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

Question

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

sudeshpatodiya · Accepted Answer

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)

Yeetyeti38 · Answer

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

CEdward · Answer

Is there a faster way to do this then to use the weighted average formula?

Biddu86 · Answer

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

Abhishek009 · Answer

Check using the options answer must be (B) -

\frac{1.27*1 + 1.29*1 + 1.32*2}{1 + 1 + 2} = 1.30

einstein801 · Answer

Care to explain your last 2 lines? Thank you

Adit_ · Answer

Take the ratio of A:C using the allegation method u get:
2:3

Similarly do it for B:C:
2:1

The reason to pick these two ratios is because u need one value always higher that the mean value for weighted averages to work

Now arrange it properly
B:C=2:1
A:C=2:3

We need to add the ratios of C since it is added twice

A:B:C = 2 : 2 : 3+1

Simplifying you get 1:1:2

Adit_ · Answer

Usually substituting values and checking will take less time but in this particular case working it out is faster.
Solving with allegations for 2 cases will take max 20 seconds and then just need to arrange and simplify should definitely take less than a minute once the idea is there.

shreyans0311 · Answer

A: $1.27
B: $1.29
C: $1.32

You want to maintain average price of $1.30 per kg

For every kg of A, you drive the average price down by $0.03 (i.e. 1.30-1.27 = -0.03)
For every kg of B, you drive the average price down by $0.01 (i.e. 1.30-1.29 = -0.01)
For every kg of C, you drive the average price up by $0.02 (i.e. 1.32-1.30 = +0.02)

What ratio of the 3 quantities will result in zero movement of the average price?

Answer: (1kg*(-0.03) + 1kg*(-0.01) + 2kg*(+0.02)) = 0

nemoquaerat · Answer

Correct answer is B. This is how I thought about it -

Average of 1.27 and 1.29 is 1.28. Average of this 1.28 and 1.32 is what we require i.e 1.30.

To get 1 kg of 1.28 I need to mix half of 1.27 and 1.29 and then I can mix that with 1kg of 1.32 . the resultant can be sold for 1.3 per kg.

That makes the ratio .5:.5:1

multiplying by 2 gives us 1:1:2

RohanNewDelhi · Answer

that is a great way of doing it

shahsahil2101 · Answer

This is the fastest way to do it. Especially when ratios are given

Fictional26 · Answer

"The reason to pick these two ratios is because u need one value always higher that the mean value for weighted averages to work"
 Does this line mean that you took the value 1.32 twice because it is higher than 1.30?

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards