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30 students decided to buy an article. At the last moment 5 students

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Sangeeta2018
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30 students decided to buy an article. At the last moment 5 students [#permalink] New post   16 Nov 2017, 12:17
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30 students decided to buy an article. At the last moment 5 students backed out because of which each student had to pay $16 extra. What was the cost of article?

A. 30
B. 80
C. 150
D. 175
E. 2400

Source: Experts' Global
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E
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generis
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Re: 30 students decided to buy an article. At the last moment 5 students [#permalink] New post   16 Nov 2017, 13:25
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Sangeeta2018 wrote:
30 students decided to buy an article.At the last moment 5 students backed out because of which each student had to pay $16 extra.What was the cost of article?

1.30
2.80
3.150
4.175
5.2400

Source: Experts' Global

This question is a bit tricky, because if you use cost per person, you have one more step: the cost of the item.

When 25 students pay for an item, it costs $16 more per person than it does when 30 students buy the same article.

Let cost per person = x
30x = 25(x + 16)
30x = 25x + 400
5x = 400
x = 80

So the cost of the article is
(30)($80) = $2,400

Check for accuracy:

Cost per person when 25 buy?
Cost per person = (x + 16) = (80 + 16)= $96
Total cost? ($96)(25) = $2,400
A match. Correct.

Answer E
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Re: 30 students decided to buy an article. At the last moment 5 students [#permalink] New post   16 Nov 2017, 23:03
Expert Reply
Sangeeta2018 wrote:
30 students decided to buy an article. At the last moment 5 students backed out because of which each student had to pay $16 extra. What was the cost of article?

A. 30
B. 80
C. 150
D. 175
E. 2400

Source: Experts' Global


30 - 5 = 25 students paid $16 extra, so paid total of 16*25 = $400 extra, which is the amount 5 people were supposed to pay.

5 people = $400 means that 30 people = 400*6 = $2400.

Answer: E.
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Re: 30 students decided to buy an article. At the last moment 5 students [#permalink] New post   17 Nov 2017, 08:02
Sangeeta2018 wrote:
30 students decided to buy an article. At the last moment 5 students backed out because of which each student had to pay $16 extra. What was the cost of article?

A. 30
B. 80
C. 150
D. 175
E. 2400

Source: Experts' Global

P: price of the item
expected price per person = P/30

after 5 folks backed out-
P = 25((P/30) +16)
P = (5/6)(480 +P)
P = 2400
---E---
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30 students decided to buy an article. At the last moment 5 students [#permalink] New post   17 Nov 2017, 23:26
But question stem says as to what's the cost of article.

How cost of article is 30x80? . This number is the cost to 30 person. Not to the cost of article.


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Re: 30 students decided to buy an article. At the last moment 5 students [#permalink] New post   18 Nov 2017, 01:50
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sun01 wrote:
But question stem says as to what's the cost of article.

How cost of article is 30x80? . This number is the cost to 30 person. Not to the cost of article.


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30 people are buying ONE item ans are splitting the price equally among themselves.
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Re: 30 students decided to buy an article. At the last moment 5 students [#permalink] New post   20 Nov 2017, 12:31
Expert Reply
Sangeeta2018 wrote:
30 students decided to buy an article. At the last moment 5 students backed out because of which each student had to pay $16 extra. What was the cost of article?

A. 30
B. 80
C. 150
D. 175
E. 2400


Let x = the cost each student had to pay originally. Thus, we have:

30x = 25(x + 16)

30x = 25x + 400

5x = 400

x = 80

Since each student originally had to pay $80, the cost of the article is 30 x 80 = $2,400.

Answer: E
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30 students decided to buy an article. At the last moment 5 students [#permalink] New post   15 Jan 2022, 08:54
Just as a logical guess, the answer should be >400 (i.e. 16*25) 2400 is the only option satisfying this condition. Time saving!
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30 students decided to buy an article. At the last moment 5 students [#permalink]
15 Jan 2022, 08:54
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