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John purchased some shirts and trousers for $600. He paid $100 less fo

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Intern
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Joined: 06 Jun 2014
Posts: 11
John purchased some shirts and trousers for $600. He paid $100 less fo  [#permalink]

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New post Updated on: 06 Mar 2016, 06:25
2
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

83% (02:05) correct 17% (02:22) wrong based on 70 sessions

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John purchased some shirts and trousers for $600. He paid $100 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?

A) 4
B) 5
C) 6
D) 7
E) 8

Originally posted by vinoo7 on 06 Mar 2016, 05:43.
Last edited by ENGRTOMBA2018 on 06 Mar 2016, 06:25, edited 2 times in total.
Reformatted the question and added the OA.
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Re: John purchased some shirts and trousers for $600. He paid $100 less fo  [#permalink]

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New post 06 Mar 2016, 06:00
vinoo7 wrote:
John purchased some shirts and trousers for $600. He paid $100 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?

A) 4
B) 5
C) 6
D) 7
E) 8


Follow posting guidelines (link in my signatures), do make sure to put the correct topic title and OA. Also, do not forget to mention the source of the question.

As for the question,

Let a,b be the number of shirts and trousers while S,T be the price of each shirt and each trouser respectively.

Thus, setting up the equations:

1) a*S+b*T = 600

2) a=5

3) -a*S+b*T = 100

4) T-S =20

4 distinct equations for 4 variables ---> solve the system to get, b=5.

From equations 1) + 3), 2b*T=700 ---> b*T=350 ---> a*S = 350-100=250 ---> as a=5 ---> S=50 $ per shirt

From 4), T= 50+20=70$ , hence b*T=350 ---> b = 350/70=5 trousers.

B is thus the correct answer.
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Re: John purchased some shirts and trousers for $600. He paid $100 less fo  [#permalink]

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New post 06 Mar 2016, 06:05
1
vinoo7 wrote:
John purchased some shirts and trousers for $600. He paid $100 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?

A) 4
B) 5
C) 6
D) 7
E) 8


Given that the total purchase of two items cost 600.
So the average purchase of one item will cost 600/2 = 300.
Its given as total shirt cost 100$ less. Hence Total Shirt cost = 300 - 50 and Total trouser cost = 300 + 50
5 shirts = 250$ ==> One shirt = 50$
One trouser = 50 + 20 = 70$
Total trousers = 350 / 70 = 5.
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Re: John purchased some shirts and trousers for $600. He paid $100 less fo  [#permalink]

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New post 26 Jul 2018, 05:35
S = Cost of a shirt
T = Cost of a trouser
N = Number of trousers

First equation: S = T - 20

Second equation: 5S + 100 = N*T

Resolution:

5(T - 20) + 100 = N*T
5T - 100 + 100 = N*T
5T = N*T
N = 5

Option B.
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Re: John purchased some shirts and trousers for $600. He paid $100 less fo  [#permalink]

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New post 30 Jul 2018, 11:48
2
vinoo7 wrote:
John purchased some shirts and trousers for $600. He paid $100 less for the shirts than he did for the trousers. If he bought 5 shirts and the cost of a shirt is $20 less than that of a trouser, how many trousers did he buy?

A) 4
B) 5
C) 6
D) 7
E) 8



Let s be the cost of the shirts; then the cost of the trousers is (s + 100). We know

s + s + 100 = 600

2s + 100 = 600

2s = 500

s = 250

Since he bought 5 shirts, each shirt costs 250/5 = $50. Since the cost of a shirt is $20 less than that of a trouser, each trouser costs 50 + 20 = $70. Since he paid 600 - 250 = $350 for trousers, he bought 350/70 = 5 trousers.

Answer: B
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Re: John purchased some shirts and trousers for $600. He paid $100 less fo &nbs [#permalink] 30 Jul 2018, 11:48
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