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Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth

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Bunuel
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Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink] New post   10 Dec 2020, 05:00
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Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed together to be sold at $1.30 per kg. In what ratio should this wheat be mixed?

A. 1:2:3
B. 1:1:2
C. 2:1:3
D. 2:2:3
E. 2:2:5
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sudeshpatodiya
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Re: Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink] New post   10 Dec 2020, 05:27
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Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed together to be sold at $1.30 per kg. In what ratio should this wheat be mixed?

A. 1:2:3
B. 1:1:2
C. 2:1:3
D. 2:2:3
E. 2:2:5


Average = Avg = 1.30 $/kg
Let three prices be, A=1.27, B=1.29, C=1.32

See how the different parts affect the average. Is it surplus or deficit.

Average Deficit is introduced by A and B
A-Avg = 127-130 = -3
B-Avg = 129-130 = -1

Surplus is introduced by C
C-Avg = 132-130 = 2

Now, for each unit of A and B, total Deficit = -4
For each unit of C, Surplus = 2

So, we need 2 units of C to compensate each unit of A and C combined to get the final average deviation as zero.

So, Ratio of A:B:C = 1:1:2

(B)
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CEdward
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Re: Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink] New post   13 Jan 2021, 21:25
Is there a faster way to do this then to use the weighted average formula?
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Re: Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink] New post   02 Mar 2021, 04:07
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A faster way to do this would be to realize that the seller is not going to take a loss in selling, also as profit margin is not mentioned, there is no profit either.
Selling price = Cost price, so the CP has to be a multiple of the three wheats' combined CP.

A)1.27+2.58+3.96=7.81 not a multiple of 1.3
B)1.27+1.29+2.64=5.20 multiple of 1.3 => Our ans is B
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Re: Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink] New post   15 Mar 2024, 08:18
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Bunuel wrote:
Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed together to be sold at $1.30 per kg. In what ratio should this wheat be mixed?

A. 1:2:3
B. 1:1:2
C. 2:1:3
D. 2:2:3
E. 2:2:5

­Check using the options answer must be (B) -

\(\frac{1.27*1 + 1.29*1 + 1.32*2}{1 + 1 + 2} = 1.30\)
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Re: Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink] New post   18 Mar 2024, 23:28
Care to explain your last 2 lines? Thank you
sudeshpatodiya wrote:
Quote:
Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed together to be sold at $1.30 per kg. In what ratio should this wheat be mixed?

A. 1:2:3
B. 1:1:2
C. 2:1:3
D. 2:2:3
E. 2:2:5

Average = Avg = 1.30 $/kg
Let three prices be, A=1.27, B=1.29, C=1.32

See how the different parts affect the average. Is it surplus or deficit.

Average Deficit is introduced by A and B
A-Avg = 127-130 = -3
B-Avg = 129-130 = -1

Surplus is introduced by C
C-Avg = 132-130 = 2

Now, for each unit of A and B, total Deficit = -4
For each unit of C, Surplus = 2

So, we need 2 units of C to compensate each unit of A and C combined to get the final average deviation as zero.

So, Ratio of A:B:C = 1:1:2

(B)

­
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Re: Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink] New post   26 Mar 2024, 14:09
this is how I did it, please let me know if this doesn't hold up

127x+129y+132z = 130(x+y+z)
2z=3x+1y <---- this is essentially a ratio, so the answer would have 2*(last number) be equal to 3*(first number) plus 1*(second number)

1:2:3 -> 3*1+1*2 =/= 2*3 doesn't work
1:1:2 -> 3*1+1*1=2*2 works, so it's B
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Re: Three types of wheat of $1.27, $1.29 and $1.32 per kg are mixed togeth [#permalink]
26 Mar 2024, 14:09
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