In what proportion must rice at $0.8 per pound be mixed with rice at

IMO E
Ratio :- 0.075/0.025 = 3:1

Differential approach is my favourite in this type:

0.8----0.825-----------0.9

No need any counting, 0.825 is three times closer 0.8 than 0.9. So, the ratio is 3:1

E

We can solve this using weighted averages

Weighted average of groups COMBINED = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Let C = pounds of Cheap flour ($0.8 per pound) needed
Let E = pounds of Expensive flour ($0.9 per pound) needed
So, the TOTAL weight = C + E
The proportion of Cheap Flour in the final mix = C/(C+E)
The proportion of Expensive Flour in the final mix = E/(C+E)

Plug all values into formula to get: 0.825 = [C/(C+E)][0.8] + [E/(C+E)][0.9]
Simplify: 0.825 = 0.8C/(C+E) + 0.9E/(C+E)
Simplify: 0.825 = (0.8C + 0.9E)/(C+E)
Multiply both sides by (C+E) to get: 0.825(C+E) = 0.8C + 0.9E
Expand: 0.825C + 0.825E = 0.8C + 0.9E
Subtract 0.8C from both sides: 0.025C + 0.825E = 0.9E
Subtract 0.825E from both sides: 0.025C = 0.075E
This is the same as: 25C = 75E
And this is the same as C = 3E

This tells is that C is 3 TIMES the value of E
So, the ratio C : E = 3 : 1

Answer: E

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8 ---- 8.25 ---- 9 = 0.75 -----------0.25

So, the required ratio is 3:1 , answer will be (E)

use allegation method
we get
ratio 3:1
IMO E

Using Allegation:
0.8 0.9

0.825

To make the calculation easier, we multiply all of them with the LCM of the fractions which is 1000.

Now, we get
800 900

825
75 : 25
3 : 1

Therefore, the answer is E.

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Solution:
Let Qty of Type A rice be X and Qty of Type B rice be Y
0.8X + 0.9Y = 0.825 (X+Y)
0.8X + 0.9Y = 0.825X + 0.825Y
X/Y = 3:1
Answer is E

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Weighted average can be used to solve this problem. In my case, I did a series of trial and error. Final solution is as follows:

Step 1: 0.8(3) + 0.9(1) = 0.33
Step 2: 0.33 / 4 = 0.825

E is our answer.