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Shortcuts learnt from todays session:

1)Amount doubling principle for Compound Interest is: after 72/r years it gets doubled .

2) Amount doubling principle for Simple Interest is: after 100/r years it gets doubled .

3)when a person makes x% profit on an item.he decides to make an additional profit of y%..then the

total profit percentage gained by him is given by

=X+y+(xy/100)

1)Sunny Leone takes personal loans at compound interest 8% and deposits into bonds yielding simple

interest at 10%. Find the maximum possible period until which she can earn money in this way?

2 years

7 years

10 years

20 years

2. Two cars, City and Civic bought for 7lakhs and 8lakhs depreciate at the rate of 8% and 10%

respectively. Find out which car is worth more at the end of 3 years.

City

Civic

Both are equal


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Data Insufficient

3. A newly launched Money bank offers compound interest of 10% and increases the interest rate at a

compound interest of 20% on all fixed deposits. Find the percentage value of the amount in the fixed

deposit at the end of 3 years.

145.5%

131%

140.4%

149.7%

4. Find the difference between the compound interest and simple interest earned on the sum of Rs

15000 at a rate of 8% in 2 years?

Rs. 96

Rs. 100

Rs. 240

Rs. 360

5 Find the difference in the number of years required to double a sum with simple interest 5% and

compound interest 3% calculated half yearly?

1 year

2 years

3 years

4 years


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Solution:From the formula for doubling principals

we know that Doubling from S.I = 100/5 = 20 periods/intervals

Doubling from C.I = 72/3 = 24 periods/intervals

Since the interests are calculated half years the difference will also be in half yearly periods. Therefore,

the total difference in years = (24 20)/2= 4/2= 2 years

Hence, the correct answer is option (b).

6. Anwar bought a computer worth Rs 30,860. He made a down payment of Rs 21,000 and remaining

amount, he paid back from his credit card in 4 equal instalments at the rate of 12.5% compound

interest. What is the value of each instalment?

4930

2485

3280.5

2980

Solution:Let the value of each instalment be Rs x.

Remaining amount to be paid = 30,860 21,000 = 9860

He has to pay a sum of Rs 9860 in 4 equal instalments at the rate 12.5% per annum.

Using the same approach as explained in solved example,

we have x /(1 + 12.5 /100 )^1 + x /(1 + 12.5 /100 )^2 + x /(1 + 12.5 /100 )^3 + x /(1 + 12.5 /100 )^4 = 9860

On solving, we get x = 3280.5

Hence, the correct answer is option (c).


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7. A certain sum amounts to Rs 235400 in 2 years and Rs 267500 in five years both at simple interest.

Find the principal?

234000

207000

254000

214000

Sol:using the formula for simple interest,

A = P + (P x r x t)/100 235400 = P (1 + 2r/100) 267500 = P (1 + 5r/100)

On dividing both the above equations, and then cross multiplying,

we get, r = 5% On substituting the value of 'r' in any one of the above equations,

we get 235400 = P (1 + 10/100) Therefore, P = 214000

Hence, the correct answer is option (d).

8. Ruchika takes a student loan which charges simple interest of 12% per annum,

Poorva takes the same loan but by handy means deposits the money into a compound interest yielding

scheme of 10% per annum.

If the principal for both loans is 20 lakhs, find in how many years will Poorva be able to set off the

interest for Ruchika and herself against the interest accrued on her bank deposit in that year.

7 years

8 years

9 years

10 years


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Sol:For Poorva to be able to pay of the interest from her as well as Ruchika's loan,

the interest from her deposit would need to be 12% + 12% = 24% of her principal annually.

Compound interest accrued in a year will be equal to the interests on the loan to be paid when 10% of

the amount becomes 24% of the principal

i.e 24/100 x 2000000 = 480000 = 10% of Amount Amount = 480000/10% = 4800000

Using the formula for compound interest

we know the amount will double up in 72/r years= 72/10 = 7.2 years. i.e in 7.2 years the total amount of

20 lakhs will become 40lakhs. In 8.2 years it'll become 44 lakhs and in 9.2 years it will become 48.4lakhs.

Therefore, approximately 9 years Hence, the correct answer is option (c).

9. RBI maintains a reserve of gold to keep the value of the Rupee against the dollar up.

It buys gold from the Indian Gold markets to keep the currency in the country itself while stacking up the

gold reserves.

The inflation cuts down on the worth of the rupee at 5% per annum,

the gold prices rises annually at 10% per annum. If the dollar grows at 1% per annum,

find out the approximate Rupee to dollar conversion ratio after 5 years.

Treat inflation as depreciation in rupee's worth, treat gold and Rupee as one entity for the increment

and inflation calculation.

Present Rupee to dollar conversion is 50 to 1.

33:1

37:1

41:1

45:1


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10) A shopkeeper sells goods at 10% loss. If he had sold it at 20% profit, he would have earned Rs 1200

more. What is the cost price of the goods?

Rs. 2000

Rs. 3000

Rs. 4000

Rs. 5000

Sol:Let the CP be 'x'. SP = (1- 10/100) x = 0.90x Had he sold at 20% profit, then SP = (1 + 20/100) x = 1.20x

Given that, 1.20x - 0.90x = 1200 or, x = 1200/0.3 = Rs 4000


11) A trader claims to his customers that he does not make any profit from the goods he sells as he sells

them at the price he bought from retailer. However what his customers don't know is that he uses a

weight of 900 gm instead of 1000 gm. What will the profit percent earned by the trader if he wishes to

make another profit of 20% from the sale?

11.11%

22.22%

33.33%

31.11%

Sol:Let us take the cost price of 1 gm = Rs 1 Selling price = Rs 1000,

Cost price = Rs 900, Profit = Rs 100

Profit % = (Profit x 100)/ CP = 100 x100 /900 = 11.11%


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To find the total profit %, we can use the successive % change formula.

Successive % increase = x + y + (xy)/100= 11.11 + 20 + (11.11 x 20)/100= 33.33%


12) A shopkeeper loses 10% by selling onions at 26 for Rs 5. How many should he sell for a rupee to gain

17%?

3.5

5

4

3

Sol:The shopkeeper loses10% for selling 26 onions at Rs.5, the SP = Rs. 0.19 per onion

So the CP = SP / (1 - loss%/100) = 0.19/(1 - 10/100) = 0.19/0.9= Rs. 0.21 per onion For a 17% profit,

his SP will be = 0.21 x (1 + 17/100) = 0.21 x 1.17 = Rs.0.247

For a rupee that will come out to 1/0.247 = approximately 4. Hence, the correct answer is option (c).

13) An honest shopkeeper professes to sell goods at cost price; however he uses 800 gm weight instead

of 1000 gm. If the shopkeeper wishes to sell it at additional 15% profit, then find the total profit

percentage gained by him?


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43.75%

36.67%

51.11%

29.87%

Sol:if the cost of 1 gm of goods = Rs 1 Selling price = Rs 1000,

Cost price = Rs 800 Profit%=((1000-800))/800=25% He wishes it sell it as 15% profit, Total profit can be

found by successive % formulae x + y + (xy)/ 100 25 + 15 + (25 x15)/100 = 40 + 3.75 = 43.75%

Hence, the correct answer is option (a).

14) Ramesh buys a gift item at a marked price of Rs 100. He decides to sell the item by increasing its

marked price by 40% and then giving a discount of 10% on the new marked price. How much profit/loss

will he make on the item?

26% loss

26% profit

24% loss

24% profit

Sol:This is a very simple question on Discount.

Marked price = 100, New marked price = 140,

10% discount = 14, Selling price = 126.Hence Ramesh makes a profit of 26%.



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15) Cost price of an article is Rs 253. By giving a discount of Rs 50, he makes a profit of 9.09%. If he

doesn't give any discount, then what is his profit percentage?

28.85%

23.25%

33.33%

37.67%

Sol:SP=CP(1+1/11)=253x12/11=276 MP = 276 + 50 = 326 Since there is no discount to be given, the SP is

equal to MP. Profit = MP - CP = 326 - 253 = 73 Profit %=(73x100)/253=28.85% The calculation can be

done mentally as shown below. 10% of 253 = 25 and 30% of 253 = 75 Therefore, our answer must belittle less than 30%.


16) Shahrukh Khan bought Kolkata Knight Riders in 2008 for 240 crores. His main expenses per annum

are franchise fees 31 crores and 20 crores of administrative costs, and 20 crores on players' salaries. He

gets 24 crores from TV rights, 15 crores from main sponsors DLF and Vodafone and 20 crores in gate

receipts per year. He has other small sponsorship deals like NOKIA, Reebok, HDIL, Tag Heuretc and

manages to rope in 32 crores per annum. When will he break even on his investment?

2010

2025

2015

2020

Sol:Expenses = 31 + 20 + 20 = 71 Cr

Income = 24 + 15 + 20 + 32 = 91 Cr


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Profit = 91 - 71 = 20 Cr

To break even he needs to make 240 Cr, at the present rate, he'll need = 240/20= 12 Years.

Therefore, he'll break even in 2008 + 12 = 2020


17) iPod prices fall by 10% every year. Rohan has been waiting for 3 years for the iPod touch to reach his

budget of Rs.5000. Find what percent discount the store must offer to make the iPod touch priced

Rs.10000 3 years back, to fall into Rohan's budget?

17.5%

31.4%

29.7%

35.5%

Sol:Using the successive discount percentage formula,

after the second year the discount on the original price will be= 10 + 10 - 10 x 10 /100= 19%

And again for the third year it will be = 19 + 10 - 19 x 10 /100= 27.1%.

Therefore, its present cost = 10000 x (1 - 27.1/100) = Rs.7290

Rohan's budget is Rs 5000, so the discount needed = (Discount) x 100/MP= (7290 - 5000) x 100/7290 =

(2290/7290) x 100= 31.41% This calculation can be done mentally as 10% of 7290 = 729, 20% of 7290 =

1558 and 30% of 7290 = 2287 Therefore, the correct answer must be little more than 30% i.e. = 31.41%



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18)Vipul buys 10 Reliance stocks each at Rs.2345, 100 ITC stocks each at Rs.195 and 50 JP Associates

stocks at Rs.760. He sells them when in dire need of money at the prices 2156, 223 and 820 respectively.

What is his profit margin?

2.81%

4.59%

3.37%

5.32%

Sol:Total investment = 10 x 2345 + 100 x 195 + 50 x 760 = 23450 +19500 + 38000= Rs. 80950

Selling Price = 10 x 2156 + 100 x 223 + 50 x 820 = 21560 + 22300 + 41000= Rs. 84860

Profit = 84860 - 80950= Rs.3900

Profit margin = (3900 x 100)/84860

This calculation can be easily done by using options

. 10% of 84860 = 8486 and 5% of 84860 = 4243

Therefore, 4% of 84860 = (4243 - 848) = 3395 So the answer lies between 4% and 5% i.e. = 4.59%


19) Sachin auctioned the two bats he had used to score his double century for charity. The auction

commissioner set a base price of 1 crore for each bat. Since no bidders came forward, he lowered it to

50lakhs. One bat went 76lakhs other went for 97lakhs. What was the percentage loss over the earlier

set base price and the percentage profit over the latter base price?

13.5% loss, 73% Profit

13.5% loss, 146% profit

27% loss, 146% profit


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27% loss, 73% Profit

We can see that the two bats went for 76lakhs and 97 lakhs. Total sale value = 76 + 97 = 173 lakhs Earlier

base price for each bat = 1 Cr Total base price = 2 Cr. Total sale = 1.73 Cr Loss = 2 - 1.73 = 0.27 Cr

Percentage loss = 0.27 x 100/2 = 13.5% Loss Later base price = 50 lakhs = Total base sale value = 1 Cr

Total sale = 1.73 Cr Profit = 1.73 - 1 = 0.73 Cr Percentage profit = 0.73 x 100 / 1 = 73% Profit


20) A shopkeeper sells two Vases, one for 15% profit over the marked price and one for 15% loss at the

price of Rs.1000. Find the net percentage profit or loss in the transaction?

Loss 1.37%

Profit 1.37%

Loss 2.22%

Profit 2.22%

The selling price for both the vase is Rs.1000. One transaction earns 15% profit, Thus CP x (1 + 15/100) =

SP CP = 1000/1.15= Rs. 869.56 Other transaction earns 15% loss, Thus CP x (1 - 15/100) = SP CP =

1000/0.85= Rs. 1176.47 Total CP = 1176.47 + 869.56 = Rs. 2046.03 Total SP = 2000 Loss % = (2046.03 -

2000) x 100/2046.03= 2.22%


21) For every 150 chocolates bought, Mentos gives 20 for free, find out the percentage discount it is

offering through this offer?

23.5%

13.33%

26.67%


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11.75%

We know that if you purchase 'x' articles and

you get 'y' articles for free on that,

then discount percentage is given by (yx100)/(x + y)

So discount = 20 x 100 / (150 + 20)= 2000 / 170

In DI, we have done reciprocal of 17 in percentage = 5.88%

So 200/17 = 2 x 5.88% = 11.77%


22) A milkman mixes water with milk in the ratio 3:5, if the milks cost him Rs.15 a litre and he sells the

mixture for Rs.25 a litre with 5% discount(he sells the mixture after giving a 5% discount on Rs.25 a litre).

Find his percentage profit.

53.33%

87.28%

153.33%

128.14%

In a litre of the mixture there is 5 parts milk and 3 parts water.

So total milk in 1 litre of mixture = 1 x 5/ (5 + 3)= 0.625 litre

Cost for the mixture = 0.625 x 15 = Rs.9.375

Selling price = 25 x (1 - 5/100)= 25 x 0.95= Rs.23.75

Profit = (23.75 - 9.375) x 100/9.375= 153.33%


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23) Arjun buys a product and sells it off to Bhim for 20% profit, Bhim sells it at 10% discount to Nakul,

Nakul sells it to 25% profit to Sahadev, who sells it at 50% discount to Yudhishtir. Find what is the final

transaction price as percentage profit/loss of the price Arjun bought it for?

32.5% Profit

32.5% Loss

67.5% Profit

67.5% Loss

Let P be the CP for Arjun, He sells it to Bhim at 20% profit i.e. at 1.2P Bhim sells it at 10% discount = 1.2P

x 0.9 = 1.08P Nakul sells it at 25% profit = 1.08P x 1.25 = 1.35P Sahadev sells it at 50% discount = 1.35P x

0.5 = 0.675P Original CP to Arjun = P Therefore Loss% = (P - 0.675P) x 100/P= 32.5% loss

Hence, the correct answer is option (b)

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