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# At a certain stationery shop, the price of a pencil is 20 cents and th

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Math Expert
Joined: 02 Sep 2009
Posts: 55266
At a certain stationery shop, the price of a pencil is 20 cents and th  [#permalink]

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25 Sep 2018, 04:56
00:00

Difficulty:

65% (hard)

Question Stats:

69% (03:04) correct 31% (02:50) wrong based on 64 sessions

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At a certain stationery shop, the price of a pencil is 20 cents and the price of an eraser is 30 cents. A boy buys a total of 20 pencils and erasers from the shop, and the average (arithmetic mean) price of the 20 pieces comes to 28 cents. How many erasers must the boy return so that the average price of the pieces that he buys is 26 cents?

(A) 2
(B) 4
(C) 6
(D) 8
(E) 10

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Manager
Joined: 23 Nov 2017
Posts: 118
Location: Singapore
Concentration: Strategy, Other
Re: At a certain stationery shop, the price of a pencil is 20 cents and th  [#permalink]

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26 Sep 2018, 00:38
4
I did this by weighted averages.
Using allegation method, I get the ratio of pencils and erasers as 1:4

20 30
28
2 8 =2 : 8 = 1:4;
Splitting the total number of items in the above ratio, i know we have 4 pencils and 16 erasers.

Calculating weighted average for the average again, I get the new ratio as 2:3
20 30
26
4 6 = 4:6 = 2:3

Keeping the number of pencils as 4, i get the number of erasers as 6.
Subtracting 6 from 16, i get 10, which is the correct answer.

Help me with a kudo!
Senior Manager
Joined: 02 Apr 2014
Posts: 477
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
At a certain stationery shop, the price of a pencil is 20 cents and th  [#permalink]

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23 Oct 2018, 23:40
1
1
Let E be number of erasers to be returned
so (28 * 20) - 30E = (20-E) * 26
560 - 30E = 520 - 26E
solving we get, E = 10 => Option (E)
At a certain stationery shop, the price of a pencil is 20 cents and th   [#permalink] 23 Oct 2018, 23:40
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