Aptitude - Alligation or Mixture - Discussion

Discussion :: Alligation or Mixture - General Questions (Q.No.5)

5. 

In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 16.50 kg?

[A]. 3 : 7
[B]. 5 : 7
[C]. 7 : 3
[D]. 7 : 5

Answer: Option C

Explanation:

By the rule of alligation:

Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind
Rs. 15 Mean Price
Rs. 16.50
Rs. 20
3.50 1.50

Required rate = 3.50 : 1.50 = 7 : 3.


Ladli said: (Jun 8, 2011)  
How you got 3.50 and 1.50? Please tell me.

Manasa said: (Jun 10, 2011)  
@ladli
(20-16.50):(16.50-15)=3.50:1.50=7:3

Sheetal said: (Aug 19, 2011)  
If cost of 1kg pulses of 2'nd kind is=15

& 1'st kind is=20...
then what will be the ans?

Please tell me...

It's depends upon the mean price?

Viswajit said: (Sep 10, 2011)  
Thank you manasa.

San said: (Sep 19, 2011)  
If we swap 15 and 20 places.

Why can't it be 3:7 ? is there any rule?

Sathish said: (Jan 4, 2012)  
How we get 3.50:1.50=7:3?

Shashank said: (Jan 18, 2012)  
350/100:150/100=35:15=7:3

Prakash said: (Feb 10, 2012)  
Its better to follow simple method boss.

Lets assume that price of A be 150 and B is 200.
Mixture to sell at 165.

Cheaper grocery profit = 165-150 = 15.
Dearer grocery loss = 200-165=35.
Ratios to sell at 165 is.

35
---- = 7:3
15

Atul Verma said: (May 17, 2012)  
Let x kg of 1st is taken and (1-x) of 2nd is taken.

Then price of mixture will be:15*x+20*(1-x)=20-5x ----(1)

Given price of mixture is 16.5 -----(2)

From Equation (1) & (2)

20-5x=16.5

=> 5x=20-16.5
=> x=3.5/5
=> x=0.7

So,ratio is x:1-x i.e. 0.7:0.3 => 7:3 ans

Krishna Teja said: (Aug 28, 2012)  
Atul thank you :).

Vinod said: (Dec 28, 2012)  
Let x=15,y=20.
We know that x+y=16.50.

We can write in eqtion form:

15x+20y = 16.50(x+y)
16.50x-15x = 20y-16.50y
1.50x =3.50y
x/y = 3.50/1.50

Just we can convert

From eq x = 350/100=35
Eqtion y = 150/100=15

There fore ratio is
x:y =35:15.

Then answer is 7:3.

Anup said: (Dec 31, 2012)  
@Atul.

Really superb solution. Unlike the theoretical approach this is quite simple to understand.

Kousik Maji said: (Feb 9, 2013)  
Let x kg first variety mixed with y kg of second variety.

So total cost of(x+y) kg is Rs. 15x+20y.

So cost of 1 kg mixture is Rs. (15x+20y)/x+y.

Now according to question,

(15x+20y)/(x+y)=16.50
=> (15x+20y)/(x+y)=33/2
=>33x+33y=30x+40y
=>3x=7y
=> x:y=7:3.

Answer is 7:3.

Praveen Shetty said: (Sep 9, 2013)  
Check the option first.

7:3 = 7*first variety/10 + 3*second variety/10 = 16.50.

7*15/10 = 10.5.

3*20/10 = 6.

By adding two you'll get 16.5.

So 7:3 is correct.

Ranjeeth K Reddy said: (Sep 20, 2013)  
In the question Rs 15 and Rs 20 are mentioned the prices of 1st and 2nd varieties sequentially so we need to take Rs 20 -16.50 as the first variant in the solution.

Sowmya said: (Jun 24, 2014)  
Is the below mentioned method correct.

15/2 = 7.5( consider it has 7).
20/2 = 10.
10-7 = 3.

So the answer is 7:3?

Shreyas Joshi said: (Oct 13, 2014)  
There is a shortcut to solve such ratio questions.

1. Take the difference between the average value and the next quantity value. similarly, take the difference between the average value and the first told quantity.

So, here it is 20 -16.50 i.e. 3.50
Now, for the first quantity it is 16.5 - 15 i.e. 1.50

Now, the ratio is 3.5 /1.5 i.e. 7:3.

My question here - I understand from the equation formation that by taking such differences I will get the answer.

However, my question is to understand visually this process of solution. How come a difference gave us the right ratio? Is there any hidden fundamental behind it? Can someone decipher this difference technique via. Singapore Maths? Why difference gave me the answer is what I am puzzled. Please don't explain me from the equation point of view.

Vikas Kohli said: (Oct 25, 2014)  
How 3.50 and 1.50 come?

Sureshkumar said: (Jan 21, 2015)  
(20-16.50)=3.50.
(16.50-15)=1.50.

If values in points means should divide by 100 or 10 based on that because ratio should not be in points. So,

3.50/100 = 35.
1.50/100 = 15.

Respectively 35:15 = 7:3.

Pooja said: (Jan 31, 2015)  
=3.50/100= 0.035.
& 1.50/100 = 0.015.

How 3.50/100 = 35., 1.50/100 = 15.?

Sumanth Geras said: (Jul 21, 2015)  
15(x)+20(y)/x+y = 16.50.

(Here x and y are the ratios in which they are to be mixed).

Then 15x+20y = 16.50x+16.50y.

On simplifying we get x:y = 7:3.

Dinaz Khan said: (Oct 28, 2015)  
I don't understand the answer please explain clearly.

Codetackler said: (Jan 2, 2016)  
Let 15 is to be added in x amount.

Then 20 is to be added in (1-x).

Then, 15(x)+20(1-x) = 16.5.

Answer is (x/(1-x)).

Madhuri said: (Jun 26, 2016)  
Why can't be the answer is 3 : 7?

Priyanka said: (Jul 19, 2016)  
I didn't get this, Please explain it again.

Anil said: (Sep 16, 2016)  
@Priyanka, it is allegation formula in a pictorial way.

Vishnu said: (Nov 12, 2016)  
I don't understand what is mean price. Please someone help me.

Suraj said: (May 12, 2017)  
20x+15(1-x) = 16.5.
x = 0.3.
1-x/x = 7/3.

Navdeep said: (Jul 9, 2017)  
The mean price is a trick , this question is particularly based on it . as we see there is only one equation made i.e [15x + 20y = 16.5] other than this we cant make any equation.

My suggestion to solve these type of question where only one equation is made to put the value of options given.

As here only one option satisfies.

Sweta said: (Sep 27, 2017)  
3.50:1.50 <=> 350:150 remove decimals and then write ratio after solving you get 7:3.

Rashmi said: (Oct 7, 2017)  
Well explained @Kousik Maji.

Shree said: (Feb 20, 2018)  
Clear and detailed explanation. Thank you.

Bitu Ojah said: (Mar 19, 2018)  
Thank you so much @Kousik Maji.

Arnab said: (May 6, 2018)  
Suppose, x kg from A.
Y kg from B.

15*x/x+y +20*y/x+y = 16.5,
x : y = 7 : 3.

Sweta said: (Aug 25, 2018)  
Let the ratio be x:y.

Suppose x kg of pulse1 and y kg of pulse2 is mixed. The total kg of the mixture will be (x+y)kg.
So, equating the costs:
15x+20y=16.5(x+y).
1.5x=3.5y.
So, x/y=3.5/1.5.
->x:y=7:3.

Daniel Chebet said: (Apr 8, 2019)  
Thanks all.

Indu said: (May 3, 2019)  
3.50/100 : 1.5/100 = 350/100 : 150/100 = 7:3.

Smita said: (Sep 19, 2020)  
How is possible in 7:3?

I mean 20-16.50 = 4.50. So how its 3.50? Please explain.

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