The ratio of a compound, by weight, consisting only of substances

I did it in 4 mins seeing the average time for correct solution is just 2 min I feel embarrassed......

Ratio x/y=4/6 is halved ; x/y=2/6
Ratio x/z=4/10 tripled now the ratio will be x/z= 12/10
x/y = 12/36 , multiplied by factor of 4 inorder to equate with the ratio x/z
Now,
x:y:z = 12:36:10 =6:18:5

x= 12/(6+18+5) * 58 = 12 Ans.........

Question ask for weight of X in the changed compound

Solve:
Original Ratio is: X:Y:Z = 4:6:10 simplify to 2:3:5

Ratio of X to Y halved:\(\frac{X}{Y} = \frac{2}{3} * \frac{1}{2} = \frac{2}{6} = \frac{1}{3}\)

Ratio of X to Z tripled: \(\frac{X}{Z} = \frac{2}{5} * 3 = \frac{6}{5}\)

Convert to new ratio by find an element that appear in the two ratios and find LCM of this common element by multiply its ratio together, in this case this element is X

X to Y is 1:3 and X to Z is 6:5

LCM is 6 ( 1 x 6)

Convert RATIO OF X to Y by multiply by 6: 1:3 to 1(6) : 3(6) = 6 : 18

Ratio of X to Z is 6:5

New ratio of X:Y:Z is : 6:18:5 = 6x+18x+5x = 29x

Total weight of the changed compound is 58 so: 58=29x ==> x = 2

Weigh of substance X in the changed compound is : 6x = 6*(2) = 12

Correct Answer: D

1) The old ratio of x to y was 4:6. If this ratio is cut in half, then the new ratio of x to y is 2:6.
2)The old ratio of x to z was 4:10. If this ratio is tripled, then the new ratio of x to z is 12:10.
3) In order to combine these two ratios into a new ratio of x:y:z, we must rewrite them so that the element in common, x, has the same coefficient. With the same x-coefficient, we can compare the ratios of x:y and x:z. Using a multiplier of 6 on the first ratio (x:y = 2:6) yields x:y = 12:36.
4)Since the new ratio of x:z is 12:10, we can combine the new x:y ratio that we multiplied by 6/6 with the new x:z ratio in order to arrive at an x:y:z ratio of 12:36:10. In other words:
x:z = 12:10
x:y = 12:36
With 12 as a common term:
x:y:z = 12:36:10
5) In order to find the weight of substance x in the total changed compound, set up an equation of the combination:
x + y + z = 58 lbs
6) Now substitute an unknown multiplier, m, for each quantity to ensure that the ratios are enforced in the equation (x=12m, y=36m, z=10m):
12m + 36m + 10m = 58 lbs
Note: The unknown multiplier is the ratio by which the 12:36:10 ratio holds true. In other words, if m = 1, the substances will be in the ratio of 12:36:10. If m = 2, the substances will be in the ratio of 12(2):36(2):10(2) = 24:72:20
7)Combining like terms simplifies the equation to 58m=58.
8)Dividing through by 58 shows a multiplier of m=1.
9)Using this multiplier in the original equation we set up, we can see that the weight of x=12(1)=12.
Thus, 12lbs or D is correct.

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