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Bulbul was paid for the pens?

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Bulbul was paid for the pens?

by sanju09 » Fri Jan 01, 2010 2:42 am
Bulbul bought 5 pens, 7 pencils and 4 erasers. Baiju bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what Bulbul had paid. What percent of the total amount paid by Bulbul was paid for the pens?

(A) 37.5
(B) 43
(C) 50
(D) 62.5
(E) Data Insufficient
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by Testluv » Fri Jan 01, 2010 3:49 am
sanju09 wrote:Bulbul bought 5 pens, 7 pencils and 4 erasers. Baiju bought 6 pens, 8 erasers and 14 pencils for an amount which was half more than what Bulbul had paid. What percent of the total amount paid by Bulbul was paid for the pens?

(A) 37.5
(B) 43
(C) 50
(D) 62.5
(E) Data Insufficient
Baiju has bought exactly twice the number of pencils and erasers that Bulbul has bought. Let the amount spent on pencils and erasers by Bulbul be x. Then, the amount spent by Baiju on pencils and erasers is 2x. Let the total amount that Bulbul paid be z. Then, the total amount that Baiju paid is 1.5z. Let price spent for each pen be y.

Then:

Bulbul: 5y + x = z

Baiju: 6y + 2x = 1.5z

and we need to solve for the fraction 5y/z (the fraction of total amount paid by Bulbul that was spent on pens). We can double Bulbul's equation, and then subtract Baiju's equation from that:

10y + 2x = 2z
6y + 2x = 1.5z
_____________

4y = z/2

y/z = 1/8; therefore, 5y/z = 5/8 or 62.5 percent.

Choose D.
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by Resurgent » Fri Jan 01, 2010 7:49 am
Testluv wrote:Baiju has bought exactly twice the number of pencils and erasers that Bulbul has bought. Let the amount spent on pencils and erasers by Bulbul be x. Then, the amount spent by Baiju on pencils and erasers is 2x. Let the total amount that Bulbul paid be z. Then, the total amount that Baiju paid is 1.5z. Let price spent for each pen be y.

Then:

Bulbul: 5y + x = z

Baiju: 6y + 2x = 1.5z

and we need to solve for the fraction 5y/z (the fraction of total amount paid by Bulbul that was spent on pens). We can double Bulbul's equation, and then subtract Baiju's equation from that:

10y + 2x = 2z
6y + 2x = 1.5z
_____________

4y = z/2

y/z = 1/8; therefore, 5y/z = 5/8 or 62.5 percent.

Choose D.
Haha...that was a lateral thinking solution. Good one.
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by Testluv » Fri Jan 01, 2010 12:33 pm
Haha...that was a lateral thinking solution. Good one.
Thanks. I don't know where sanju gets them, but these are pretty fun questions.
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by truplayer256 » Fri Jan 01, 2010 2:16 pm
I think he makes these up on his own but here's how I did the problem.

PS= The price of each pen.

PE=The price of each pencil.

E=The price of each eraser.

5PS+7PE+4E=p

6PS+14PE+8E=3p/2

Notice that 14PE+8E=2(7PE+4E)

7PE+4E=p-5PS

6PS+2(p-5PS)=3p/2

-4PS=-p/2

p=8PS

5PS/8PS=5/8=0.625
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by Testluv » Fri Jan 01, 2010 2:24 pm
I think he makes these up on his own but here's how I did the problem.
I think you're right!
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