Question

Farhan, Kharul, Huixian, Shirley and Jun share a sum of money. Farmhand takes 1/5 of the sum of money. After Farhan has taken his share, Khairul takes 1/3 of the remaining money. After Khairul has taken his share, Huixian takes 1/4 of the remaining money. After Hujxian has taken her share, Shirley takes 1/7 of the remaining money. After Shirley has taken her share, Jun takes all of the remaining money. What fraction of the sum of money is Jun's share?

Answer 1

Dear respected student,

Since, it's your exam time we'll solve it quicker and make the solution more clearer. So, here's my process on fractional values and shares of the respective holders, as per the question :

The fraction of the sum in the "total money" which is left by Farhan after he has taken the "share" will be :

Subtract the total money from it's given share of "1/5" that is,

$\bf{Farhan's \: \: Share = 1 - \dfrac{1}{5}}$

$\bf{FS = \dfrac{5}{5} - \dfrac{1}{5}}$

$\bf{FS = \dfrac{5 - 1}{5}}$

$\bf{\therefore \quad FS = \dfrac{4}{5}}$

Therefore, the fraction of the sum in the total money which is left by the second man named Khairul who has taken the given share will be the share of "Farhan" and the subtraction from "total money" in the current share that is;

$\bf{[1 - \dfrac{1}{3}] \times \dfrac{4}{5}}$

$\bf{[\dfrac{3}{3} - \dfrac{1}{3}] \times \dfrac{4}{5}}$

$\bf{[\dfrac{3 - 1}{3}] \times \dfrac{4}{5}}$

$\bf{\dfrac{2}{3} \times \dfrac{4}{5}}$

$\bf{\dfrac{2 \times 4}{3 \times 5}}$

$\bf{\dfrac{8}{3 \times 5}}$

$\bf{\dfrac{8}{15}}$

Therefore, the fraction of the sum in the total money which is left by the third man named Huixian who has taken the given share will be the share of "Khairul" and the subtraction from "total money" in the current share that is;

$\bf{[1 - \dfrac{1}{4}] \times \dfrac{8}{15}}$

$\bf{[\dfrac{3}{3} - \dfrac{1}{3}] \times \dfrac{4}{5}}$

$\bf{[\dfrac{4 - 1}{4}] \times \dfrac{8}{15}}$

$\bf{\dfrac{3}{4} \times \dfrac{8}{15}}$

$\bf{\dfrac{3 \times 8}{4 \times 15}}$

$\bf{\dfrac{24}{4 \times 15}}$

$\bf{\dfrac{24}{60}}$

$\bf{\dfrac{2}{5}}$

Therefore, the fraction of the sum in the total money which is left by the third woman named Shirley who has taken the given share will be the share of "Huixian" and the subtraction from "total money" in the current share that is;

$\bf{[1 - \dfrac{1}{7}] \times \dfrac{2}{5}}$

$\bf{[\dfrac{7}{7} - \dfrac{1}{7}] \times \dfrac{2}{5}}$

$\bf{[\dfrac{7 - 1}{7}] \times \dfrac{2}{5}}$

$\bf{\dfrac{6}{7} \times \dfrac{2}{5}}$

$\bf{\dfrac{6 \times 2}{7 \times 5}}$

$\bf{\dfrac{12}{7 \times 5}}$

$\boxed{\bf{\underline{\therefore \quad Jun \: \: Wei's \: \: Share = \dfrac{12}{35}}}}$

Which is the required solution for this type of query.

Hope it helps you and clears your doubts in taking in the fractional share of values !!!