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%	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%?

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.

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.

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 = 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

5. Cost price of Chair
6. Cost price of Table
7. Selling price of Chair
8. 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.

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 home minister 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 state
13. Final total bribe paid by these land mafias
14. 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.

15. Find total number of cars
16. 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	Total borrowed Rs. 6000 4800 from Mehta 1200 from Mohanlal. 15.2% interest rate (overall)
Jetha	Cost price Chair =2500 CP Table= 3500. Selling price of Table (+10% profit)=1.1 x 3500=3850 Selling price of Chair (-10% loss)=0.9 x2500=2250
School	Boys/Girls=8/7 16 boys and 14 girls. 4 new girls need to be admitted.
Home minister	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. 30 mafia x avg 20 crores=600 crores paid by them. 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	Number of cars=45. New avg. no. of tires per vehicle=3

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