 Case: Loan taken from two banks
 Case: Profit on Single commodity
 Case: No. of Employees based on Avg Salary
 Case: Profit on Two commodities
 Summary
 Mock Questions
Consider these four questions
 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?
 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%?
 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.
 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 Ā at 8% interest and Ā 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 āvisual moveā of Wine and water mixture
109.5=SBI ā¦eq 1
Similarly
9.58=ICICIā¦.eq 2 (donot make mistake of 89.5 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 = Ā¼
Therefore, SBI =10,000/4=Rs.2500
It means Dr.Haathi has borrowed Rs.2500 from SBIĀ Bank.
Verifying the answer and concept
Amount borrowed  Interest rate  
SBI  2500  8% of 2500=200 
ICICI  10k2500=7500  10% of 7500=750 
Total  8500  200+750=Rs.950 paid inĀ interestĀ = 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 1000400=Rs.600
Draw a table.
Profit  10%  20%  M% 
Overall  
Cards worth (cost price)  400  1000400=600 
Apply the visual move of winewater mixture
M20=400ā¦.eq1
2010=600ā¦.eq2 (donot make mistake of 1020 because we donāt 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% 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 = m7.
Draw the table.
Salary (Rs.)  7800  8500  10000 
Overall  
Employees (total =m)  m7  7 cooks 
Apply the visual move
10,000 minus 8500 = (m7)ā¦eq1
8500 minus 7800=7ā¦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
Weāll 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 
Thatās it. Just apply the visual move BUT with care!
20 minus 2=printerā¦eq 1
Be Careful while approaching second equation
2 minus (10)=laptop
2(10)=laptop
Hence 2+10=laptop ā¦eq2
Rest is easy. Just divide eq.1 with eq.2
When you simplify it further, you get the ratio
printer/laptop=3/2
weāre interested in the Cost price of laptop. So weāll 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  20,0008000=12,000  10% loss on 12k=Minus 1200 
Total  20,00  16001200=+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 weāve 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 āvisualā move and get the answer.
Mock Questions
Case: Journalist Popatlal took some loan from MatkaaKing 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
 Total amount borrowed
 Money borrowed from Mehta
 Money borrowed from Mohan
 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.Ā Answer following questions
 Cost price of Chair
 Cost price of Table
 Selling price of Chair
 Selling Price of Table
Case: In Tappuās class, the average weight of boys and girls is 77.5kg, 70kg respectively.Ā Overall average weight of all students is 74 kg.
 Find Ratio of Boys: girls
 If total number of students is 30, how many boys study in Tappuās class?
 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 Desiliquor dens and Land mafias is 100. They pay total Rs.1650 crores bribe to home minister every year. Average bribe paid by each Desiliquor den and land mafia is 15 crores and 20 crores respectively.
 Find total number of land mafias in this state
 Final total bribe paid by these land mafias
 Owing to mediapressure, the home minister orders police to close down some of the desiliquor 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.
 Find total number of cars
 If 5 cars are added and 5 bikes are removed, whatāll be the new average number of tires per vehicle?
Answers
Popat in debt 

Jetha 

School 

Home minister 

Parking lot 

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54 Comments on “[Aptitude] Alligation: Advanced applications in Interest rates, Profitloss, Average Wages (WineWater Concept)”
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
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 950x
0.5/1.5=950x/x
solving
x=237.5
In mock question 3, how many girls should be added to make number of boys and girls equal ?
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?
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
Anyone can explain 3rd mock question???
you are a champ sir……
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