Mrunal [Aptitude] Alligation_ Advanced Applications in Interest Rates, Profit-loss, Average Wages (Wine-Water Concept) » Mrunal

7/26/2014 Mrunal [Aptitude] Alligation: Advanced applications in Interest rates, Profit-loss, Average Wages (Wine-Water Concept) » Mrunal

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

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 somemoney from ICICI at 10% interest.The total loan amount is Rs.10,000. He pays total Rs.950 as interest rate at the endof 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.400at 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 7cooks is Rs.10,000.If the average salary of remaining employees, is Rs. 7800. Find the total number of peopleemployed 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 problemsof weighted average.We can quickly solve them using the allegation (wine and water mixture) method.

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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 heborrow 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 1Similarly9.5-8=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 valueSBI /10000 = ¼Therefore, SBI =10,000/4=Rs.2500It 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%?

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.600Draw a table.

Profit 10% 20% M%

Overall

Cards worth (cost price) 400 1000-400=600

Apply the visual move of wine-water mixtureM-20=400….eq120-10=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)% interestrate.

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) >10000Suppose 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 move10,000 minus 8500 = (m-7)…eq18500 minus 7800=7…eq2Now Divide equation 1 with equation 2

When you simplify this further, you get m=22Therefore, 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 equation2 minus (-10)=laptop2-(-10)=laptopHence 2+10=laptop …eq2

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



When you simplify it further, you get the ratioprinter/laptop=3/2we’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.20000Plug in the value20000/laptop=5/2Therefore 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 TaarakMehta @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 borrowed2. Money borrowed from Mehta3. Money borrowed from Mohan4. 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 gainedRs.100. Answer following questions

5. Cost price of Chair6. Cost price of Table7. Selling price of Chair8. 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 allstudents is 74 kg.

9. Find Ratio of Boys: girls



10. If total number of students is 30, how many boys study in Tappu’s class?11. 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 homeminister every year. Average bribe paid by each Desi-liquor den and land mafia is 15 crores and 20 crores respectively.

12. Find total number of land mafias in this state13. Final total bribe paid by these land mafias14. 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 parkingplot.

15. Find total number of cars16. If 5 cars are added and 5 bikes are removed, what’ll be the new average number of tires per vehicle?

Answers

Popat indebt

1. Total borrowed Rs. 60002. 4800 from Mehta3. 1200 from Mohanlal.4. 15.2% interest rate (overall)

Jetha

5. Cost price Chair =25006. CP Table= 3500.7. Selling price of Table (+10% profit)=1.1 x 3500=38508. Selling price of Chair (-10% loss)=0.9 x2500=2250

School

9. Boys/Girls=8/710. 16 boys and 14 girls.



11. 4 new girls need to be admitted.

Homeminister

12. 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.

13. 30 mafia x avg 20 crores=600 crores paid by them.14. 20% of 1650=330. And 330/15=22 liquor dens were closed down. So new ratio is (70-

22):30=48:30=8/5

Parkinglot

15. Number of cars=45.16. New avg. no. of tires per vehicle=3

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Mrunal [Aptitude] Alligation_ Advanced Applications in Interest Rates, Profit-loss, Average Wages (Wine-Water Concept) » Mrunal