Josh and Marcia bought a number of chairs at an auction. The average

Question

Josh and Marcia bought a number of chairs at an auction. The average price of the chairs Marcia purchased was $50, and the average price of the chairs Josh purchased was $62. If the average price of all the chairs purchased was $53, what was the ratio of the number of chairs purchased by Marcia to the no. purchased by Josh?

A. 1:1
B. 1:2
C. 1:3
D. 3:1
E. 2:1

A. 1:1 
B. 1:2 
C. 1:3 
D. 3:1 
E. 2:1

Kinshook · Answer

Given:  Josh and Marcia bought a number of chairs at an auction. The average price of the chairs Marcia purchased was $50, and the average price of the chairs Josh purchased was $62. The average price of all the chairs purchased was $53.
 Asked:  What was the ratio of the number of chairs purchased by Marcia to the no. purchased by Josh?

Let number of chairs purchased by Marcia be m
Let number of chairs purchased by Josh be j

50m+62j=53 (m+j) = 53m + 53j
3m = 9j
m:j = 3:1

IMO D

unraveled · Answer

Josh and Marcia bought a number of chairs at an auction. The average price of the chairs Marcia purchased was $50, and the average price of the chairs Josh purchased was $62. If the average price of all the chairs purchased was $53, what was the ratio of the number of chairs purchased by Marcia to the no. purchased by Josh?

A. 1:1
B. 1:2
C. 1:3
D. 3:1
E. 2:1

A. 1:1 
B. 1:2 
C. 1:3 
D. 3:1 
E. 2:1

Let number of chairs bought by Josh and Marcia is 'J' and 'M' respectively. 
Avg. price of chairs purchased by Marcia and Josh is $50 and $62 respectively. 
Avg. price of chairs of all chairs i.e. 'J+M' is $53.

Now, we have to find ratio 'M:J'.

As 62J + 50M = 53(J+M)
=> 9J = 3M
=> M:J = 3:1

Answer (D)

RajatVerma1392 · Answer

Let the number of chairs purchased by Josh is a.
Let the number of chairs purchased by Marcia is b.

50b+62a=53 (a+b)
50b + 62a = 53a + 53b
9a = 3b 
so,  \frac{b}{a}  =  \frac{9}{3}  =  \frac{3}{1}

IMO the answer is D.

firas92 · Answer

Use allegation method for weighted averages

Josh's Average----------------------------Overall Average--------Marcia's Average
------|----------------------------------------------------------------------|----------
------|----------------------------------------------------------------------|----------
---No. of Josh's chairs----------------------------------------------No. of Marcia's chairs

-----62-----------------------------------------------53------------------50---------
------|----------------------------------------------------------------------|----------
------|----------------------------------------------------------------------|----------
---No. of Josh's chairs----------------------------------------------No. of Marcia's chairs

\frac{No. of Marcia's Chairs}{No. of Josh's Chairs} = \frac{62-53}{53-50} = \frac{9}{3} = \frac{3}{1}

Answer is (D)

CrackverbalGMAT · Answer

This is a straightforward question on alligation. Drawing the alligation diagram will help you solve this question in a jiffy.

The alligation diagram can be drawn as shown in the figure below:

Attachment:

24th July 2019 - Reply 3.JPG [ 20.88 KiB | Viewed 2832 times ]

From the diagram, it’s clear that the ratio of the number of chairs purchased by Marcia and Josh is 3:1. The correct answer option is D.

Alternatively, you can use the weighted average concept to arrive at the same answer, since the alligation diagram is nothing but an alteration of the weighted average equation.
Hope this helps!

Archit3110 · Answer

let price chair of Josh Pj and Marcia Pm
total chair of Josh Cj and Marchia Cm
need to find Cm/Cj
given 
50=Pj/Cj
Pm/cm=62
also
Pj+Pm/Cj+cm=53
so
we can say
50cj+62cm=53cj+53cm
we get Cj/Cm = 3:1
IMO D

EgmatQuantExpert · Answer

Solution

Given:  
 • Josh and Marcia bought a number of chairs at an auction.
• Average price of the chairs Marcia purchased = $50
• Average price of the chairs Josh purchased = $62
• Average price of all the chairs purchased = $53

To find:  
 • The ratio of the number of chairs purchased by Marcia to the no. purchased by Josh

Approach and Working

Method -1)    weighted Average

We are given that average price of the chairs Marcia purchased = $50
 • Therefore, Price of all the chairs bought by Marcia/ Number of chairs purchased by Marcia = $ 50
 o Let us assume that total number of chairs purchased by Marcia = M 
• Hence, Price of all the chairs bought by Marcia/ M = $ 50 
Price of all the chairs bought by Marcia = $ 50 M

We are also given that average price of the chairs Josh purchased = $62
 • Therefore, Price of all the chairs bought by Josh / Number of chairs purchased by Josh = $ 62
 o Let us assume that total number of chairs purchased by Josh = J 
• Hence, Price of all the chairs bought by Josh / J = $ 62 
Price of all the chairs bought by Josh = $ 62 J

Next, we have the average price of all the chairs purchased = $53
 • Therefore, Price of all the chairs bought / Number of chairs purchased = $ 53
• ($ 50 M + $62 J)/ (M + J) =$ 53
 o $ 50 M + $62 J = $ 53 (M + J)
o $ 50 M + $62 J = $ 53 M + $ 53 J
o 9 J = 3M
o 3 J = M
o M: J = 3: 1

Hence, the correct answer is D.

Correct answer: Option D

EgmatQuantExpert · Answer

Method -2)     Alligation

https://e-gmat.com/blogs/wp-content/uploads/2019/07/Capture-3.png

M: J = (62-53) : (53 – 50) = 9 : 3 = 3:1

Hence, the correct answer is D.

Correct answer: Option D

Josh and Marcia bought a number of chairs at an auction. The average

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Josh and Marcia bought a number of chairs at an auction. The average

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards