Saturday, 2 April 2016

[Q] Mixture and Alligation Tricks - 1

"One Topic, to rule them all"

Yes...Mixture and Alligation has its own charm. A good hold of it can help you in solving a wide range of questions.

Alligation is a method of solving arithmetic problems related to mixtures of ingredients. Please note that alligation method is applied for percentage value, ratio, rate, prices, speed, etc. and not for absolute value. That is whenever per cent, per km, per hour, per kg, are being compared, we can use Alligation.

Common trick for Ratio-Proportion and Mixture Alligation : Almost 50% of the questions are solvable just by going through the options. Just go through the questions I have solved in this article and you will know the approach.

Rule of Alligation

Ingredient A : Ingredient B = M - Y : X - M
Here Mean Price is something which applies on the whole thing. If two varieties  of tea costing Rs. X and Rs. Y respectively are mixed and sold at Rs. Z, then Z is the mean price because it is price of the mixture.
Now I will take up some SSC CGL questions of Ratio-proportion and Mixture-Alligation.


Note that Rs. 180/kg and Rs. 280/kg are cost prices, while Rs. 320 is the selling price. To apply the alligation formula, all the three prices should be similar. So we will convert SP into CP
Given SP = Rs. 320/kg, Profit = 20%
Hence CP = 320/1.2 = Rs. 800/3
So the Mean price is Rs. 800/3 per kg
Now you can apply the formula-
Type 1 : Type 2 = 280 - 800/3 : 800/3 - 180 = 2 : 13
Answer : (B)

Q. 2)

Both the containers have equal capacity. Let us assume that both containers are of 28 litres. Why 28? Because 28 is the LCM of (3 + 1) and (5 + 2) or 4 and 7. So taking the capacity as 28 litres will make your calculations easier.
In Container 1, we have (3/4)*28 = 21 litres of milk and (1/4)*28 = 7 litres of water.
In Container 1, we have (5/7)*28 = 20 litres of milk and (2/7)*28 = 8 litres of water.
Total milk in both the containers = 21 + 20 = 41
Total water in both the containers = 7 + 8 = 15
Milk : Water = 41 : 15
Answer : (D)
Container 1 has 3 times more milk than water
Container 2 has 2.5 times more milk than water
When the contents of the two containers are mixed, the milk will still be more than water. How much more ? Somewhere between 2.5 and 3 times
(D) is the only option where the quantity of milk is around 2.7 times (i.e. between 2.5 and 3) that of the water.
Q. 3) 

Milk in vessel A = 4/7
Milk in vessel B = 2/5
Milk in vessel C = 1/2 (because in vessel C, milk and water are present in 1:1 ratio)
You have to mix 4/7 and 2/5, to produce 1/2. Hence 1/2 is the Mean Price.
A : B = (1/2 - 2/5)/(4/7 - 1/2) = 14 : 10 = 7 : 5

Q. 4)

Final ratio of the three varieties is 5 : 7 : 9
The question asks us the quantity of third variety of tea in the final mixture. From the above ratio, it is clear that the quantity of the third variety is a multiple of 9. So 45 is the only option possible.
Answer : (D)
Let the three quantities be 4x, 5x and 8x
New quantities are 4x + 5, 5x + 10 and 8x + p
Now 4x + 5 : 5x + 10 : 8x + p = 5 : 7 : 9
(4x + 5)/(5x + 10) = 5/7 and (4x + 5)/(8x + p) = 5/9
Solving 1st equation, we get x = 5
Solving 2nd equation, we get p = 5
In the final mixture the quantity of the third variety is 8x + p = 8*5 + 5 = 45

Q. 5)

In this question we will use the below formula

So from the above formula
(Quantity of acid left)/(Quantity of acid in the original mixture) = (1 - 4/20)^2 = 16:25
Answer : (A)

Q. 6)

Let the original quantities of A and B be 4x and x
In 10 litres, quantity of A = 4/5 * 10 = 8 litres
In 10 litres, quantity of B = (10 - 8) = 2 litres
New quantities of A and B are 2x and 3x
(Original Quantity of A) - (New quantity of A) = 8 litres[Because after taking out 10 litres of the mixture, the quantity of liquid A reduced by 8 litres]
So, 4x - 2x = 8
or x = 4
Hence quantity of liquid A in original mixture = 4*4 = 16 litres
Answer : (C)
Note : In the above question, there were two different ratios 4:1 and 2:3, then too I took the same constant of proportionality for them, i.e. 'x' because the following two conditions were met:
1. The volume of mixture did not change (Like in this question 10 litres were replaced, not removed)
2. The two ratios had same no. of parts (4:1 and 2:3 both have 5 parts)
You can take different constant to solve the question, but that will make the calculations little lengthy.

Q. 7)

Since the ratio of alcohol and water is 1:4, hence quantities of alcohol and water in the mixture are 3 litres and 12 litres respectively.
Total volume will become 18 litres after adding 3 litres water
% of alcohol = 3/18 * 100 = 50/3%
Answer : (B)

Q. 8) 

Originally there are 1512 story books
Final ratio of Story books : Others = 15:4
That means the story books are a multiple of 15.
Just look at the options and see which number when added to 1512, will give a multiple of 15
Answer : (C)
Let the no of story and other books be 7x and 2x respectively
Given 7x = 1512
x = 216
Now let the final quantity of story and other books be 15y and 4y respectively.
Since only story books are added to the collection, hence the quantity of other books has remained unchanged.
So 2x = 4y or y = x/2 = 108
We have to find 15y - 7x = 15y - 14y = y [Since x = 2y]
So answer is 108.

In Part-2, I will solve Speed-Distance, Algebra, Profit-loss, etc. questions with Alligation formula...

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  1. Thank u sir, I've been eagerly waiting for ur post..

  2. This comment has been removed by the author.

  3. In q.6.....we have two ratios 4:1 and 2:3....yoi have taken same constant of proportionality x in both the can we take same constant of prop for both ratios??kindly explain sir...

    1. Thanks that you pointed it out. We can take the same constant if 2 conditions are satisfied -
      1. The volume of mixture is not changed (Like in this question 10 litres are replaced, not removed)
      2. The two ratios have same no. of parts. Here 4:1 and 2:3 both have 5 parts.

    2. Grt,we can not take same constant of prop,if any one of these two conditions is violated....isn't it???

    3. TY RAJ SIR

    4. Thanx a lot:)

  4. Thank u very much sir...
    Prasanth Kishore is great political adviser for this time.
    As a resemblance
    Prasanth Raj is great adviser of our sschacks bloger cgl aspirants....

  5. please solve this -

    5/2^2*3^2 + 7/3^2*4^2 + 9/4^2*5^2

  6. Thank you sir.....earlier I was in the state of confusion where to use method particularly identification of problem... thank you ��

  7. Another useful article! Thanks for sharing these tricks. One doubt again- In question no. 4, why did you add 5 to 4x when 5 KG from 4x was selected?

    1. Dint get you...The initial quantity of first variety was 4x. Then 5 kg tea of the first variety was added to the mixture. Hence the quantity became 4x + 5

  8. Sir, in the Q.5, if we use formula x((1-y/x)^2), answer will be 64/5. So, could you please explain how you reached the final ratio? Thanks in advance..

  9. x(1-y/x)^2) gives you the quantity of acid left after 2 operations. You don't have to find the quantity here. You have to find the ratio = (Quantity of acid left)/(Quantity of acid in the original mixture)
    This ratio is given by (1-y/x)^2

  10. A shopkeeper cheats to the extent of 10% while buying as well as selling, by using false weights. His total gain is ?

    Can you please give me the answer

    1. Let us suppose he buys 10 items. But actually he will pay only for 9 items. Now again he will sell 10 items, but actually he sell them for the the price of 11 items.
      Total CP = 9
      Total SP = 11
      Profit % = 22.22

    2. Sir, why can't we apply the formula a+b+ab/100 here?

  11. A : B = (1/2 - 2/5)/(4/7 - 1/2) = 14 : 10 = 7 : 5
    please explain this step of 3 and thanks for your support sir.

  12. Sir my 1st choice is also mea. How can i good score in english .please give me ur valuable tips and tricks.

  13. Thankyou sir. Your blocks are great panacea for us. More power to you :-)

  14. To attract more visitors,zoo authority announces 20% discount on every ticket which costs 25p. for this reason sale of ticket increases by 28%.Find the increase in the number of visitors.

    Sir ye q nhi smjh aa rha kuch bhi.plz help out

    1. Total sales = Number of visitors * Price of each ticket
      Old price of ticket(P1) = 25p
      New price of ticket(P2) = 20p (price is reduced by 20%)
      Let Old sales be S1 and New Sales be S2.
      Given S2 = 1.28*S1 or S2/S1 = 1.28(Since sales increased by 28%)
      S1 = N1 * P1 ... (1)
      S2 = N2 * P2 ... (2)
      Divide equation (2) by (1)
      S2/S1 = N2/N1 * P2/P1
      1.28 = N2/N1 * 20/25
      N2/N1 = 1.28*5/4
      N2/N1 = 1.6
      Hence 60% increase in the number of visitors

    2. thnq sir
      sir 5-6 q h jo ek-ek ppr me fas rhe h
      kya wo sb pooch skta hu yha?

    3. yes post them...but dont expect an immediate reply :)

    4. ok sir thnq
      aap din bhr me kbhi kr dena

    5. n sir vocab part k liye sp bkshi k vocab rat lu ya paramount k.
      idiom phrase jo daily ka krne ko bola tha aapne wo sp bkshi k 200-250 jo diye h wo kr rha hu.
      baki kuch english k liye jo aap bolo

    6. Just learn 10 words, idioms, phrasal verbs each from whichever book you like...

  15. Thanku sir... Plzz post some more reasoning tricks

  16. Thanku sir u r giving such valuable tips now i know that in competition we can solve questions with using less pen paper
    Plz..... post more tricks
    Thanku very much

  17. Sir, could u plz guide us how to solve the questions related to letter series quickly in which we have to fill the gap for exm. A_b_ca_b_c_a_cc
    One or two qquestions are always asked and sometimes it takes a lot of time.

  18. what is the remainder if (32)^(32)^(32) is divided:

    1. i) 4
      ii) 5
      Such questions are not asked by SSC, so dont bother about them...

  19. sir plzz look at this

    itni km vacancy rhegi to kya hoga?

    1. please read my recent post regarding reduction in the number of vacancies

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  21. This comment has been removed by the author.

  22. thank you so much sir....plz keep updating blog

  23. sir plz explain that series problem like that..
    Thanks a million

  24. Sir didnt got Q6 , u calculated 4/5 of 10litres, but 10 litre is not thw total mixture. It is just a part which is replaced by B

    1. 10 litre of the "mixture" was replaced by B. The ratio of A and B in the mixture is 4:1
      So in 10 litres of the mixture, the quantity of A was 8 litres and quantity of B was 2 litres.
      After replacing 10 litre of the mixture with liquid B, the quantity of A will decrease by 8 litres, but the quantity of B will increase by 8 litres (10 litres - 2 litres)

  25. Sir didnt got Q6 , u calculated 4/5 of 10litres, but 10 litre is not thw total mixture. It is just a part which is replaced by B

  26. Very much liked your solving the problem using the final ratio and thinking answer as multiple of the ratio.

  27. Hi,

    please help me with the below question:-

    The ratio of income and expenditure of a person is 4 : 3. If income is increased by 20% and expenditure is decreased by 10% then what is the percentage increase or decrease in the savings?