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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Mon Feb 08, 2010 7:38 am

A container contains pure orange juice. Harish mixes pure water equal to 1/4 th of the volume of the orange juice in the container. Manish does not know it and sells 1/4 th of this mixture and adds water to it to replenish the quantity that he sold. What is the current proportion of water and orange juice in the container?

a) 2 : 3
b) 3 : 2
c) 1 : 3
d) 3 : 4
e) 4 : 3

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Source: Beat The GMAT — Problem Solving | Mon Feb 08, 2010 7:38 am

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 7:41 am

shashank.ism wrote:A container contains pure orange juice. Harish mixes pure water equal to 1/4 th of the volume of the orange juice in the container. Manish does not know it and sells 1/4 th of this mixture and adds water to it to replenish the quantity that he sold. What is the current proportion of water and orange juice in the container?

a) 2 : 3
b) 3 : 2
c) 1 : 3
d) 3 : 4
e) 4 : 3

Let it be 100ml(pure orange juice)
Water mixed = 25 ml.
total volume = 125 ml.(O-100 , W - 25)

1/4th of 125 = 31.25 .( O -25 , W - 6.25)
Remaining = 125 - 31.25 = 93.75 (O - 75 , W - 18.75)
Now, water added = (100 - 93.75) = 6.25

Total water = 25.
[spoiler]Proportion = W/O = 25/75 = 1:3 = C[/spoiler]

It takes time and effort to explain, so if my comment helped you please press Thanks button

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Mon Feb 08, 2010 7:45 am

What ??? thats about it ??? is there a step after this ? or am i missing onto something ???

harsh.champ wrote:
shashank.ism wrote:A container contains pure orange juice. Harish mixes pure water equal to 1/4 th of the volume of the orange juice in the container. Manish does not know it and sells 1/4 th of this mixture and adds water to it to replenish the quantity that he sold. What is the current proportion of water and orange juice in the container?

a) 2 : 3
b) 3 : 2
c) 1 : 3
d) 3 : 4
e) 4 : 3
Let it be 100ml(pure orange juice)
Water mixed = 25 ml.
total volume = 125 ml

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harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Mon Feb 08, 2010 8:11 am

bhumika.k.shah wrote:What ??? thats about it ??? is there a step after this ? or am i missing onto something ???

harsh.champ wrote:
shashank.ism wrote:A container contains pure orange juice. Harish mixes pure water equal to 1/4 th of the volume of the orange juice in the container. Manish does not know it and sells 1/4 th of this mixture and adds water to it to replenish the quantity that he sold. What is the current proportion of water and orange juice in the container?

a) 2 : 3
b) 3 : 2
c) 1 : 3
d) 3 : 4
e) 4 : 3
Let it be 100ml(pure orange juice)
Water mixed = 25 ml.
total volume = 125 ml

No,thts definitely not it bhumika.
I just wanted to give a shorter approach so I wrote down the above hint.
As for your doubt ,I have posted the complete soln.

I wrote

Let it be 100ml(pure orange juice)
Water mixed = 25 ml.
total volume = 125 ml

so that anyone doesn't go by the longer approach i.e. taking water = x and orange juice = y.
That method is very tedious and cumbersome and takes up a lot of time.

Please refer to my upper post again and ask if you have any doubts now.

It takes time and effort to explain, so if my comment helped you please press Thanks button

Just because something is hard doesn't mean you shouldn't try,it means you should just try harder.

"Keep Walking" - Johnny Walker

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Mon Feb 08, 2010 10:32 am

shashank.ism wrote:A container contains pure orange juice. Harish mixes pure water equal to 1/4 th of the volume of the orange juice in the container. Manish does not know it and sells 1/4 th of this mixture and adds water to it to replenish the quantity that he sold. What is the current proportion of water and orange juice in the container?

a) 2 : 3
b) 3 : 2
c) 1 : 3
d) 3 : 4
e) 4 : 3

Say initially the bottle had x ml of pure orange juice
Harish adds 0.25x ml of water

Now we have 1.25x ml of juice of which x ml is juice
Manish shells 0.3125x ml of juice which contains 0.25x ml of pure juice and replaces it with 0.3125x of water

Now we have 1.25xml of juice which has 0.75x ml of juice and 0.5x ml of water

The proportion of water and juice = 0.5x:0.75x = 2:3
A

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