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

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% 8 9.5 10 Bank SBI Overall ICICI

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 borrowed Interest rate SBI 2500 8% of 2500=200 ICICI 10k-2500=7500 10% of 7500=750 Total 8500 200+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%?

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.

 Profit 10% 20% M% Overall Cards worth (cost price) 400 1000-400=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.

 Cards already sold @10% interest 10% x 400=Rs.40 Remaining cards sell @26 (2/3) 26 (2/3)% x 600=Rs.160 Total profit Rs 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.) 7800 8500 10000 Overall Employees (total =m) m-7 7 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

 Number Avg. salary Total cost to Sodhi Cooks 7 10000 7 x 10k=70k Others 15 7800 1,17,000 Total 15+7=22 — 70k+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 price Printer Laptop

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 price Profit/loss Laptop 8,000 20% profit on 8k=1600 Printer 20,000-8000=12,000 10% loss on 12k=Minus 1200 Total 20,00 1600-1200=+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?

## 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

## Mrunal recommends

Books: UPSC Prelims Books: UPSC Mains Books: Maths /Reasoning

## 54 Comments on “[Aptitude] Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept)”

1. thanks mrunal for sharing this fast method

2. 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. 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. Another one sir, Roshan Singh Sodhi’s question

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

4. 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. 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.

1. on the number line: -10<2<20.

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

7. @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. Thanks Viren dear, I took the question as 5 bikes are added :)

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

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

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

1. 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. Hi,

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

1. In first ques how 15.2 is arrived

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

15. 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. Cud any one explain moc que 5?

1. @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. 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. 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. @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. Thanku very much :)
god bless you..

2. Gourav,u r most welcome :D

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

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

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

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

23. 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 ????

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%

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

28. 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. 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. 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.