rational word problem

Question

Five boys Alan, Ben , Chris, Den and Eng share a sum of money.

Alan takes 1/5 of the sum of money.

After Alan has taken his shares, Ben takes 1/3 of the remaining money.

After Ben has taken his share, Chris takes 1/4 of the remaining money.

After Chris has taken his share, Den takes 1/7 of the remaining money.

After Den has taken his share, Eng takes all the remaining money.

What fraction of the sum of money is Eng's share?

Answer 1

Let's use T for the total amount of money.

After Alan takes (1/5)*T, the amount remaining is T - (1/5)*T = (4/5)*T

After Ben takes his (1/3)*(remaining) = (1/3)*(4/5)*T, there is (2/3)*(4/5)*T remaining

Then Chris takes (1/4)*(remaining), leaving (3/4)*(2/3)*(4/5)*T

And, Den takes (1/7)*(remaining), leaving (6/7)*(3/4)*(2/3)*4/5)*T for Eng

Now, cancel out numbers to get  (12/35)*T

   The fraction that Eng gets is 12/35

Answer 2

ALAN takes 1/5    leaving   4/5

BEN takes 1/3*4/5 = 4/15  leaving 4/5 - 4/15 = 8/15

CHRIS takes 1/4*8/15 = 8/60 = 2/15  leaving 8/15 - 2/15 = 2/5

DEN takes 1/7*2/5 = 2/35  leaving 2/5 - 2/35 = 14/35 - 2/35

 

= 12/35 ANSWER

Answer 3

Hi Rajendra,

Let's say the boys have $100 to start (easiest to make percentages / fractions).

 

Alan takes 1/5 = $20

So now $80 is left.

Ben takes 1/3 = $26.67

So now $53.33 is left.

Chris takes 1/4 = $13.33

So now $40 is left.

Den takes 1/7 = $5.71

So now $34.29 is left for Eng to take.

34.29/100 is how much Eng has, which "simplifies" to 3429/10000.