[Aptitude] Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept)

Aptitude53 Comments

  1. Case: Loan taken from two banks
  2. Case: Profit on Single commodity
  3. Case: No. of Employees based on Avg Salary
  4. Case: Profit on Two commodities
  5. Summary
  6. Mock Questions

Consider these four questions

  1. Dr.Haathi has taken some loan from State bank of India at 8% interest rate per annum.He has also borrowed some money from ICICI at 10% interest.The total loan amount is Rs.10,000. He pays total Rs.950 as interest rate at the end of first year.How much money did he borrow from the State bank of India?
  2. Jethalal purchased some mobile phone memory cards for Rs.1000. He sold memory cards worth rupees worth Rs.400 at 10% profit.At what percent profit should he sell the remaining memory cards, to gain overall profit of 20%?
  3. Roshan Singh Sodhi is the owner of a big hotel. The average salary of all employees is Rs.8500. The average salary of 7 cooks is Rs.10,000.If the average salary of remaining employees, is Rs. 7800. Find the total number of people employed by Roshan Singh Sodhi.
  4. Bhide master bought a set of laptop and printer for Rs.20000.He sold the laptop for 20% profit and printer for 10% loss.Overall, he made 2% profit. Find the cost price of laptop.
  • Superficially, ^these questions seem different from one another. But if you pay close attention, these are all problems of weighted average.
  • We can quickly solve them using the allegation (wine and water mixture) method.

Case #1: Loan taken from two banks

Dr.Haathi has taken some loan from SBI  at 8% interest and  ICICI at 10% interest.
The total loan amount is Rs.10,000. He pays total Rs.950 as interest rate at the end of first year. How much money did he borrow from the SBI

The question is mentioning two interest rates: 8% and 10%
the effective interest rate, that Dr Haathi has to pay, will be in between these two numbers 8 and 10.
The question also says that he paid Rs.950 as interest rate.
So in terms of percentage he has paid
(950/10000) x 100 =9.5% interest rate (overall).

Arrange these numbers in to ascending (increasing) order

Interest rate%89.510
BankSBIOverallICICI

Now apply the “visual move” of Wine and water mixture

10-9.5=SBI …eq 1
Similarly
9.5-8=ICICI….eq 2 (donot make mistake of 8-9.5 because we donot want negative difference)

Divide eq. 1 with eq 2

If you simplify this further, you get

SBI / ICICI =1/3

Apply Componendo at bottom

But we know that SBI + ICICI=Rs.10,000 that Dr.Haathi has borrowed!

Plug in the value
SBI /10000 = ¼
Therefore, SBI =10,000/4=Rs.2500
It means Dr.Haathi has borrowed Rs.2500 from SBI  Bank.

Verifying the answer and concept

Amount borrowedInterest rate
SBI25008% of 2500=200
ICICI10k-2500=750010% of 7500=750
Total8500200+750=Rs.950 paid in interest = matches the question Description!0

Case: Profit on Single commodity

  • Jethalal purchased some mobile phone memory cards for Rs.1000.
  • He sold memory cards worth rupees worth Rs.400 at 10% profit.
  • At what percent profit should he sell the remaining memory cards, to gain overall profit of 20%?

He already made 10% profit on part of his card.
If he wants to have overall (average) profit of 20% then he must sell the remaining cards at a profit higher than 20%
The question says he sold cards worth Rs.400 (cost price). Meaning the cost price of remaining cards is 1000-400=Rs.600
Draw a table.

Profit10%20%M%
Overall
Cards worth (cost price)4001000-400=600

Apply the visual move of wine-water mixture
M-20=400….eq1
20-10=600….eq2 (donot make mistake of 10-20 because we don’t want negative)
Now Divide equation 1 with equation 2

Meaning, if Jethalal wants to make overall profit of 20%, he must sell the remaining memory cards @26 (2/3)% interest rate.

Verifying the answer

Cards already sold @10% interest10% x 400=Rs.40
Remaining cards sell @26 (2/3)26 (2/3)% x 600=Rs.160
Total profitRs 40 +160 =200. And 200 is 20% of Rs.1000 so it matches our question condition.

Case: No. of Employees based on Avg Salary

  • Roshan Singh Sodhi is the owner of a big hotel.
  • The average salary of all employees is Rs.8500.
  • The average salary of 7 cooks is Rs.10,000.
  • If the average salary of remaining employees, is Rs. 7800. Find the total number of people employed by Sodhi.

The question is talking about three sets of salaries
7800 > 8500 (average) >10000
Suppose total number of employees =m.
And we already know there are 7 cooks.
So remaining employees = total minus 7 = m-7.

Draw the table.

Salary (Rs.)7800850010000
Overall
Employees (total =m)m-77 cooks

Apply the visual move
10,000 minus 8500 = (m-7)…eq1
8500 minus 7800=7…eq2
Now Divide equation 1 with equation 2

When you simplify this further, you get m=22
Therefore, Total number of employees is 22.

Verification

NumberAvg. salaryTotal cost to Sodhi
Cooks7100007 x 10k=70k
Others1578001,17,000
Total15+7=2270k+1,17,000=1,87,000

Avg salary of all employees
=(Total salary paid)/(Total number of employees)
=187000/22
=Rs.8500 = matches the question condition.

Case: Profit on Two commodities

  • Bhide master bought a set of laptop and printer for Rs.20000.
  • He sold the laptop for 20% profit and printer for 10% loss.
  • Overall, he made 2% profit. Find the cost price of laptop.

Approach

We’ll take 10% loss =-10%
Now the question is talking about three rates : -10% , +2% (avg) and +20%

Profit/loss-10%2%20%
Overall
Cost pricePrinterLaptop

That’s it. Just apply the visual move BUT with care!
20 minus 2=printer…eq 1

Be Careful while approaching second equation
2 minus (-10)=laptop
2-(-10)=laptop
Hence 2+10=laptop …eq2

Rest is easy. Just divide eq.1 with eq.2

When you simplify it further, you get the ratio
printer/laptop=3/2
we’re interested in the Cost price of laptop. So we’ll apply componendo @top

But question already said hat total investment (cost price) of printer +laptop =Rs.20000
Plug in the value
20000/laptop=5/2
Therefore cost price of laptop=(2/5) x 20000=Rs.8000

Verification

Cost priceProfit/loss
Laptop8,00020% profit on 8k=1600
Printer20,000-8000=12,00010% loss on 12k=Minus 1200
Total20,001600-1200=+400 Rs. as profit

So overall he received Rs.400 profit on the investment of Rs.20,000
=(400/20000) x 100
=2% profit= matches the condition given in question statement.

Summary

  • Weighted average method works when we’ve 3 rates (including one average) and 2 quantities.
  • First arrange the rates in ascending order. Then draw the table with corresponding rates and quantities.
  • Apply “visual” move and get the answer.

Mock Questions

Case: Journalist Popatlal took some loan from Matkaa-King Mohanlal @36% interest rate and some loan from Taarak Mehta @10% interest rate. Total money borrowed Rs.6000. At the end of first year, Popat paid total interest of Rs.912. Answer following questions

  1. Total amount borrowed
  2. Money borrowed from Mehta
  3. Money borrowed from Mohan
  4. Effective interest rate on total borrowing?

Case: Jethalal bought a chair+table set @Rs.6000. Later he sold Chair @10% loss and table @10 profit. Overall he gained Rs.100. Answer following questions

  1. Cost price of Chair
  2. Cost price of Table
  3. Selling price of Chair
  4. Selling Price of Table

Case: In Tappu’s class, the average weight of boys and girls is 77.5kg, 70kg respectively. Overall average weight of all students is 74 kg.

  1. Find Ratio of Boys: girls
  2. If total number of students is 30, how many boys study in Tappu’s class?
  3. At present, total number of students is 60. If school administration wants to have equal number of boys and girls in this class, how many new girls should be admitted?

Case: In a state, total number of Desi-liquor dens and Land mafias is 100. They pay total Rs.1650 crores bribe to home minister every year. Average bribe paid by each Desi-liquor den and land mafia is 15 crores and 20 crores respectively.

  1. Find total number of land mafias in this state
  2. Final total bribe paid by these land mafias
  3. Owing to media-pressure, the home minister orders police to close down some of the desi-liquor dens. Now his total bribe income declined by 20%. What is the new ratio of liquor den: land mafias?

Case: A parking lot has only cars and bikes. Average number of tires per vehicle is 2.9. There are 55 bikes in this parking plot.

  1. Find total number of cars
  2. If 5 cars are added and 5 bikes are removed, what’ll be the new average number of tires per vehicle?

Answers

Popat in debt

  1. Total borrowed Rs. 6000
  2. 4800 from Mehta
  3. 1200 from Mohanlal.
  4. 15.2% interest rate (overall)

Jetha

  1. Cost price Chair =2500
  2. CP Table= 3500.
  3. Selling price of Table (+10% profit)=1.1 x 3500=3850
  4. Selling price of Chair (-10% loss)=0.9 x2500=2250

School

  1. Boys/Girls=8/7
  2. 16 boys and 14 girls.
  3. 4 new girls need to be admitted.

Home minister

  1. Avg. annual bribe is 1650/100=16.5 Now the rates are 15>>16.5>>20. Ratio of liquor-dens:mafia=7:3. Since total are 100, number of Mafia=3/10 x 100=30.
  2. 30 mafia x avg 20 crores=600 crores paid by them.
  3. 20% of 1650=330. And 330/15=22 liquor dens were closed down. So new ratio is (70-22):30=48:30=8/5

Parking lot

  1. Number of cars=45.
  2. New avg. no. of tires per vehicle=3

For the Archive of all [Aptitude] Articles, visit Mrunal.org/aptitude

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So far 53 Comments posted

  1. harsh

    thanks mrunal for sharing this fast method

  2. Anshuman Rai

    Sir the verification of that Dr Haathi question 1 is not correct
    2500 par 8% hai, so answer is 200
    7500 par 10% hai, so 750

    750+200 = 950
    kindly correct it 🙂

    1. Vishal Dhage

      Dear Friend, Answer is correct. You can solve directly by equations,
      x+y=10000
      0.08x+0.1y=950

      Try … You will get ans 2500

  3. Anshuman Rai

    Another one sir, Roshan Singh Sodhi’s question

    The simplification owe us m = 22, so need to add further 7 in 15

  4. Anshuman Rai

    Mock question
    At present, total number of students is 60. If school administration wants to have equal number of boys and girls in this class, how many new girls should be admitted?

    Ans) 4 new girls needed sir

  5. anonymous kashmiri

    sir plz corect me if um wrng.
    U tld us to arang tablz n asndng ordr…bt n last prblm it shd b prntr,cost pric,laptop for -10,2 and 20 prcnt rspctvly..??
    Dn it wl b n right ordr…plz sir clear ds cnfujn.

  6. Anshuman Rai

    Mock Question
    Parking Lot :
    Ans 16 ) its not 3, answer is 32/11 = 2.909

  7. viren

    @anshumn
    Bikes to car 55 to 45
    New sit. 50 bike 50 cars so total tires 200+100=300
    Divided by total vehicles 100
    Avg tires 3

    1. Anshuman Rai

      Thanks Viren dear, I took the question as 5 bikes are added 🙂

  8. adi

    sir i have been preparing for history mains.i am covering IGNOU B.A now.should i read M.A too in depth.i have alrdy covrd bipin chandra books and NCERT.my other optional being pub admin which i plan to cover after prelims.Ur suggestion sir?AM i on rite track

  9. Abhi

    Dear Sir,
    For popat @ debt case: Is data given sufficient to solve the problem? If Popat borrowed 5000 from mohanlal (5000 is the answer given in solution) @ 36% then this interest would be Rs. 1800 at the end of year (more than Rs. 912). Please Clarify.

  10. kkp

    sir,
    for popat problem if total amount is 6000 then amounts are 4800 @10% AND 1200 @ 36% THEN AND TOTAL S.I AMOUNTS 912 AND MY DOUBT IS you have given only both interest rates and total interest which i found data was not sufficient i think the total amount 6000 should also be given .plz clear this doubt!

  11. Subbu

    Sir, Kindly explain Currency swap facility. Why it is very flexible method of foreign exchange? How it is done to get around exchange controls?

  12. Avinash

    Hi

    Case: Profit on Single commodity
    1. Jethalal purchased some mobile phone memory cards for Rs.1000.
    2. He sold memory cards worth rupees worth Rs.400 at 10% profit.
    3. At what percent profit should he sell the remaining memory cards, to gain overall profit of 20%?

    I think the answer as 25%

    Total Profit is 20%..i.e 1200 Rs made out of 1000Rs.

    Of these 1200, he has already sold some part@ 10% for 400Rs.
    i.e 40Rs profit made by selling 360Rs as 400Rs.

    So remaining (1000-360) is sold as 800Rs.
    i.e (800-640)/640 = 25%..

    1. Mrunal

      The 400 worth memory cards= it is in context of cost price 400.

  13. karmesh

    Sir, which atlas is better for GS preparation, orient blackswann or oxford? Kindly name only one.

  14. PooJA

    unable to solve 1st mock ques., if anyone has solved it, pls help.

    1. kaushal jha

      total % of interest=15.2%
      36-15.2/15.2-5=20.8/5.2=4/1=tarak/mohan
      tarak/tarak+mohan=4/1+4=4/5
      4/5=x/6000
      x=4800=tarak
      6000-4800=1200=mohan…

      answr is wrong..plz check,its 1200-mohan
      4800-tarak…
      now cross check-1200*36/100=432rs
      4800*10/100 = 480 rs
      total interst income=912rs…

      1. Manjunath Bangera

        Hi,

        How you got that 15.2 % from question data? Pls explain

        1. Johnson

          In first ques how 15.2 is arrived

          1. sarah

            Heya johnson, the 15.2 is aarived with the help of case no. 1
            912/6000×100=15.2

  15. Yashwanth

    Hello Mrunal,
    Could you please brief us about the post preferences of SSC CGL exam, as we hardly know about the posts description as to which is at top preferred and how the job is..???

    Regards,
    Yashwanth.

  16. Priyanka

    Cud any one explain moc que 5?

    1. Pradipta

      @priyanka
      let no of cars be=x,total no of tires including both bikes and cars=(55+x)*2.9
      again total no of bike tires =55*2,total no of car tires =x*4
      The total no tires should be equal to the individual sum of tires of bikes and cars
      (55+x)*2.9=55*2+x*4
      x=45
      total nos=55+45=100(ans.)
      Cross check:total tires based on avg.=2.9*100=290
      total tires based on individual counting=55*2+45*4=290

    2. Pradipta

      Visual move:
      Avg. tyre=2.9,car tires=4,bike tires=2

      tires 4 2.9 2
      Avg
      Vehicle Car bike

      So the equations are:
      2.9-2=car…..eq.1
      4-2.9=bike….eq.2
      car/bike=0.9/1.1=9/11
      car=bike*9/11=55*9/11=45
      total vehicles=100
      part2:
      now total bike=50,car=50
      total tires=50*2+50*4=300
      avg=300/100=3

  17. Gaurav Dixit

    IN the 2nd moc question..
    i am getting the chair cost is : 3480
    table cost : 2520

    my order is (-10) <(1.6) <(10)

    8.4/11.6 = table / chair

    8.4/20 = table / (table + chair)

    every thing is corrent but why my answer is not matching ????

    please Sir help me out 🙁

    1. Pradipta

      @gaurav
      order should be (-10)<(5/3)<10
      dont use the fraction 1.6 instead of 5/3
      10-(5/3)=chair
      (5/3)-(-10)=table
      chair/table=(25/3)/(35/3)=25/35
      so chair =25/60*6000=2500
      table=3500

      1. Gaurav Dixit

        Thanku very much 🙂
        god bless you..

    2. Pradipta

      Gourav,u r most welcome 😀

      1. Johnson

        sir even i could not arrive at the order u have mentioned, HELP me

  18. BSajjan

    In the first mock question
    ans 1200 from Mehta and 4800 from Mohan

  19. Shweta

    Hello sir,

    the answer for Mock Ques 1 should be 1200 Rs to be borrowed from Mohan lal and 4800 to be borrowed from Jeethalal. This would appropriately provide 912 as an overall amount for the year.

  20. kkp

    hi gaurav 100 is 1.666666…% of hundred so when you take 1.6% you get wrong answers since its not exact value try taking atleast two points decimal then you will get answer as 3499.8 which is equal to 3500 (approx) hope i cleared your doubt

    1. Gaurav Dixit

      Thank you KKP at that moment i was Blocked … couldn’t thought of it 🙂
      thanks a lot for your concern.

  21. alok

    Mrunal sir, kindly suggest a (one and only one) good practice book(better if it has mock papers only) for SSC-CGL exam. I am not looking for theory at all. Plz oblige.

  22. afsal

    please explain second mock question how it get 5/3 in middle

  23. Harshit

    sir your method is simple.
    sir i got the ans of {Case: Profit on Single commodity} using another method, but my method is right or wrong-simple or not-time saving or not ????
    please advise me…..

    Case: Profit on Single commodity
    1. Jethalal purchased some mobile phone memory cards for Rs.1000.
    2. He sold memory cards worth rupees worth Rs.400 at 10% profit.
    3. At what percent profit should he sell the remaining memory cards, to gain overall profit of 20%?

    ovrall profit is 20%
    there for 1000*20% =200
    we get Rs.200 total profit
    now He sold memory cards worth rupees worth Rs.400 at 10% profit.
    so, 400*10% =Rs.40
    the cost price of remaining cards is 1000-400=Rs.600
    now for selling remaining cards he get profit is 200-40=Rs.160
    now profit on Rs.600 in % = 160/600 *100%
    now Ans is 26.66%

    please advise me……..

  24. Gautam shrivastava

    At what ratio milk and water should be mixed, that even if we sale the mixture on the cost price, we will get 20% profit.( sirji plz use the same method of allegation, i tried but not got clear idea..)

  25. gautam

    @mrunal sir A cistern contains 50 liters of water. 5 litres of water is taken out of it adn replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.

    i couldn’t do it with same concept…plz help me anyone..

  26. mansi

    solve this question
    A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

  27. kaka

    HI SIR AM NEW TO UR SITE. AM IMPRESSED. ANY BOOK FROM U. AM WAITING FOR REPLY

  28. faizan

    Can u please solve this problem….

    A jar full of whisky contains 40%
    alcohol. A part of this whisky is
    replaced by another containing
    19% alcohol and now the
    percentage of alcohol was found to
    be 26%. The quantity of whisky
    replaced is:

  29. arun

    Dear sir,
    Thanks for good information. I need aptitude books for your techniques. I have learn to home via books. Pls advise me because I m trying to solve IBPS.

    Regards
    arun

  30. Parth

    Three varieties of sugar costing Rs.10/kg , Rs.13/kg and Rs.18/kg are mixed in such a way that the average price of mixture is Rs.15/kg.Find ratio in which the three varities are mixed.
    How to solve such que containing more than 2 concentrations/interest rates/price etc.

  31. mukesh pareek

    this was really helpful in understanding thanks a lot for such a lucid explanation.

    please do also provide study plan for IBPS PO and CLERK

    Regards

  32. Mahesh

    Sir,

    I tried the ICICI/SBI in a different way, but this doesnt seem to get the same answer. Any idea why?

    Interest 8 9.5 10
    Int paid x 950 950-x

    0.5/1.5=950-x/x

    solving
    x=237.5

  33. jagpreet

    In mock question 3, how many girls should be added to make number of boys and girls equal ?

  34. Gokila

    hi mrunal,
    how to solve the below question by money problem??

    A batsman in his 17th innings makes a score of 85 and thereby increases his avg by 3.what is his average after 17th innings?

  35. Suresh Babu

    Help me. How to solve this question?
    Qn. A vessel contains a mixture of milk and water in the ratio of 14:3. 25.5L of mixture is taken out from the vessel and 2.5L of pure water and 5L of pure milk is added to the mixture. If the resultant mixture contains 20% of water, what was the initial quantity of mixture in the vessel before the replacement? Ans : 68L

  36. Ram

    Anyone can explain 3rd mock question???

  37. manoj

    you are a champ sir……

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