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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Fri Sep 30, 2011 1:21 am

15 lts are taken of from a container full of liquid A and replaced with Liquid B. Again 15 more lts of the mixture is taken and replaced with liquid B. After this process, if the container contains Liquid A and B in the ratio 9:16,What is the capacity of the container?

A:45
B:25
C:37.5
D:36
E:42

c

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Source: Beat The GMAT — Problem Solving | Fri Sep 30, 2011 1:21 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Fri Sep 30, 2011 1:47 am

Let X be the capacity of the container.

% of Liq A left / % of A originally present = (1- (Vol of soln replaced/vol of container)) ^ n

[Note this formula is applied for repeated iterations such as these and 'n' = Number of iterations(in this case 2)]

9/25 = (1-15/x)^2 ...... [(9/9+16) / 1(Liq A present originally)]

3/5 = 1 - (15/X)

X=37.5

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knight247: Legendary Member; Posts: 504; Joined: Tue Apr 19, 2011 1:40 pmFollowed by: 11 members; Thanked: 114 times

by knight247 » Fri Sep 30, 2011 3:23 am

Hey Ashwin
Good use of the formula. But how would u do this without alligation? Using standard ratios and equations

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Fri Sep 30, 2011 4:30 am

Wasnt able to format the reply.. See attached pic

Attachments

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LalaB: Master | Next Rank: 500 Posts; Posts: 425; Joined: Wed Dec 08, 2010 9:00 amFollowed by: 7 members; Thanked: 56 times; GMAT Score:690

by LalaB » Fri Sep 30, 2011 9:48 pm

Could u please explain me this -(1-15/x)*15?
Ä° didnt get why u multiplied by 15/ I mean why u use multiplication, not substraction?

p.s. sorry for a stupid question

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phoenix111: Senior | Next Rank: 100 Posts; Posts: 47; Joined: Thu Jun 16, 2011 8:55 am; Location: San Francisco, CA; Thanked: 4 times

by phoenix111 » Fri Sep 30, 2011 10:05 pm

This will be calculation intensive esp. if one does'nt remember the formula.
So to do it within 2-3 mins we will have to use subsitution of option:

Since ratio( A:B) is 9:16 so let A be 9x and B be 16x
Total Volume : 25x

So the answer would probably be either B or C ( 25 or 37.5)

Let try for 25:
Intial : A25 B0
First mixing : A10 B15
Second mix : A4 B21 ( On removing 15lt B will be 6 then adding 15)
Final ratio 4:21 ( Incorrect)

Let try for 37.5:
Intial : A37.5 B0
First mixing : A22.5 B15 ( 22.5:15 is 3:2, so removing 15lt will remove A9 B6)
Second mix : A13.5 B24 ( On removing 15lt B will be 9 then adding 15)

Final Ratio : 13.5:24 => 9:16 (Bingo!!)

Answer : 37.5

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Fri Sep 30, 2011 10:42 pm

@LalaB

Could u please explain me this -(1-15/x)*15?

I think you meant [(X-15)/X] * 15

When you do the replacement for the first time, its straightforward, (You remove 15 Lts of A and replace it by 15 Lts of B)

When this is done the second time, while removing the 15 Lts, you remove some quantity of A and some of B.

To find quantity of A remaining, we need to find the amount of A removed in the 2nd step.

For ease of explanation, consider concentration of A to be 20% (remaining is B 80%) in a 100 Ltr solution. Now if we remove 20 Lts of this solution, quantity of A removed could be found by;

(20/100 )* 20 = 4 Lts (Quantity of A/Total Quantity) * Amount Removed.

Now, [(X-15)/X] * 15 is the same thing as above

X-15 - Quantity of A
X - Total quantity
15 - Amount removed.

Hope it makes sense

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thestartupguy: Master | Next Rank: 500 Posts; Posts: 150; Joined: Thu May 05, 2011 10:04 amFollowed by: 4 members; Thanked: 5 times

by thestartupguy » Mon Nov 14, 2011 9:43 am

shankar.ashwin wrote:Let X be the capacity of the container.

% of Liq A left / % of A originally present = (1- (Vol of soln replaced/vol of container)) ^ n

[Note this formula is applied for repeated iterations such as these and 'n' = Number of iterations(in this case 2)]

9/25 = (1-15/x)^2 ...... [(9/9+16) / 1(Liq A present originally)]

3/5 = 1 - (15/X)

X=37.5

I understood the part % of Liq A left = 9. But I am not sure how % of A originally present = 25. Isn't 9+16=25 the solution mixture after the two replacements? I am jinxed.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Nov 14, 2011 10:49 am

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Mon Nov 14, 2011 11:40 am

msr4mba wrote:
I understood the part % of Liq A left = 9. But I am not sure how % of A originally present = 25. Isn't 9+16=25 the solution mixture after the two replacements? I am jinxed.

Yeah you're right 'replacement' is replacing a certain quantity of 'A' with equal quantity of 'B'. (You don't add B increasing quantity)

The total quantity at the end of each step remains the same. So initial A will be 9+16

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user123321: Master | Next Rank: 500 Posts; Posts: 385; Joined: Fri Sep 23, 2011 9:02 pmFollowed by: 6 members; Thanked: 62 times

by user123321 » Mon Nov 14, 2011 9:49 pm

Just for fun. A different take on the problem.

If we carefully observe, we are always replacing the same fraction of component from available A each time we remove 15 litres and add 15 litres of B.

lets say each time we replace p fraction of A
initially lets say we have x litres of A component
after first replacement the A component will be x.p - (1)
after second replacement the A component will be x.p^2
we know xp^2/x = 9/25 (nothing but final amt of A/total amt of solution)
p = 3/5 -(2)

so we are removing a fraction of 3/5 each time we are removing 15 litres and adding 15 litres of B
so use material balance after first replacement:
we know that amount of A present after first replacement is x-15
and also we know it is x.p = 3x/5 from (1)&(2)
=> 3x/5 = x-15 => 2x/5 = 1 5=> x = 37.5

user123321

Just started my preparation

Want to do it right the first time.

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