In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg

Question

In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?

A. 3:2 
B. 3:4
C. 3:5
D. 4:5
E. 5:9

chetan2u · Accepted Answer

STEP I : Find the average price without gain  
Gain of 10%=110x/100, if x is the average
So  68.20=\frac{110x}{100}.........x=\frac{682}{11} = 62

STEP II : Use weighted average method to find the ratio  
60....62........65
So 60:65= \frac{65-62}{62-60} =3/2=3:2

A

dvishal387 · Answer

Let x be the cost he incurs. So, Selling price = 1.1x
=>1.1x=68.2=>x =62= The price he incurs
Assume x be the amount of 60/kg tea and y amount of 65/Kg are mixed
Now, (60x+65y)/(x+y)=62=>2x=3y
So, 3:2 i.e option A is the correct choice.

vishusahni9 · Answer

68.2/1.1 = 62

Now use allegations

60 65
 62
(65-62):(62-60)

3:2 ratio

gracie · Answer

let x and y=two varieties
60x+65y=10/11*68.2*(x+y)
2x=3y
x/y=3/2
3:2
A

ScottK · Answer

I understand what the problem is trying to say, however, to say that he gains 10% does not mean the same as making a 10% profit. Please correct that.

Abhishek009 · Answer

It simply means that 68.20 is 110% of COst Price....

Hope this helps!!

mdsaddamforgmat · Answer

what if in the above answer choices we have both 3:2 and 2:3 options?

Manicks · Answer

10% of 68.20 = 6.82
68.20-6.82=61.38
Therefore, tea worth Rs. 60 per kg is in a higher ratio in the mixture.

So, we can eliminate options B to E as the tea worth Rs. 65 per kg is the higher ratio in the mixture.

Ans: A. 3:2

jaisonsunny77 · Answer

Here's the step wise explanation for this problem.

ShreyasJavahar · Answer

Thanks for the detailed explanation. Your last step needs a slight modification, it's A/B = 3.3/2.2 whereas you've got B/A = 3.3/2.2

yashikaaggarwal · Answer

We can solve it using allegation and teeter totter method as well..

Teeter Totter Method :
68.20 is 110% value. 
62 is the original price of the mixture.
Since 62 is more inclined towards 60 price. That means the average of the mixture have more quantity of 60$ mixture.
If it have been costing 63$, the mixture would had more of 65$ mixture in it.

The only option with 60$ mixture more than 65$ is A

Or,

Allegation :

60_____:_____65
_______62_______
3______:______2

So, 60$ mixture is mixed in 3 parts. Whereas 65$ mixture is mixed in 2 parts.

Option A is the Answer.

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Vaibs146 · Answer

Let 'x' be the amount of the Rs. 60 a Kg mixture 
Let 'y' be the amount of the Rs. 65 a Kg mixture

Therefore, the equation will be as follows

(60x + 65y) * 110/100 = 68.20 (x+y) .
6600x + 7150y = 6820x + 6820y 
6600x - 6820x = 6820y + 7150y
-220x = -330 y

From this, we obtain the ratio 3:2.

Option A is the answer.

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In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg

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In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg

Prep Toolkit

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