

Therefore, let the total number of the pile of sweets be N N and

A A , B B and C C respectively take away 3 : 2 : 1 = 3 6 : 2 6 : 1 6 = 1 2 : 1 3 : 1 6 3:2:1 = \dfrac {3}{6} : \dfrac {2}{6} : \dfrac {1}{6} = \dfrac {1}{2} : \dfrac {1}{3} : \dfrac {1}{6} portions of sweets.

Therefore, the number of sweets n n unclaimed is:

n = ( 1 1 2 ) ( 1 1 3 ) ( 1 1 6 ) N = 1 2 × 2 3 × 1 6 × N = 5 18 N n = (1-\frac {1}{2})(1- \frac {1}{3})(1-\frac {1}{6})N = \frac {1}{2} \times \frac {2}{3} \times \frac {1}{6}\times N = \frac {5}{18}N

The part of sweets unclaimed n N = 5 18 = 0.278 \frac {n}{N} = \frac {5}{18} = \boxed {0.278}

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