In what ratio must a person mix three kinds of tea costing $60/kg, $75

Question

In what ratio must a person mix three kinds of tea costing $60/kg, $75/kg and $100 /kg so that the resultant mixture when sold at $96/kg yields a profit of 20%?

A. 1 : 2 : 4
B. 3 : 7 : 6
C. 1 : 4 : 2
D. 1 : 4 : 3
E. 1 : 4 : 4

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Kinshook · Accepted Answer

Asked: In what ratio must a person mix three kinds of tea costing $60/kg, $75/kg and $100 /kg so that the resultant mixture when sold at $96/kg yields a profit of 20%?

Cost of price of mixture required = $96/1.2 = $80

A. 1 : 2 : 4; Cost price of mixture = 80 + (-20) + 2(-5) + 4(20) = $130: Incorrect
B. 3 : 7 : 6; Cost price of mixture = 80 + 3(-20) + 7(-5) + 6(20) = $105: Incorrect
C. 1 : 4 : 2; Cost price of mixture = 80 + (-20) + 4(-5) + 2(20) = $80: Correct
D. 1 : 4 : 3; Cost price of mixture = 80 + (-20) + 4(-5) + 3(20) = $100: Incorrect
E. 1 : 4 : 4; Cost price of mixture = 80 + (-20) + 2(-5) + 4(20) = $120: Incorrect

IMO C

azamatboden · Answer

is there an alternative solution?

priyabaheti · Answer

In what ratio must a person mix three kinds of tea costing $60/kg, $75/kg and $100 /kg so that the resultant mixture when sold at $96/kg yields a profit of 20%?

A. 1 : 2 : 4
B. 3 : 7 : 6
C. 1 : 4 : 2
D. 1 : 4 : 3
E. 1 : 4 : 4

Can someone please provide a solution to this question?
thanks in advance

testtakerstrategy · Answer

Bunuel , can you please explain the wording here? "yields a profit of 20%?" and how that is derived into a formula??

harshittahuja · Answer

By checking options one by one
I got the answer c 
As Cost price of mixture =96/1.20= 80

Posted from my mobile device

ABHISEKGMAT123 · Answer

We can have multiple ratio to satisfy the situation. Solving through options is the right way, I guess.

Racer22 · Answer

I solved this problem using 3 way ratio as follows:

Firstly, assuming x = cost price 
1.2x = 96
x=96/1.2 = 80

Using the number line method:

60-----------75---80---------100

Distance between 60 to 80 = 20
Distance between 75 to 80 = 5
Distance between 100 to 80 = 20
The distance between 60 to 80 and 80 to 100 are same, however, the 75/kg price pulls down the average, also, the minimum quantity for 100/kg is 20, 
So, 5 X  4  =20
Total on LHS = 20 +20 =40
RHS = 20 X 2  =40
So final ratio = 1 : 4 : 2

Please comment whether this is an acceptable way to solve the problem.

KarishmaB · Answer

If the selling price is $96 and profit is 20%, it means the cost price is $80. 20% of $80 will be $16. Familiarity with numbers will help you see it quickly. If not, use the formula
 \frac{Profit}{100} = \frac{SP}{CP} - 1

Avg of some ratio of 60, 75 and 100 should be 80. One simple case is 50% $60 tea and 50% $100 tea but that is not in the options. We must mix $75 tea too. Since 3 of the options have $60 and $75 in the ratio 1:4, I will check that first.

Visualise the scale method. The distance of 15 between them in split in the ratio 4:1 i.e. 12 and 3. So average is 12 away from $60 i.e. their avg is $72.

Now the avg of $72 and $100 should be $80. So again visualise the scale or use the formula

\frac{w1}{w2} = \frac{A2 - Avg}{Avg - A1} = \frac{100 - 80}{80 - 72} = \frac{5}{2}

For 5 parts of $72, we need 2 parts of $100. Hence 1:4:2 works. (1 part of $60 and 4 parts of $75 give 5 parts of $72. So we need 2 parts of $100 now)

Answer (C)

Learn all about Percentages and weighted averages by registering for the free Super Sunday tomorrow. Details in my signature.

Jayesh20201 · Answer

A Quick and reasonably simple method is to rely on 3 foundations: 
1. What is cost price based on profit. 
 120/100 (Cost) = 96 since 96 accommodates 20% Profit. 
 Therefore: Cost is 80

2. Since cost is 80, the answer would be easier to find as it will be a multiple of 80, easier to discern than some other value.

3. Trial and error with ratios. Since the percentages are 60/75/100: Question will be in a format: 
 60x + 75y + 100z/x+y+z = x+y+z(80)

Here use trial and error and it will be easy to rule out what is not a multiple of 80 and what is. 
 C forms the answer sequence and fits in it, answer cannot be anything else.

HarshavardhanR · Answer

- Selling the mix at $96/kg yielded a profit of 20%

This means that Selling Price of the mixture = 1.2 Cost Price of the mixture.

So,

Cost Price of the mixture = 96/1.2 =  $80/kg .

Let the 3 types of tea be mixed in the ratio of a:b:c.

Overall Cost Price of the mix =  \frac{(60a + 75b + 100c) }{ (a + b + c)}  = $80/kg

Simplifying this,

60a + 75b + 100c = 80a + 80b + 80c
=> 20c = 20a + 5b
=> 4c = 4a + b

We can use the choices here . For which of the five choices of a:b:c is 4c = 4a+b?

We can see that only choice C fits.

1:4:2 ->

-> 4c = 8
-> 4a + b = 4(1) + 4 = 8

Answer: Choice C.  1:4:2 .

---
Harsha

JayBKK · Answer

Identify that cost is 96/1.2 = 80.

Find the answer choice that cost total is 80.

Checking each answer choices,

A. 1 : 2 : 4
= 1/760 + 2/775 + 4/7*100
= (60 + 150 + 400)/7
= 610/7 ≈ 87.14 → Incorrect

B. 3 : 7 : 6
= 3/1660 + 7/1675 + 6/16*100
= (180 + 525 + 600)/16
= 1305/16 ≈ 81.56 → Incorrect

C. 1 : 4 : 2
= 1/760 + 4/775 + 2/7*100
= (60 + 300 + 200)/7
= 560/7 = 80 → Correct

D. 1 : 4 : 3
= 1/860 + 4/875 + 3/8*100
= (60 + 300 + 300)/8
= 660/8 = 82.5 → Incorrect

E. 1 : 4 : 4
= 1/960 + 4/975 + 4/9*100
= (60 + 300 + 400)/9
= 760/9 ≈ 84.44 → Incorrect

luisdicampo · Answer

Deconstructing the Question  
 
Teas cost  60 ,  75 , and  100  per kg.

The mixture is sold at  96  per kg with a  20%  profit.

So selling price =  1.2 	imes  cost price, hence the required cost price of the mixture is:

\frac{96}{1.2} = 80

Now we need a ratio that gives a weighted average cost of  80 .

Step-by-step

Start by testing with the most similar answers so C, D, E

Test option C  1:4:2 :

Total cost:

1\cdot 60 + 4\cdot 75 + 2\cdot 100 = 60 + 300 + 200 = 560

Total parts:

1+4+2=7

Average cost:

\frac{560}{7} = 80

So the required ratio is  1:4:2 .

Answer: C

kaalibilli · Answer

The fastest way to do this is- SP is 96 with a profit of 20% so CP is CP+ 0.2*CP = SP, => 96/1.2 = CP = 80

Now, just check each of the options, add the ratios and multiply by 80, and multiply individual ratios to their prices.

Eg: 
A. 1 : 2 : 4- sum of ratios is 7, so total should be 560. 1*60 + 2*75 + 4*100 = 610 eliminated
B. 3 : 7 : 6 sum of ratios is 16, so total should be 1280. 3*60 + 7*75 + 6*100 = 1305 eliminated
C. 1 : 4 : 2 sum of ratios is 7, so total should be 560. 1*60 + 4*75 + 2*100 =560 RIGHT ANSWER- STOP!
D. 1 : 4 : 3
E. 1 : 4 : 4

kaalibilli · Answer

The fastest way to do this is- SP is 96 with a profit of 20% so CP is CP+ 0.2*CP = SP, => 96/1.2 = CP = 80

Now, just check each of the options, add the ratios and multiply by 80, and multiply individual ratios to their prices.

Eg: 
A. 1 : 2 : 4- sum of ratios is 7, so total should be 560. 1*60 + 2*75 + 4*100 = 610 eliminated
B. 3 : 7 : 6 sum of ratios is 16, so total should be 1280. 3*60 + 7*75 + 6*100 = 1305 eliminated
C. 1 : 4 : 2 sum of ratios is 7, so total should be 560. 1*60 + 4*75 + 2*100 =560 RIGHT ANSWER- STOP!
D. 1 : 4 : 3
E. 1 : 4 : 4

In what ratio must a person mix three kinds of tea costing $60/kg, $75

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GMAT Problem Solving (PS) Questions

In what ratio must a person mix three kinds of tea costing $60/kg, $75

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