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

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

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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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