At a certain reception, punch is served in glasses of two sizes, small

Question

At a certain reception, punch is served in glasses of two sizes, small and large. If a bowl of a certain size, when filled with punch will 24 small glasses or 15 large glasses, then 10 such bowls, when filled with punch, will fill 72 small glasses and how many large glasses?

A) 90
B) 105
C) 120
D) 135
E) 150

A) 90
B) 105
C) 120
D) 135
E) 150

Navnit99 · Accepted Answer

24 small glass = 1 bowl, so 72 small glass = 3 bowls

Now there are 7 bowls for large glasses.

1 bowl = 15 large glasses, so 7x15= 105 large glasses

Ans = 105 glasses option "B"

Kinshook · Answer

Given: At a certain reception, punch is served in glasses of two sizes, small and large. 
Asked: If a bowl of a certain size, when filled with punch will 24 small glasses or 15 large glasses, then 10 such bowls, when filled with punch, will fill 72 small glasses and how many large glasses?

I bowl will filll punch in = 24 small glasses = 15 large glasses
10 bowls will fill punch in = 240 small glasses = 150 large glasses

72 small glasses = 45 large glasses

10 bowls will fill punch in 72 small glasses and (150-45=105) large glasses.

IMO B

gmatophobia · Answer

Let's assume that the volume of the bowl = LCM (24, 15) =  8 * 3 * 5

As the bowl of punch can fill  15  large glasses, the volume of each large glass =  8  cubic units, and the volume of each small glass =  5  cubic units.

The volume of punch in  10  bowls =  8 * 3 * 5 * 10 = 1200  cubic units.

The volume of punch that can be accommodated by  72  small glasses =  72 * 5 = 360  cubic units.

Remaining volume of punch=  1200 - 360 = 840  cubic units

Number of large glasses required to fill  840  cubic units of punch =  \frac{840}{8} = 105

Option B

rakman123 · Answer

Simple Logical Approach

Bowls can either fit 24 small (x) or 15 large (y). There are 10 bowls, so x+y=10.

STEM says some of these 10 bowls fit 72 small glasses.

72 small glasses / 24 small glasses (which is the capacity per bowl x) = 3. You are now left with 7 bowls since --> 3+y=10 ---> y=7.

7 bowls * 15 large glasses =  105 large glasses.

Voila.

mooh · Answer

The question wants us to find the no of  large glasses   required to fill 10 bowls in addition to 72 small glasses

24 small glasses will fill 1 bowl
x small glasses will fill 10 bowls

x = 240, so 240 small glasses will fill 10 bowls and we already have 72 of those

so there are (240-72)small glasses left to fill the bowl and this equals 168small glasses left

Now we need to determine how many large glasses is equal to 168 small glasses

From the question 24 small glasses = 15 large glasses
therefore 168 small glasses = x large glasses

with cross multiplication, x= 105 large glasses
 Answer = B

hemanthPA · Answer

Given:
 1B = 24S or 15L
10B = 72S + (?)L

10 B will fit 10 *15L’s that’s 150

But already 72S is present

So if 24S = 15L, then 72S = is how many L?
72*15/24 = 15*3 = 45L
>>72S = 45L

So the 10B’s are already filled with 45L’s, so how many more L’s can it be filled with?

150L - 45L = 105L’s

c'est tout!

SwethaReddyL · Answer

Bunuel , could you please confirm if this is a correct approach

if it is fully of small glasses, then we need 240; out of which 72 is small which is 72/240 = 3/10th
balance 7/10 should be filled with large glasses, if all is large ones then we need 150 large glasses; 7/10 0f 150 = 105

Thanks in advance,
Swetha

egmat · Answer

Hi SwethaReddyL,

Yes, your method is completely valid, and it's actually one of the cleanest ways to think about this. Let me show you  why  it works so you can trust it next time.

The whole question is really about one fixed thing:  the total volume of punch in 10 bowls.  Nothing about that volume changes - we're just measuring it in different cup sizes.

Here's your logic, confirmed:

- If you poured all of it into small glasses, you'd need  240  of them ( 10  bowls ×  24 ).
- You actually pour  72  small glasses, which is  72 / 240  =  3/10  of the total volume.
-  Therefore7/10  of the volume is still left in the bowls.
- If that  entire  volume went into large glasses, it would fill  150  ( 10  ×  15 ). Since only  7/10  of the volume remains, you fill  7/10  ×  150  =  105  large glasses. ✓

The key idea that makes this airtight:  a fraction of the total volume is the  same fraction  no matter which glass you measure it in. The  72  small glasses eat up  3/10  of the punch, and  3/10  of the punch is  3/10  whether you count it in small glasses or large ones. That's why you can apply the leftover  7/10  directly to the  150  large-glass capacity.

Notice this matches the other solutions in the thread exactly - Kinshook found  72  small =  45  large, leaving  150  -  45  =  105 , and you got there by working with fractions of capacity instead. Same volume, same answer.

So your approach isn't a lucky shortcut - it's built on the constant-volume idea, and it will work every time a problem gives you "this many of size A  or  that many of size B."

Answer: B

GMATMaverickPro · Answer

First time writing a solution, so I apologise in advance for any typos!

Used algebra to solve this. Assume bowl volume to be X, small cup volume to be S, large cup volume to be L. 
-> X = 24S (OR) X = 15L
-> From this we can derive that S = (15/24)*L

Questions can be rephrased as, 10X = 72S + (?)L, where  (?) represents the number of large glasses required.  
-> 10X - 72S = (?)L
-> Convert everything in terms of L,
-> (?)L = 150L - 45L
->  (?)L = 105L

Thus we need 105 bigger glasses to fill the rest of the volume of punch.

At a certain reception, punch is served in glasses of two sizes, small

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At a certain reception, punch is served in glasses of two sizes, small

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