Abhishek Khurana is teaching live on Unacademy Plus
Abhishek Khurana B.Com (Honours) from Panjab University MBA in Marketing from NMIMS 2009-2011 Plus Educator on Unacademy 8 years teaching experience 6 times 99 percentiler in CAT
AVERAGES & ALLEGATIONS
Course structure Types of questions asked in exam Concepts explained in detail Application of concepts Logical approach to solve question (don't cram formulae Derivation as well as shortcut explained Easy, medium & difficult questions included Suitable for: CAT, XAT, IIFT, NMAT, SNAP GRE, GMAT Bank PO, SSC & all government jobs
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AVERAGE AND ALLEGATIONS
Introduction Averages-sum of observations/ no of observations Different Question Type: People joining or leaving group: Q1. A person joins a group of 8 people and hence the average of the group drops from 75 kgs to 72 kgs. Find the weight of the person joining the group?
Introduction Q1. A person joins a group of 8 people and hence the average of the group drops from 75 kgs to 72 kgs. Find the weight of the person joining the group? Solution: 75*8+x 72*9 x-648-600 48
Introduction Q2.On scoring 20 runs in the 25th over, the batting average increased by 0.64.Find the average after 25th over? the average affer 2sm over av
Introduction av Q2.On scoring 20 runs in the 25th over, the batting average increased by 0.64.Find the average after 25th over? Solution: A is the average till 24th over. A*24+20 (A+0.64)*25 24A+20-25A+16 A-4 so average-4.64 d the average aft5erhe
Introduction Q3.The average age of all members of a family is 40 years . If the youngest member,12 years old and the eldest member, 78 years is excluded. The average age of the rest of drops by 2 years. Find the total no of members of the family?
Introduction Q3.The average age of all members of a family is 40 years . If the youngest member,12 years old and the eldest member, 78 years is excluded. The average age of the rest of drops by 2 years. Find the total no of members of the family? Solution: Let the number of family members is n. 40n-(12+78)-38* (n-2) 40n-90-38n-76 2n-14
Introduction Q4. If a person weighing 70 kgs joins a group, the average weight increases by 1 kg. Had the person weighed only 55 kgs, the average would have increased by 2 kgs . Find the number of the people in the group?
Introduction Q5. The average age of a couple 10 years ago was 27 years. Today also the average age of the couple and their one child is 27 years. Find the age of the child. Solution Concept: suppose Average -Al no of people n so from this equation we can find that A2- A1+X so 10 years back average age of couple-27 Today average age-37
eighted Average Q6. Score of written test is 80% of 40 and score of viva is 60% of 10.So overall percentage?
Alligations Let us try to understand the concept of mixture with an example. Example: A shopkeeper has two varieties of wheat with him. One of them costs Rs. C1 per kg while the other costs Rs. C2 per kg. The shopkeeper mixes them in the ratio a: b. What will be the price of the mixture per kg? Solution: The weighted average of the prices of the two varieties of wheat will give the price of the mixture (C) ...............( We can re-write the formula in (i) above as follows: a/b-c2-c/c-cl The leads us to the concept of Alligation which gives the relationship between prices and quantities of various types of an item in a mixture.
Alligations The above rule can be described as follows Quantity of cheaper item/quantity of dearer item- (price of dearer -average price of the mixture)/(average price of the mixture-price of cheaper)
Alligations Q7. Two salt solutions have concentrations 15% and 40%. In what ratio should they be mixed to get a solution of concentration 30%?
Alligations Q7. Two salt solutions have concentrations 15% and 40%. In what ratio should they be mixed to get a solution of concentration 30%? Solution: (a) 15% 40% (b) 30% (c) 10% (b-c) 15% (c -a) So they should be mixed in the ratio of 2:3.
Alligations Q9. Some part of a sugar solution which contains 40% sugar is replaced with another sugar solution which contains 19% sugar. Part of sugar in the mixture became 26% what fraction of the original sugar solution wa replaced with another sugar solution?
Alligations Q10. There are total 50 cons of 1 rupee and 50 paise in a bag. Total value of the coins is Rs. 35. What is the number of 50 p cons in the bag?
Alligations Q11.A shopkeeper mixes 30 kgs of sugar at Rs 20/kg and 45 kgs of sugar at 10/kg. What is the average price of the mixture? Solution: Sol: Let average price be x. 10, 45 30 x-10/20-x 30/45 Rs.14/kg # => x:
Alligations Q12. Amit covers 200 km in 10 hours. The first part of journey is travelled by bus at the speed of 15 km/hr and second part by a car at the speed of 25 km/hr. What is the ratio of distances covered by bus and car?
Alligations Solution: Average speed 250/10 10 km/hr. Let time travelled by bus be 'a and by car be 'b Applying alligation methoo
Alligations Q13. Product P is produced by mixing chemical X and chemical Y in ratio of 5:4. Chemical X is prepared by mixing two raw materials, A and B, in the ratio of 1 :3. Chemical Y is prepared by mixing raw materials, B and C in the ratio of 2:1. Then the final mixture is prepared by mixing 864 units of product P with water. If the concentration of the raw material B in the final mixture is 50%, how much water had been added to product Pe Solution: First, we need to find the proportion of B in Product P. It can be easily found as its proportion in chemical X and Y is given and proportion of X and Y in P is also given. P is produced by mixing chemical X and chemical Y in the ratio 5:4. Hence, 5/9th of product P is chemical X and 4/9th of product P is chemical Y.
Alligations 7/108 54/1 864 X-368
Alligations Q15 : In a mixture of milk and water, there is only 75% milk. After replacin the mixture with 5 litres of water, percentage of milk in the mixture becomes 60%.. what is the total quantity of the mixture?
Alligations Q15 : In a mixture of milk and water, there is only 75% milk. After replacing the mixture with 5 litres of water, percentage of milk in the mixture become 60%,What is the total quantity of the mixture? Solution: Let total quantity of mixture be T. We will consider milk as it is getting reduced. Initial amount 75% (if absolute values are not given, proportion/percentage can also be used) Final amount:-60% n 1. Then, 60 75 x (1 5/T) >T 25 litres.
Alligations QI 6 : Some part of a sugar solution which contains 40% sugar is replaced with another sugar solution which contains 19% sugar. Concentration of sugar in the new mixture became 26%. What fraction of the first suga solution was replaced with second sugar solution?
Alligations Q18: 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?
ligations Q19: How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing Rs.24 per kg so that he makes a profit of 25% on selling the mixture at Rs.40/kg? Solution: As the trader makes 25% profit by selling the mixture at Rs.40/kg, his cost per kg of the mixture Rs.32/kg. C.P of 1 kg of rice of 1st kind Rs. 42 C.P of 1 kg of rice of 2nd kind Rs. 24 Mean price Rs. 32
Alligations Q20 : A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is?