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28 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
Achal bought a second-hand car for $Rs. 2,25,000$ and spend $Rs. 25,000$ for repairing. If he sold it for $Rs. 3,25,000$, what is his profit per cent?
Answer
The cost price of second hand car $= Rs. 225000$
Also, Achal spends for repairing $= Rs. 25000$
So, actual cost for car $= Rs. 225000 + Rs. 25000 = Rs. 250000$
She sold the car $= Rs. 325000 $
Profit $= Rs. 325000 - Rs. 250000 = Rs. 75000$
$\text{Profit}\%=\frac{\text{Profit}}{\text{CP}\times100}$$=\frac{75000}{250000}\times100=\frac{7500}{250}=30\%$
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Question 23 Marks
$S.P. = Rs. 9,250$ and discount = $7\frac{1}{2}\%$
Answer
Selling price $(SP) = Rs. 9250$ discount$\% = 7\frac{1}{2}$% =$\frac{15}{2}\%$
Let marked price be Rs. $x$
$\text{Selling price}=\text{Marked price}-\frac{\text{Discount}\%}{100}\times\text{Marked price}$
$9250=\text{x}-\frac{15}{2\times100}\times\text{x}$
$9250=\frac{185\text{x}}{200}$
$\text{x}=\frac{9250\times220}{185}$
$\text{x}=\frac{1550000}{185}=\text{Rs.} \ 10000$
Hence, the marked price $= Rs. 10000$
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Question 33 Marks
A lady bought an air-conditioner for Rs. $15,200$ and spent Rs. $300$ and Rs. $500$ on its transportation and repair respectively. At what price should she sell it to make a gain of $15\%?$
Answer
The cost price of air conditioner $= Rs. 152000$
Also, spent amount on transportation $= Rs. 300$
Spent amount on repair $= Rs. 500$
Actual cost price of air conditioner with transportation charge & repair charges $= Rs. 15200 + Rs. 300 + Rs. 500 = Rs. 15500 + Rs. 500 = Rs. 16000$
For gain $15\%$ she should sell it for$=16000+16000\times\frac{15}{100}$$=16000+160\times15$
$=16000+2400=\text{Rs.} \ 18400$
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Question 43 Marks
In $1975$, the consumption of water for human use was about $3850$ cu.km/year. It increased to about $6000$ cu.km/year in the year $2000$. Find the per cent increase in the consumption of water from $1975$ to $2000$. Also, find the annual per cent increase in consumption (assuming water consumption increases uniformly).
Answer
The consumption of water for human in $1975 = 3850$ cu km/year
The consumption of water for human in $2000 = 6000$ cu km/year
Increase in consumption of water in $1975$ to $2000 = 6000 – 3850 = 2150$ cu km/year
In percentage$=\frac{2150}{3850}\times100=55.84\%$ In $25yr$
total increase in water consumption $= 2150$ cu km/year
Annually, i.e., per year water consumption$=\frac{2150}{25}=86 \text{cu km}\text\ \text{year}$
In percentage$=\frac{86}{3850}\times100=\frac{8600}{3850}=2.23\%$
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Question 53 Marks
The population of a town was decreasing every year due to migration, poverty and unemployment. The present population of the town is $6,31,680$. Last year the migration was 4% and the year before last, it was $6\%$. What was the population two years ago?
Answer
Let the population two years ago = P(principle) Present population of the town $= A = 631680$
Rate of migration in 1st year $= 4\%$
Rate of migration in 2nd year $= 6\%$ By using the formula,$\text{A}=\text{P}\Big(1-\frac{\text{R}}{100}\Big)(1-\frac{\text{R}}{100}\Big)$
$631680=\text{P}\Big(1-\frac{\text{4}}{100}\Big)(1-\frac{\text{6}}{100}\Big)$
$631680=\text{P}\times\frac{24}{25}\times\frac{47}{50}$
$\text{P}=\frac{631680\times25\times50}{24\times47}$
$=560\times1250=700000$
Hence, the population of town was $700000$ two years ago.
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Question 63 Marks
For an amount, explain why, a $20\%$ increase followed by a $20\%$ decrease is less than the original amount.
Answer
Let the original amount $= Rs. 100 20 \%$ increase in Rs. $100$
will be$=100+\frac{20}{100}\times100$$=100+20=\text{Rs.} \ 120$
Now, $20\%$ decrease in$\text{Rs}. \ 120=120-\frac{20}{100}\times120=120-24=\text{Rs}. \ 96$
Hence, decreased price is less than the original amount.
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Question 73 Marks
Lemons were bought at Rs $48$ per dozen and sold at the rate of Rs. $40$ per $10$. Find the gain or loss per cent.
Answer
Cost of $12$ lemon $= Rs. 48$ Cost of $1$ lemon$=\text{Rs.} \ \frac{48}{12}=\text{Rs.} \ 4$ lso, $10$ lemons sold by = $\text{Rs}. \ 40$ Selling price of $1$ lemon$=\text{Rs.}\frac{48}{10}=\text{Rs.} \ 4$
Cost price of $1$ lemon = Selling price of $1$ lemon No profit & no loss.
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Question 83 Marks
Rahim borrowed $Rs. 10,24,000$ from a bank for one year. If the bank charges interest of $5\%$ per annum, compounded half-yearly, what amount will he have to pay after the given time period. Also, find the interest paid by him.
Answer
Borrowed amount by Rahim $(P) = Rs. 1024000$ Time period $(T) = 1$ year Interest rate $(R) 5\%$ per annum compounded half yearly
Let amount $= A$ For compounded half-yearly, $\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{2\text{T}}$$=\text{1024000}\Big(1+\frac{\text{5}}{100}\Big)^{2}$
$=1024000\times\frac{41}{40}\times\frac{41}{40}$
$=640\times41\times41=\text{Rs.} \ 1075840$
Compound interest, $\text{CI}=\text{A}-\text{P}=\text{Rs.} \ 1075840$$\text{Rs.} \ 1024000=\text{Rs.} \ 51840$
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Question 93 Marks
The marked price of an article is $Rs. 500$. The shopkeeper gives a discount of $5\%$ and still makes a profit of $25\%.$ Find the cost price of the article.
Answer
Given, marked price of an article $= Rs. 500$ Discount $\% = 5\%$
But it makes a profit of $25\%.$
Let the cost price of the article be Rs. $x.$
Cost price after 5% discount$=5-\frac{5}{100}\times500$$=500-25=\text{Rs.} \ 475$
According to the question, (100 + 25)% of x = 475$\frac{125}{100}\times\text{x}=475$
$\text{x}=\frac{475\times100}{125}$
$=38\times100=\text{Rs.} \ 380$
Hence, cost price of an article is $Rs. 380$
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Question 103 Marks
Jyotsana bought a product for $Rs. 3,155$ including $4.5\%$ sales tax. Find the price before tax was added.
Answer
A product bought by Jyotsana for Rs. $3155$ including $4,5\%$ sales tax.
Let the price of the product before sales tax be Rs. $x$
So, $\text{x}+\text{x}\times\frac{45}{100}=3155$
$\text{x}+\frac{\text{x}\times45}{1000}=3155$
$\text{x}=\frac{3155\times1000}{1045}$
$=\frac{3155000}{1045}=\text{Rs}. 3019.1387$
$\text{x}=\text{Rs.} \ 3019.14$
Hence, the price of the product before sales tax is $Rs. 3019.14$
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Question 113 Marks
A new computer costs $Rs. 1,00,000$. The depreciation of computers is very high as new models with better technological advantages are coming into the market. The depreciation is as high as $50\%$ every year. How much will the cost of computer be after two years?
Answer
The cost of the new computer = Rs. $100000$ The depreciation rate $= 50\%$ per annum Time period $(T) = 2$ year Let the cost of computer after $2$ year = Rs. A$\text{A}=\text{P}\Big(1-\frac{\text{R}}{100}\Big)^{\text{T}}$
$=\text{100000}\Big(1-\frac{\text{50}}{100}\Big)^{\text{2}}$
$\text{A}=100000\times\frac{1}{2}\times\frac{1}{2}$
$\text{A}=\text{Rs}. \ 25000\times1$
Hence, the cost of computer after $2$ year is Rs.$25000.$
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Question 123 Marks
A shopkeeper was selling all his items at $25\%$ discount. During the off season, he offered $30\%$ discount over and above the existing discount. If Pragya bought a skirt which was marked for $Rs. 1,200$, how much did she pay for it?
Answer
Marked price of the skirt $= Rs. 1200$ During normal season discount$@ \ 25\%=\frac{25}{100}\times1200=25\times12=\text{Rs.} \ 300$ Price of the skirt after discount = $=\text{Rs.} \ 1200$
$-\text{Rs}. \ 300=\text{Rs.} \ 900$ In off season, the shopkeeper also after discount$@ \ 30\%=\frac{30}{100}\times900=\text{Rs.} \ 270$
Price of skirt after $30\%$ discount = $=\text{Rs.}900-270=\text{Rs.} \ 630$
So, Rs. $630$ paid by Pragya for the skirt.
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Question 133 Marks
Find discount in per cent when: $M.P. = Rs. 900$ and $S.P. = Rs. 873$
Answer
Marked price $(MP) = Rs. 900$
Selling price $(SP) = Rs. 873$
Discount = Marked price - Selling price $= Rs. 900 - Rs. 873 = Rs. 27$
$\text{Discount}\%=\frac{\text{Discount}}{\text{Marked price}}\times100$
$=\frac{27}{900}\times100=\frac{27}{9}=3\%$
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Question 143 Marks
Ayesha announced a festival discount of $25\%$ on all the items in her mobile phone shop. Ramandeep bought a mobile phone for himself. He got a discount of Rs. $1,960$. What was the marked price of the mobile phone?
Answer
Let the marked price of the mobile phone be Rs. $x$
Festival discount on mobile phone $= 25\%$
Ramandeep got total discount $= Rs. 1960$
 According to the question,$1960=\text{x}\times\frac{25}{100}$
$1960=\frac{\text{x}}{4}$
$\frac{\text{x}}{4}=1960$
$\text{x}=1960\times4=\text{Rs}. \ 7840$
Hence, marked price of the mobile phone Rs. $7840$
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Question 153 Marks
Three bags contain $64.2\ kg$ of sugar. The second bag contains$\frac{4}{5}$ of the contents of the first and the third contains $45\frac{1}{2}$% of what there is in the second bag. How much sugar is there in each bag?
Answer
The total weight of sugar in three bags $= 64.2kg$
Let the first bag contains $x$ kg sugar. The second bag contains$=\text{x}\times\frac{4}{5}\text{kg}=\frac{4\text{x}}{5}\text{kg}$
Third beg contains$=\text{x}\times\frac{4}{5}\times\frac{91}{2}\%=\text{x}\times\frac{4}{5}\times\frac{\frac{91}{2}}{100}=\frac{91\text{x}}{250}\text{kg}$
According to the question$\text{x}+\frac{4\text{x}}{5}+\frac{91\text{x}}{250}=64.2$
$\frac{250+200\text{x}+91\text{x}}{250}=64.2$
$541\text{x}=64.2\times250$
$\text{x}=\frac{16050}{541}=29.67\text{Kg}$
So, first bag contains the sugar = $28.73\text{kg}$
Second bag contains the sugar$=29.67\times\frac{4}{5}=23.73\text{kg}$
third bag contains the sugar$=\frac{91}{250}\times29.67=10.8\text{kg}$
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Question 163 Marks
$S.P. = Rs. 495$ and discount $= 1\%$
Answer
Selling price $(SP) = Rs. 495$ Discount $\% = 1%$
Let the marked price be Rs. $x$
$\text{Selling price}=\text{Marked price}-\frac{\text{Discount}\%}{100}\times\text{Marked price}$
$495=\text{x}-\frac{1}{100}\times\text{x}$
$495=\text{x}-\frac{100\text{x}-\text{x}}{100}$
$495=\text{x}-\frac{99\text{x}}{100}$
$99\text{x}=49500$
$\text{x}=500$
Hence, the marked price $= Rs. 500$
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Question 173 Marks
In the year $2001$, the number of malaria patients admitted in the hospitals of a state was $4,375$. Every year this number decreases by 8%. Find the number of patients in $2003.$
Answer
The number of malaria patients admitted in a hospital in $2001 = 4375$
Rate of decrement of malaria patients $= 8\%$
Time period $2yr$ i.e., $2003-2001 = 2yr$
Let the number of patients in $2003$ be A By using formula,$\text{A}=\text{P}\Big(1-\frac{\text{R}}{100}\Big)^{\text{T}}$
$=4375\Big(1-\frac{8}{100}\Big)^2$
$=4375\times\frac{23}{25}\times\frac{23}{25}$
$=7\times23\times23=3703$
Hence, the number of patients in $2003$ was $3703.$
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Question 183 Marks
In Delhi University, in the year $2009 – 10, 49,000$ seats were availablefor admission to various courses at graduation level. Out of these $28,200$ seats were for the students of General Category while $7,400$ seats were reserved for $\text{SC}$ and $3,700$ seats for $\text{ST.}$ Find the per centage of seats available for:
$i.$ Students of General Category.
$ii.$ Students of $\text{SC}$ Category and $\text{ST}$ Category taken together.
Answer
The total number of seats available for admission in $2009-10 = 49000$
Seats reserved for General Category students $= 28200$
Seats reserved for $\text{SC}$ Category students $= 7400$
Seats reserved for $\text{ST}$ Category students $= 3700$
$i.$ Amount for $2^{nd}$ year$=43200\Big(1+\frac{8}{100}\Big)^1$
$=43200\times\frac{108}{100}=432\times108=\text{Rs.}46656$
Compound interest, $\text{CI}=\text{A}-\text{P}=\text{Rs.} \ 46656$$-\text{Rs.} \ 43200=\text{Rs.} \ 3456$
$ii.$ Now, if period i.e., time $(n) = 2$ year
Principal $= Rs. 40000$ and rate $= 8\%$ per annum
$\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{n}}$
$\text{A}=\text{40000}\Big(1+\frac{\text{8}}{100}\Big)^{\text{2}}$
$=40000\times\frac{108}{100}\times\frac{108}{100}=\text{Rs.}46656$
Amount , $\text{A}=\text{Rs.} \ 46656$
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Question 193 Marks
The following items are purchased from showroom: T-Shirt worth $Rs. 1200$. Jeans worth $Rs. 1000. 2$ Skirts worth Rs. $1350$ each.
Answer
T-Shirt worth $Rs. 1200$.
Jeans worth $Rs. 1000. 2$
Skirts worth Rs.$1350$ each.
Total cost $= Rs. 1200 + Rs. 1000 + Rs. 1350 = Rs. 3550$
Shikha have to pay sale tax $= 7\%$
So, the total amount to be paid$=3550+\frac{7}{100}\times3550$
$=3550+248.5=\text{Rs.} \ 3798.5$
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Question 203 Marks
Find discount in per cent when
$M.P. = Rs. 625$ and $S.P. = Rs. 562.50$
Answer
$MP = Rs.625$ and $SP = Rs.562.50 $Discount = Marked price – Selling price $= Rs. 625 − Rs. 562.5 = Rs.$ 62.5$\text{Discount}\%=\frac{\text{Discount}}{\text{Marked price}}\times100$
$=\frac{62.5}{62.5}\times100=\frac{6250}{6250}=10\%$
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Question 213 Marks
Brinda purchased $18$ coats at the rate of $Rs. 1,500$ each and sold them at a profit of 6%. If customer is to pay sales tax at the rate of $4\%$, how much will one coat cost to the customer and what will be the total profit earned by Brinda after selling all coats?
Answer
The cost of each coat $= Rs. 1500$
The total number of coat $= 18$
The total cost of $18$ coat $= Rs. 1500 \times 18 = Rs. 27000$
If Brinda sold them at profit $= 6\%$
The amount received by Brinda$=27000+27000\times\frac{6}{100}$$=27000+270\times6$
$=27000+1620=\text{Rs.} \ 28620$
If customer pay sale tax $=4\%$
So, cost price with sale tax$=28620+\frac{4}{100}\times28620$
$=28620+114.8=\text{Rs.} \ 29764.80$
Cost price of one coat for customer$=\frac{29764.8}{18}=\text{Rs.} \ 1653.60$ Profit earned by Brinda $=\text{Rs}. \ 28620-\text{Rs.} \ 27000=\text{Rs.} \ 1620$
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Question 223 Marks
Harshna gave her car for service at service station on $27-05-2009$ and was charged as follows:
$a. 3.10$ litres engine oil $@ Rs. 178.75$ per litre and $\text{VAT} @ 20\%.$
$b. Rs. 1,105.12$ for all other services and $\text{VAT} @ 12.5\%.$
$c. Rs. 2,095.80$ as labour charges and service tax $@10\%.$
$d. 3\%$ cess on service Tax.
Find the bill amount.
Answer
$a.$ The total litres of engine oil used $= 3.10 L$
Rate of engine oil per litres $=Rs. 178.75$
The cost of engine oil $= 3.10 \times 17875 = Rs. 554.125$
The cost of engine oil including $20\%\ \text{VAT}=55.4125+554.125\times\frac{20}{100}$
$=55.4125+\frac{554.125}{5}$
$554.125+110.825=\text{Rs}. \ 1243.26$
$b.$ amount paid for all services $= Rs. 1105.12$
Amount paid including $12.5\%\ \text{VAT}=1105.12+\frac{12.5}{100}\times1105.12$
$= 1105.12 + 138.14 =\text{ Rs}. \ 1243.26$
$c.$ Labour charges $= Rs. 2095.80$
Service tax $= 10\%$
Total labour charges including $10\%$ service tax
$2095.80+\frac{10}{100}\times2095.8$
$=2095.80+209.58$
$=\text{Rs.} \ 2305.38$
$d.$ Cess on service tax $@ \ 3\%=209.58\times\frac{3}{100}=2.095\times3$
$\text{Rs.} \ 6.285=\text{Rs.} \ 6.29$
Thus, total bill amount$=\text{Rs.}664.95+\text{Rs.} \ 1243.26+\text{Rs.}2305.38+\text{Rs.} \ 6.29$
$=\text{Rs.} \ 4219.88$
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Question 233 Marks
How much more per cent seats were won by $X$ as compared to $Y$ in Assembly Election in the state based on the data given below.
Party
Won (Out of 294)
$X$
$158$
$Y$
$105$
$Z$
$18$
$W$
$13$
Answer
On the basis of above give table, The total number of seats won by party $X = 158$
The total number of seats won by party $Y = 105$
Total number of seats in election $= 294$
Percentage of seats won by party$\text{X}=\frac{158}{294}\times100=53.74\%$
Percentage of seats won by party$\text{Y}=\frac{105}{294}\times100=35.71\%$
So, difference of percentage $=(53.74-35.71)\%=18.03\%$
Hence, party $X$ won $18.03\%$ compared to party $Y.$
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Question 243 Marks
What price should a shopkeeper mark on an article that costs him Rs. $600$ to gain $20\%$, after allowing a discount of $10\%.$
Answer
The cost price of the article $= Rs. 600$ Gain$% = 20\%\text{Gain}=\frac{600\times20}{100}=\text{Rs}. \ 120$
$SP =$ Gain $+ CP = Rs. 600 + Rs. 120 = Rs. 720$
Let marked price be Rs. $x$ Since, he allow a discount of $10\%$
According to the question, $x − 10%$ of$ x = Rs. 720$
$\text{x}-\frac{10\times\text{x}}{100}=720$
$\frac{100\text{x}-10\text{x}}{100}=720$
$\frac{90\text{x}}{100}=720$
$\text{x}=\frac{720\times100}{90}=\text{Rs.} \ 800$
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Question 253 Marks
The table shows the cost of sunscreen of two brands with and without sales tax. Which brand has a greater sales tax rate? Give the sales tax rate of each brand.
 
 
Cost
Cost+Tax(In Rs)
$1$
$X (100 \ gm)$
$70$
$75$
$2$
$Y(100 \ gm)$
$62$
$65$
Answer
Brand $X$ sunscreen cost $= Rs. 70$
With sales tax $= Rs. 75$
Sales tax paid $= Rs. 75 - Rs. 70 = Rs. 5$ Brand $Y$ sunscreen
cost = Rs. 62 With sales tax $= Rs. 65$
Sales tax paid $= Rs. 65 - Rs. 62 = Rs. 3$
Hence, brand $X$ has greater sales tax rate. Sales tax for brand$\text{X}=\frac{5}{70}\times100=\frac{50}{7}=7.14\%$
Sales tax for brand$\text{Y}=\frac{3}{62}\times100=\frac{300}{62}=4.838=4.84\%$
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Question 263 Marks
A store is having a $25\%$ discount sale. Sheela has a $Rs. 50$ gift voucher and wants to use it to buy a board game marked for $Rs. 320.$ She is not sure how to calculate the concession she will get. The sales clerk has suggested two ways to calculate the amount payable.
Method $1:$ Subtract $Rs. 50$ from the price and take $25\%$ off the resulting price.
 Method $2:$ Take $25\%$ off the original price and then subtract $Rs. 50.$
$a.$ Do you think both the methods will give the same result? If not, predict which method will be beneficial for her.
$b.$ For each method, calculate the amount Sheela would have to pay. Show your work.
$c.$ Which method do you think stores actually use? Why?
Answer
$a.$ Marked price of a board game $= Rs. 320$
Discount in store $= 25\%$
Sheela have a gift voucher value $= Rs. 50$
In method $1:$
$Rs. 320 - Rs. 50 = Rs. 270$
Now, $25\%$ discount on $\text{Rs}. \ 270=270-\frac{25}{100}\times270$
$=270-67.5=\text{Rs}. \ 202.5$
In method $2:$
$25\%$ off on $Rs. 320$, then subtract $Rs. 50$
$=320-\frac{25}{100}\times320-50$
$=320-80-50$
$=\text{Rs.} \ 190$
Hence, method $2$ will be beneficial for her.
$b.$ In method $1$ : Amount paid $= Rs. 202.5$
In method $2$ : Amount paid $= Rs. 190$
$c.$ Method $1$ will be used by stores because in this method actual discount in loss.
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Question 273 Marks
In $2007 – 08$, the number of students appeared for Class $X$ examination was $1,05,332$ and in $2008–09$, the number was $1,16,054$. If $88,151$ students pass the examination in $2007–08$ and $103804$ students in $2008–09$. What is the increase or decrease in pass $\%$ in Class $X$ result?
Answer
Number of students appeared in $2007-08 = 105332$ Number of students appeared in $2008-09 = 116054$ Number of students passed in $2007-08 = 88151$ Number of students passed in $2008-09 = 103804$ Passed percentage of students in $2007-08$$=\frac{\text{Number of students passed in 2007-08}}{\text{Number of students appeared in 2007-08}}\times100$
$=\frac{88151}{105332}\times100$
$=\frac{8815100}{105332}=83.68\%$
Passed percentage of students in $2008-09=\frac{\text{Number of students passed in 2007-08}}{\text{Number of students appeared in 2007-08}}\times100$
$=\frac{10394}{116054}\times100$
$=\frac{10380400}{110654}=89.44\%$
Increase in percentage = $89.44-83.68=5.76\%$
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Question 283 Marks
Living on your own: Sanjay is looking for one-bedroom appartment on rent. At Neelgiri appartments, rent for the first two months is $20 \%$ off. The one bedroom rate at Neelgiri is Rs. $6,000$ per month. At Savana appartments, the first month is $50 \%$ off. The one bedroom rate at Savana appartments is Rs. $7000$ per month. Which appartment will be cheaper for the first two months? By how much?
Answer
The one bedroom rate at Neelgiri $= Rs. 6000$
per month Also, $20\%$ off first two months, Rent for first $2$ months$=2\times\Big(6000-\frac{20}{100}\times6000\Big)$$=2\times4800=\text{Rs.} \ 9600$ In comparison of Savana apartments,
it offers $50\%$ off for first month, where the rent for bedroom is $Rs. 7000$
per month$=7000-\frac{50}{100}\times7000$$=7000-3500=\text{Rs}. \ 3500$
But rent for two months in Savana apartment $=\text{Rs.} \ 3500+\text{Rs.} \ 7000=\text{Rs.} \ 10500$
Hence, Neelgiri apartment will be cheaper by $=\text{Rs.} \ 10500-\text{Rs.} \ 9600=\text{Rs.} \ 900$
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