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let b = weight of base, f = weight of fragrance, g = weight of gel. Let w be the total weight

b +f + g = w -- > initial case

b + b/3 +f +g = w + b/3 -- > final case

Statement 1

Initial f = 1/5 w
final f = 1/6(w+b/3)
f = f ==> 1/5w = 1/6(w + b/3)

solving for b/w = 3/5 . Statement 1 alone is sufficient

Statement 2
in final case, weight of b/ total weight = 2/3
(b+b/3)/(w+b/3) = 2/3

solving 4b = 2w + 2/3b
b/w = 3/5

Statement 2 alone is sufficient

Each statement alone is sufficient. Option B
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Both Statements are sufficient

sol
Let us assume the total base = 15

So the base liquid was increased by = 1/3

1) After the addition of base liquid , the ratio of F/W decreased from 1/5 to 1/6

so 1/5 of 15 = 15/5 = 3 grams of fragrance
But the F weight did not change but base liquid was added to total weight increasing it by 1/6

so new total weight = 15 + 3 = 18 grams

So base liquid = 18 -15 = 3 grams of base was added

So 1/3 of the base is 3 grams so total base = 3x3 = 9
Ration of base to total weight = 9/15 = 3/5

Statement is sufficient

2) After the addition on base liquid , the ration of weight of base liquid to total = 2/3

let us assume total weight to be 12

So 12 x 2/3 = 8 grams of new base

The original w was increased by 1/3
8 grams is 4/3 of the original base so
6 grams is the original base


So base grew from 6 to 8 grams so 2 grams are added to the , 12- 2 = 10 - original

final ratio = 6/10 = 3/5


Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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After addition
Base=4b/3
total=t+b/3

we need b/t?

statement 1
f/t=1/5
f/(t+b/3)=1/6

equate f,

t/5=(t+b/3)/6
solve and we get b/t=3/5

SUFFICIENT

statement 2

given
(4b/3)/(t+b/3)=2/3

this too can be solved to get b/t=3/5
SUFFICIENT

hence both are suffiecient, option D IMO
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total weight before: t1 = b+f+g
ratio before: r1 = b/t1

total weight after: t2 = t1 + b/3
ratio after: r2 = (4b/3)/t2

r1?

(1)
f/t1 = 1/5 -> f = t1/5
f/t2 = 1/6 -> f = t2/6

t1/5 = t2/6 -> t2 = 6t1/5

As t2 = t1 + b/3 -> 6t1/5 = t1 + b/3 -> b = 3t1/5

r1 = b/t1 = 3/5

Sufficient

(2)
r2 = (4b/3)/t2 = 2/3
4b/t2 = 2
t2 = 2b

As t2 = t1 + b/3 -> 2b = t1 + b/3 -> 6b = 3t1 + b -> b = 3t1/5

r1 = b/t1 = 3/5

Sufficient

IMO D
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We know that,
Liquid formula consists of base liquid, fragrance oil and gel stabilizer
Let,
Weight of base liquid = b
Weight of fragrance oil = f
Weight of gel stabilizier = g

Initial ratio of base liquid = b/ b+g+f

We know that 1/3rd base liquid was added more to the formula.
=> New total weight = 4b/3 + f + g
But we need to find ratio of initial base liquid to the total weight

We are given statements,
STatements(1) -> After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6

Initial fragrance oil ratio
=> f /b+f+g = 1/5
=> b+f+g = 5f. ---- 3

After the addition the fragrance ratio
=> f/(4b/3) + f + g = 1/6
=> 4b/3 + f + g = 6f. ------4

Now subtracting both the equations 3 and 4 we get,
4b/3 + f + g -(b+f+g) = 6f - 5f
=> b = 3f

Substituting this in 3 we get,
3f+f+g = 5f
=> g = f

Initial ratio = 3f/3f+f+f = 3/5

Statement(1) is sufficient

Statement(2) -> After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3

=> (4b/3)/(4b/3)+f+g = 2/3
=> 2b/3 = f + g

Initial Ratio = b/b + (f+g) = b/(b + (2b/3)) = 3/5

Statement (2) is sufficient

D. Each statement alone is sufficient
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Total formula T= b+f+g we need the old ratio of B/T ??

ST 1 Old ratio of F >> f/T =1/5--eq1 and new ratio f/1/3b+t =1/6 ---eq2 >> f=t/5 substitute in eq 2 gives f/+3t/3>> 3f/b+3t=1/6 gives us 18f=b+3t and we know f=t/5 which gives us 18t/5= b+3t solving b=18t-15t/5 which is b=4t/5 and b/t=3/5

ST 2 4/3B /1/3B+T=2/3 >> 4B=2/3B+2T which gives 10b/3 =3t and b/t=3/5

ans D
Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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original weight: T = B + F + G
after weight: TA = B + F + G + B/3 = T + B/3

As we need to find B/T then we need to find a relation between TA and T or between TA and B.

(1)
F/T = 1/5
F/TA = 1/6

F = T/5 = TA/6
TA = 6T/5 -> relation between TA and T

TA = 6T/5 = T + B/3
T/5 = B/3
B/T = 3/5

Condition (1) is sufficient

(2)
(4B/3)/TA = 2/3
2B/TA = 1
TA = 2B -> relation between TA and B

2B = T + B/3
6B = 3T + B
5B = 3T
B/T = 3/5

Condition (2) is sufficient

The answer is D
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Assume base liquid be b, fragrance oil o, and gel stabilizer g. Base liquid changed to 4/3b (Total = b+f+g)
S1 Use the LCM of the fractions which is 30 meaning the initial total weight is 30 and the new weight is 36 and since only b changed it means b changed by 6 so we can find b given that 4/3b-b=6 hence sufficient
S2 This means 4/3b/t+1/3b=2/3. You simplify this and you get 10b=6t meaning b/t=3/5 hence sufficient
Ans D
Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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Let the original weights of Base liquid, Fragrance Oil and Gel be b, f and g respectively
Total weight T = b + f + g

We need to find out the ratio b/T

Lets look at statement 1
Before addition: f/T = 1/5
After addition: f/(T + b/3) = 1/6

Divide both the equations and we would get b/T = 3/5 (Definite value)

Lets look at statement 2 now
After addition: (b + b/3)/(T + b/3) = 2/3
Solve the equation and we would get b/T = 3/5 (Definite value)

Hence option D is the correct answer

Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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So this one is a tricky question if the method adopted is not understood properly:

Let the total weight ordinarily = B + F + G
W(new) = B + 1/3B + F + G = 4/3B + F + G

Now according to Statement 1:
We need to find the ratio of fragrance oil to the total weight of the formula which decreased from 1/5 to 1/6. Representing this in equation form we get:

F / 4/3B + F + G = 1/6

However, trying to solve this we could not solve for F alone because we are not able to gauge the value of B or G. Hence the Statement No. 1 is insufficient.

Now moving on to Statement 2:

Statement 2 asks us for the ratio of weight of base liquid to the total weight is 2/3. In equation form:

4/3B divided by W(New) = 2/3

2W = 4B
Hence W = 2B.

Now that we have this we incorporate it into the weight formula already derived:

W = 4/3B + F + G
2B = 4/3B + F + G

2B - 4/3B = F + G

2/3B = F + G

We can again incorporate F + G into the Weight formula

W = 4/3B + 2/3B = 2B

So B/W = 1/2 Hence the ratio is 1/2 and using Statement No 2 we can solve the ratio of Base Liquid to the Total weight. Hence Statement 2 is sufficient
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IMO - ANS is C
Given - Base Liquid (x), Fragrance oil (y) & Gel Stabilizer (z) => then Base Liquid is increased to 1/3 so now 1.33x and y& z remain same ask is x/(x+y+z)
Statement 1 give y/x+y+z = 1/5 and y/(1.33x+y+z) =1/6 so we get the ratio of total old to total new but not the ratio of x/old total.
Statement B gives 1.33x/1.33x + y + z = 2/3 so B also insufficient
Combining both will give the required ratio

from Statement B we get 1.33x = 2*(1.33x +y + z)/3 & from statement 1 = > 1.33x +y +z = 6/5 (x+y+z) we can get easily x/x+y+z so ans is C combining both. Thanks!
Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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The question is the ratio of BL : (BL+FO+GS) before the increase (adding 1/3 BS to all)

(1) FO : (BL+FO+GS) -> 1:5 become 1:6 -> meaning we can calculate the increase of BL -> can caculate the initial ratio
Sufficient

(2) BL : (BL+FO+GS) = 2:3 (after the increase) -> cannot decide the comparison before it was added.
Insufficient

So the answer is A.
Bunuel
A cosmetics lab prepared a liquid formula that consisted of base liquid, fragrance oil, and gel stabilizer. The weight of the base liquid in the formula was increased by 1/3 by adding more base liquid, while the weights of the fragrance oil and gel stabilizer remained unchanged. Before this increase, what was the ratio of the weight of the base liquid to the total weight of the formula?

(1) After the addition of base liquid, the ratio of the weight of fragrance oil to the total weight of the formula decreased from 1/5 to 1/6.

(2) After the addition of base liquid, the ratio of the weight of base liquid to the total weight of the formula became 2/3.


 


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Given:
B + F + G = T
(4/3)B + F + G = New T

(A)
F/New T = 1/6
F/T = 1/5
Dividing
New T/T = 6/5 =1 + 1/5

This means (1/5T) =(1/3)B which is the increase This is sufficient to identify B/T

(B) (4/3)B by New T = 2/3
=> New T by (4/3)B =3/2
((1/3)B +T) by (4/3)B = 3/2
We can solve ahead hence this is sufficient too

(D) is the answer
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Let the total weight of Base liquid be x, fragrance be y and gel stabilizer be z
Total weight of the solution will be = x+y+z
It is also given that when x/3 is added, y and z remains unchanged - Accordingly, the total of new solution has the weight of = x+y+z+ 1/3 x = Original Weight + 1/3 x
The question has asked us to find the ratio of x/(x+y+z)

Option 1 - After adding 1/3 x, ratio of y/(x+y+z) has changed
Original Ratio = > 1/5 = y/(x+y+z)
New Ratio => 1/6 = y ( x+y +z+ 1/3x)

Since we have 2 equations we can solve to get the answer and hence Statement 1 is sufficient

Option 2 - This mentions that after addition of 1/3x, the ratio of the (x+1/3x)/ (x+y+z+1/3x )= 2/3
This is a little confusing since we don't have 2 equations, we might think that this is not sufficient, but we are not required solve for individual x, y or z, we just want the ratio x/ x+y+z

Accordingly, on simplifying the ratio, we get -> (4x/3)/(4x/3 + y+ z) = 2/3
4x/(4x+3y + 3z) = 2/3
4x/(3(x+y +z)+ x) = 2/3
2x = 2/3 ((x+y+z) +x/3)
x -x/6 =1/3 (x +y +z)
5/6 x = 1/3 (x+y+z)
5/2 x = x+y +z

Hence we are able to get solution, this is also sufficient

Correct answer is Option D
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