ratio problem

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TeddyBonham: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sat Mar 28, 2015 2:21 am

ratio problem

by TeddyBonham » Sat Mar 28, 2015 4:28 am

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The ratio of statues to paintings in Ann's villa was 3:10. After 30 paintings were stolen from Ann's house the ratio of statues to paintings became 12:25. What was the original number of statues in Ann's house?

(A) 18 (B) 24 (C) 30 (D) 48 (E) 80

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Source: Beat The GMAT — Problem Solving | Sat Mar 28, 2015 4:28 am

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by GMATGuruNY » Sat Mar 28, 2015 6:22 am

TeddyBonham wrote:The ratio of statues to paintings in Ann's villa was 3:10. After 30 paintings were stolen from Ann's house the ratio of statues to paintings became 12:25. What was the original number of statues in Ann's house?

(A) 18 (B) 24 (C) 30 (D) 48 (E) 80

After the theft, S : P = 12:25, implying the following options:
S=12, P=25
S=24, P=50
S=36, P=75.

Before the theft, there were 30 more paintings, with the result that S : P = 3:10.
Adding 30 paintings to the options above, we get:
S=12, original P = 25+30 = 55, resulting ratio = 12:55.
S=24, original P = 50+30 = 80, resulting ratio = 24:80 = 3:10. This works.

Thus, S=24.

The correct answer is B.

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by Brent@GMATPrepNow » Sat Mar 28, 2015 6:39 am

TeddyBonham wrote:The ratio of statues to paintings in Ann's villa was 3:10. After 30 paintings were stolen from Ann's house the ratio of statues to paintings became 12:25. What was the original number of statues in Ann's house?

(A) 18 (B) 24 (C) 30 (D) 48 (E) 80

Here's an algebraic solution.

Let S = original number of statues
Let P = original number of paintings

The [original ] ratio of statues to paintings in Ann's villa was 3:10
So, S/P = 3/10
Cross multiply to get 3P = 10S
Rearrange to get: 3P - 10S = 0

After 30 paintings were stolen from Ann's house the ratio of statues to paintings became 12:25
New number of paintings = P - 30
Number of statues still = S
So, S/(P-30) = 12/25
Cross multiply to get: 25S = 12(P - 30)
Expand to get: 25S = 12P - 360
Rearrange to get: 12P - 25S = 360

We now have the following system:
3P - 10S = 0
12P - 25S = 360

Multiply blue equation by 4 to get:
12P - 40S = 0
12P - 25S = 360

Subtract the red equation from the blue equation to get -15S = -360
Solve to get: S = 24

Answer = B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Sat Mar 28, 2015 10:02 am

Hi TeddyBonham,

Since the question asks for the original number of statues, and the answer choices are NUMBERS, we can TEST THE ANSWERS.

We're told that the original ratio of statues to paintings was 3:10. This means that the number of statues MUST be a multiple of 3 and the number of paintings MUST be an equivalent multiple of 10. Next, we're told that after 30 paintings were stolen, the ratio become 12:25 (now, a multiple of 12 and an equivalent multiple of 25).

Since the original number of statues MUST be a multiple of 3, answer E can be eliminated (it's NOT a multiple of 3). We just need to do the necessary arithmetic to prove which of the remaining 4 answers matches the above information.

Answer A: 18 statues

With 18 statues (3x6), we have 60 paintings. Removing 30 paintings gives us a ratio of:
18: 30
This reduces to 3:5 which is NOT a match. Eliminate A.

Answer B: 24 statues

With 24 statues (3x8), we have 80 paintings. Removing 30 paintings gives us a ratio of:
24: 50
This reduces to 12:25 which IS a match. This MUST be the answer.

Final Answer: B

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Pndydpk: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Thu Sep 05, 2019 2:19 am

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by Pndydpk » Tue Sep 10, 2019 8:22 am

let's say "S" denotes no of statues and "P" denotes no of paintings.
Given that,
S/P = 3/10 => P/S = 10/3 (making it reverse) ----(1)
Also, S/(P-30) = 12/25 => (P-30)/S = 25/12 (making it reverse).....(2)
Eq (2) can be rewritten as:
P/S - 30/S = 25/12
=> 10/3 - 30/S = 25/12 (from eq 1) => 10/3 - 25/12 = 30/S
On solving we get S= 24

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by Scott@TargetTestPrep » Tue Sep 17, 2019 8:39 am

TeddyBonham wrote:The ratio of statues to paintings in Ann's villa was 3:10. After 30 paintings were stolen from Ann's house the ratio of statues to paintings became 12:25. What was the original number of statues in Ann's house?

(A) 18 (B) 24 (C) 30 (D) 48 (E) 80

We can create the equation:

3x/(10x - 30) = 12/25

25(3x) = 12(10x - 30)

75x = 120x - 360

360 = 45x

8 = x

Therefore, there are 3(8) = 24 statues in Ann's house.

Answer: B

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