A nut mix contains, by weight, 20 percent peanuts and...

[swerve]

A nut mix contains, by weight, 20 percent peanuts, and 80 percent cashews. If the mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A. 10%
B. 12.5%
C. 15.0%
D. 22.5%
E. 25.0%

The OA is B.

I think that I can solve this PS question in the following way,

Let the price of 100g peanuts be 100$.

So the price of 100 g mix = 110(20 g peanut + 80 g cashews).

Now 500 g mix will be 550(100 g peanut+400 g cashew).

As we know the price of 100 g peanut is 100; the price of 400 g cashews is 450.

So (450/400)*100=112.5, 12.5% more than the price of 100 g peanuts, right?

Is there a strategic approach to this question? Can any experts help, please?

[mbawisdom]

A nut mix contains, by weight, 20 percent peanuts, and 80 percent cashews. If the mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A. 10%
B. 12.5%
C. 15.0%
D. 22.5%
E. 25.0%

The OA is B.

I think that I can solve this PS question in the following way,

Let the price of 100g peanuts be 100$.

So the price of 100 g mix = 110(20 g peanut + 80 g cashews).

Now 500 g mix will be 550(100 g peanut+400 g cashew).

As we know the price of 100 g peanut is 100; the price of 400 g cashews is 450.

So (450/400)*100=112.5, 12.5% more than the price of 100 g peanuts, right?

Is there a strategic approach to this question? Can any experts help, please?

P = cost of bag of peanuts
C = cost of bag of cashews
T1 = cost of mixture 1
T2 = cost of mixture 2

T1 = 0.2P + 0.8C
T2 = 1P

We know that T1 = 1.1T2
0.2P + 0.8C = 1.1(P)
0.8C = 0.9P
C/P = 0.9/0.8 = 1.125

Cashews cost 12.5% more than Peanuts
Answer = B.

[Jeff@TargetTestPrep]

A nut mix contains, by weight, 20 percent peanuts, and 80 percent cashews. If the mixture costs 10 percent more than the cost of an equal quantity of pure peanuts, by what percent are cashews more expensive than peanuts?

A. 10%
B. 12.5%
C. 15.0%
D. 22.5%
E. 25.0%

We can assume that are 10 lbs of mixed nuts; so there are 2 lbs of peanuts and 8 lbs of cashews. We can also assume that the peanuts cost $10 per pound; so the mixed nuts cost $11 per pound. Now if we let c = the cost of cashews, we have:

2(10) + 8c = 10(11)

20 + 8c = 110

8c = 90

c = 90/8 = 45/4 = 11.25

Thus, the cashews are (11.25 - 10)/10 = 1.25/10 = 0.125 = 12.5% more expensive than the peanuts.

Answer: B