Question 11 Mark
The cost price of $10$ tables is equal to the sale price of $5$ tables. The profit per cent in this transaction is ________.
AnswerThe cost price of $10$ tables is equal to the sale price of $5$ tables. The profit per cent in this transaction is $100\%.$
Solution:
Let the cost price of $1$ table be $Rs. 1$.
The cost price of $10$ tables $=$ Sale price of $5$ tables Profit $=$ Cost price of $5$ tables $= Rs. 5$ Profit percentage$=\frac{\text{profit}}{\text{Cp}}\times100=\frac{5}{5}\times100=100\%$
View full question & answer→Question 21 Mark
Simple interest on a given amount is always less than or equal to the compound interest on the same amount for the same time period and at the same rate of interest per annum.
AnswerFor $1$ year, the simple interest and compound interest for same amount on same rate of interest are equal. But for $2$ year, the simple interest is less than the compound interest for same amount on same rate of interest.
View full question & answer→Question 31 Mark
Four times a number is a _______ $\% $ increase in the number.
AnswerFour times a number is a $3\%$ increase in the number.
Solution:
Let $x$ be the number. So, four times of $x$ is $Ax.$
Hence, $Ax$ is greater than $x$ by $4x – x = 3x$
View full question & answer→Question 41 Mark
The value of a car, bought for $Rs. 4,40,000$ depreciates each year by $10\%$ of its value at the beginning of that year. So its value becomes $Rs. 3,08,000$ after three years.
AnswerThe value of a car i.e. principal $= Rs.440000$ Rate of depreciation $(R\%) = 10\%$ per annum Time period $(T) = 3$ year The value of the car after depreciation in $3$ year is given by$\text{A}=\text{P}\Big(1-\frac{\text{R}}{100}\Big)^{\text{T}}$
$=440000\Big(1-\frac{10}{100}\Big)^{3}$
$=440000\times\frac{9}{10}\times\frac{9}{10}\times\frac{9}{10}$
$=440\times729=\text{Rs.} \ 320760$
View full question & answer→Question 51 Mark
The compound interest on $Rs. 8,000$ for one year at $16\%$ p.a.
compounded half yearly is ________ given that $(1.08)^2 = 1.1664.$
AnswerThe compound interest on $Rs. 8,000$ for one year at $16\%$ p.a.
compounded half yearly is _______ given that $(1.08)^2 = 1.1664.$
Solution:
Given, Principal $(P) = Rs. 8000$
Time period $(T) = 1$ year
Rate $(R) = 16\%$ per annum compounded half-yearly
View full question & answer→Question 61 Mark
A man purchased a bicycle for $Rs. 1,040$ and sold it for $Rs. 800.$ His gain per cent is $30\%$.
AnswerCost pride of the bicycle $= Rs. 1040$
Selling price of the bicycle$ =Rs. 800$
Loss = Cost price – Selling price $= Rs. 1040 - Rs. 800 = Rs. 240$
Hence, loss$\% = \frac{\text{Loss}}{\text{Cost price}}\times100$
$=\frac{240}{1040}\times100$
$=\frac{240}{104}=23.07\%$
View full question & answer→Question 71 Mark
The loss per cent on selling $140$ geometry boxes at the loss of $S.P.$ of $10$ geometry boxes is equal to ________.
AnswerLet the selling price of $1$ geometry box be $Rs. 1.$
So, the selling price for $140$ geometry boxes $= Rs. 1 \times 140 = Rs. 140$
Similarly, selling price of $10$ geometry boxes $= Rs. 1 \times 10 = Rs. 10v$
Loss = Selling price of $10$ geometry boxes $= Rs.10$
Loss percentage$=\frac{\text{Loss}}{\text{Cp}}\times100$
$=\frac{10}{140+10}\times100$
$=\frac{10}{150}\times100=\frac{20}{3}\%=6\frac{2}{3}\%$
View full question & answer→Question 81 Mark
Compound interest is the interest calculated on the previous year’s amount.
Answer$V$ Compound interest, $Cl = A - P$ Where,
$\text{A}=\text{P}\Big[1+\frac{\text{R}}{100}\Big]^{\text{n}}$
Here, $P =$ Principal on previous year’s amount and $A =$ Present year’s amount $R =$ Rate of interest and $n =$ time
View full question & answer→Question 91 Mark
Abida bought $100$ pens at the rate of $Rs. 3.50$ per pen and pays a sales tax of $4\%.$ The total amount paid by Abida is _______.
AnswerAbida bought $100$ pens at the rate of $Rs. 3.50$ per pen and pays a sales tax of $4\%.$ The total amount paid by Abida is $Rs. 364.$
Solution:
Number of pens bought by Abida $= 100$
Rate of per pen $= Rs. 3.50$
So, cost of $100$ pens $= 100 × 3.50 = 1350$
Abida also paid $4\%$ sales tax on $Rs. 350.$
So, the total amount paid by Abida$=350\times\frac{4}{100}+350$
$=350\times\frac{1}{25}+350=14+350=\text{Rs.}364.$
View full question & answer→Question 101 Mark
The compound interest on a sum of $Rs.P$ for $T$ years at $R\%$ per annum compounded annually is given by the formula$\text{P}\Big(1+\frac{\text{R}}{100}\Big).$
AnswerThe compound interest on a sum of $Rs.P$ for $T$ years at $R\%$ per annum compounded annually is given by the formula Compound interest $= A - P$
Where, $\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{T}}$
View full question & answer→Question 111 Mark
Sita is practicing basket ball. She has managed to score $32$ baskets in $35$ attempts. What is her success rate in per centage$?$
AnswerSita managed to score $32$ baskets in $35$ attempts.
Her success rate$=\frac{32}{35}\times100=\frac{3200}{35}=91.428\%=91.43\%$
View full question & answer→Question 121 Mark
Percentages are _________ to fractions with _________ equal to $100.$
AnswerPercentages are equal to fractions with denominator equal to $100.$
Solution:
Percentages are equal to fractions with denominator equal to $100$. e.g. $8\%$ means $8/100.$
View full question & answer→Question 131 Mark
Find the $S.P.$ if: $M.P. = Rs. 5450$ and discount $= 5\%$
AnswerMarked price $= Rs. 5450,$
Discount $\% = 5\%$
$\text{Selling price}=\text{Marked price}-\frac{\text{Discount}\%}{100}\times\text{Market price}$
$=5450-\frac{5}{100}\times5450$
$=5450-272.5=\text{Rs.} \ 5177.5$
View full question & answer→Question 141 Mark
The time period after which the interest is added each time to form a new principal is called the _________.
AnswerThe time period after which the interest is added each time to form a new principal is called the Conversion period.Solution:
The time period after which the interest is added each time to form a new principal, is called the conversion period.
View full question & answer→Question 151 Mark
$5\%$ sales tax is charged on an article marked $Rs. 200$ after allowing a discount of $5\%,$ then the amount payable is _______ .
Answer$5\%$ sales tax is charged on an article marked $Rs. 200$ after allowing a discount of $5\%,$ then the amount payable is $Rs. 199.50.$
Solution:
The marked price of the article $= 1200$
Discount $= 5\%$
Selling price of the article$=200-\frac{5}{100}\times200$
$= 200 - 10 = \text{Rs} . 190$
Selling price including $5\%$ sales tax$=190+\frac{5}{100}\times190$
$= 190 + 9.5 = \text{Rs}. 199.5$
Payable amount $= \text{Rs.} 199.50$
View full question & answer→Question 161 Mark
Discount $=$ Discount $\%$ of _________.
AnswerDiscount $=$ Discount $\%$ of Market price.
Solution:
Discount $=$ Discount $\%$ of marked price $[$discount is a reduction given on marked price$]$
View full question & answer→Question 171 Mark
Additional expenses made after buying an article are included in the cost price and are known as Value Added Tax.
AnswerIn the selling price $($known as $MRP)$ include the tax known as $VAT ($Value Added Tax$).$
Hence, $VAT$ is always included in selling price
View full question & answer→Question 181 Mark
______expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.
AnswerOverhead expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase. Solution: Overhead expenses are the additional expenses incurred by a buyer for an item over and above its cost of purchase.
View full question & answer→Question 191 Mark
By selling an article for $Rs. 1,12,000$ a girl gains $40\%$. The cost price of the article was ________.
AnswerBy selling an article for $Rs. 1,12,000$ a girl gains $40\%$.
The cost price of the article was $Rs.80000.$
Solution:
Selling price of an article $= Rs.112000$
Gain$\% = 40\%$ .
Let $Rs. x$ be the cost price of the article.
Cost price $=$ Selling price $–$ Profit$\%$ on cost price Selling price $=$ Cost price $+$ Profit$\%$ on cost price
So, $112000=\text{x}+\text{x}\times\frac{40}{100}$$112000=\frac{7\text{x}}{5}$
$\text{x}=\frac{112000\times5}{7}=16000\times5=\text{Rs.}80000$
View full question & answer→Question 201 Mark
If the discount of $Rs. y$ is available on the marked price of $Rs. x,$ then the discount percent is $\frac{\text{x}}{\text{y}}\times100\%$.
AnswerMarked price $= Rs. x$
Discount amount $= Rs. y$
Discount percentage $=$ Discount / Marked price $x$
$100\%=\frac{\text{y}}{\text{x}}\times100\%$
View full question & answer→Question 211 Mark
Selling price of $9$ articles is equal to the cost price of $15$ articles. In this transaction there is profit of $66\frac{2}{3}\%$.
AnswerSelling price of $9$ articles $=$ Cost price of $15$ articles It means,
$15$ articles $-\ 9$ articles $= 6$ articles Cost price of $6$ articles is the profit on transaction.
$\text{profit}\%=\frac{6}{9}\times100=\frac{600}{9}=\frac{200}{3}=66\frac{2}{3}\%$
View full question & answer→Question 221 Mark
The original price of a shampoo bottle bought for $Rs. 324$ if $8\%\ VAT$ is included in the price is $Rs. 300.$
AnswerThe original price of a shampoo bottle $= Rs.300$
Cost price of shampoo bottle after $8\%\ VAT$$=300+\frac{8}{100}\times300$
$300+8\times3=300+24=\text{Rs.} \ 324$
View full question & answer→Question 231 Mark
$15\%$ increase in price of an article, which is $Rs. 1,620,$ is the increase of $Rs$ _______.
Answer$15\%$ increase in price of an article, which is $Rs. 1,620,$ is the increase of $Rs.212.$
Solution:
Let the price of the article be $Rs. x.$ After $15\%$ increased in price, became $Rs.1620$
So, $1620=\text{x}+\text{x}\times\frac{15}{100}$$1620=\frac{115\text{x}}{100}$
$115\text{x}=1620\times100$
$\text{x}=\frac{1620\times100}{115}$
$\text{x}=\text{Rs.} \ 1408$
Hence, increase in price $= Rs. 1620 - Rs. 1408 = Rs. 212$
View full question & answer→Question 241 Mark
Number of students appearing for class $X$ $CBSE$ examination increases from $91,422$ in $1999-2000$ to $11,6054$ in $2008–09.$ Increase in the number of students appeared is approximately $27\%.$
AnswerNumber of students increase from $116054$ in $2008-09$ to $91422$ in $1999-2000 = 116054 - 91422 = 24632$
Percentage of increase in number of students$=\frac{\text{Number of students increase}}{\text{Number of students in previous year}}\times100$$=\frac{24632}{91422}\times100=02694\times100=26.9=27\%$
View full question & answer→Question 251 Mark
Sales tax $=$ tax $\%$ of ________.
AnswerSales tax $=$ tax $\%$ of Bill amount.
Solution:
Sales tax $=$ Tax $\%$ of bill amount
View full question & answer→Question 261 Mark
Sales tax is always calculated on the cost price of an item and is added to the value of the bill.
AnswerFalse Solution: Sales tax is always calculated on the selling price of an item and is added to the value of the bill.
View full question & answer→Question 271 Mark
The cost of a book marked at $Rs. 190$ after paying a sales tax of $2\%$ is $Rs. 192.$
AnswerMarked price of a book $= Rs.190$
Sales tax $= 2\%$
The cost price of a book after $2\%$
sales tax$=190+\frac{2}{100}\times190$
$=190+\frac{190}{50}=190+3.8=\text{R.s}=193.8$
View full question & answer→Question 281 Mark
Madhu’s room measures $6m × 3m.$ Her carpet covers 8m2. What per cent of floor is covered by the carpet$?$
AnswerMadhu’s room measures $= 6m × 3m$
Area of the room $= 6 × 3 = 18m^2$
Her carpet covers $= 8m$
Area covered by the carpet in percentage$=\frac{8}{18}\times100=\frac{800}{18}=44.44\%$
View full question & answer→Question 291 Mark
Amount when interest is compounded annually is given by the formula _________.
AnswerAmount when interest is compounded annually is given by the formula $\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{T}}$.
Solution:
Amount when interest is compounded annually is given by the formula $\text{A}=\text{P}\Big(1+\frac{\text{R}}{100}\Big)^{\text{T}}$
where, $P =$ principal,
$R =$ rate per annum and
$T =$ time
View full question & answer→Question 301 Mark
Discount $=$ ________ $–$ ________$.$
AnswerDiscount = Market price – Selling price.
Solution: Discount $= MP – SP$
Here, $MP =$ Marked price, and
$SP =$ Selling price
View full question & answer→Question 311 Mark
_________ is a reduction on the marked price of the article.
AnswerDiscount is a reduction on the marked price of the article.
View full question & answer→Question 321 Mark
$2500$ is greater than $500$ by ________$\%.$
Answer$2500$ is greater than $500$ by $400\%.$
Solution:
Difference between $2500$ and $500 = 2500 – 500 = 2000$
Hence, $\frac{2000}{500}\times100=\frac{2000}{5}=400\%$
View full question & answer→Question 331 Mark
The cost of a tape-recorder is $Rs. 10,800$ inclusive of sales tax charged at $8\%.$ The price of the tape-recorder before sales tax was charged is ______.
AnswerThe cost of a tape-recorder is $Rs. 10,800$ inclusive of sales tax charged at $8\%.$ The price of the tape-recorder before sales tax was charged is $Rs.10000.$
Solution:
The cost of tape recorder, inclusive of $8\%$ sales tax $= Rs.10800$
Let the price of the tape recorder before sales tax be $Rs. x$
So, $\text{x}+\text{x}\times\frac{8}{100}=10800$$\frac{108\text{x}}{100}=10800$
$\text{x}=\frac{10800}{108}\times100=100\times100$
$\text{x} = \text{Rs.} 10000$
Hence, the price of the tape recorder before sales tax charged is $Rs.10000$
View full question & answer→Question 341 Mark
The buying price of $5\ kg$ of flour with the rate $Rs. 20$ per kg, when $5\%\ ST$ is added on the purchase is $Rs. 21.$
AnswerTrueSolution:
Total flour bought $= 5\ kg$ Rate of $1\ kg$ flour $= Rs.20$ Cost of $5\ kg$ flour with $5\%$ sales tax$=5\times20+\frac{5}{100}\times(5\times20)$
$=100+\frac{5}{100}\times100=100+5=\text{Rs.}105$
Per $kg$ flour rate after $5\%$ sales tax$=\frac{105}{5}=\text{Rs.} 21$
View full question & answer→Question 351 Mark
Discount is a reduction given on cost price of an article.
AnswerFalseSolution:
Discount is a reduction given on marked price not on cost price.
View full question & answer→Question 361 Mark
In the first year on an investment of $Rs. 6,00,000$ the loss is $5\%$ and in the second year the gain is $10\%,$ the net result is ________.
AnswerIn the first year on an investment of $Rs. 6,00,000$ the loss is $5\%$ and in the second year the gain is $10\%,$ the net result is $Rs.627000.$
Solution:
Investment amount $= 7600000$ In $1st$ year, the loss in $1st$ year $= 5\%.$
So, investment in $1st$ year$=600000-\frac{5}{100}\times600000$
$= 600000 – 30000 = Rs. 570000$ In $2nd$ year, the gain is $10\%.$
So, net investment$=570000+\frac{10}{100}\times570000$
$=570000+57000=\text{Rs.}627000$
View full question & answer→Question 371 Mark
$C.P. = M.P.\ -$ Discount.
AnswerFalse Solution: The relation between marked price and discount is given by Selling price $=$ Marked price $-$ Discount
View full question & answer→Question 381 Mark
Increase of a number from $150$ to $162$ is equal to increase of _______ per cent.
AnswerIncrease of a number from $150$ to $162$ is equal to increase of $8$ percent.
Solution: Initial number $= 150$
Final number $= 162$
Increased number $= 162 -150 = 12$ Per cent of increased number$=\frac{12}{150}\times=\frac{120}{15}=8\%$
View full question & answer→Question 391 Mark
$M.P. = Rs. 1300$ and discount $= 1.5\%:$
AnswerMarked price $(MP) = Rs. 1300$
Discount $\% = 1.5\%$
$\text{Selling price}=\text{Marked price}-\frac{\text{Discount}\%}{100}\times\text{Marked price}$
$=1300-\frac{5}{100}\times1300$$=1300-19.5=\text{Rs.} \ 1280.5$
View full question & answer→Question 401 Mark
In case of loss, $C.P.=\frac{100\times\text{S.P.}}{100+\text{Loss}\%}$
AnswerLoss $=$ Cost price $-$ Selling price$\text{Loss}\%=\frac{\text{Loss}}{\text{Cost price}}\times100$
$\text{Cost price}=\frac{100}{100-\text{loss%}}\times\text{selling price}$
View full question & answer→Question 411 Mark
A student used the proportionn$\frac{\text{n}}{100}=\frac{5}{32}$ to find $5\%$ of $32$. What did the student do wrong$?$
Answer$5\%$ of $32$ will be calculated as$\frac{5}{100}\times32=\frac{32}{20}=1.6$
But student finding percent is $5$ of $32.$
View full question & answer→Question 421 Mark
When principal $P$ is compounded semi-annually at $r\%$ per annum for $t$ years, then Amount = ________.
AnswerWhen principal $P$ is compounded semi-annually at $r \%$ per annum for $t$ years, then Amount = $\text{A}=\text{P}\Big(1+\frac{\text{r}}{200}\Big)^{\text{2t}}$.
Solution:
When principal $P$ is compounded semi-annually at $r\%$ per annum for $t$ years. i.e., Rate$=\frac{\text{r}}{2}$ and time, $t = 2 × t$ then, amount = Principal
$\Big(1+\frac{\text{Rate}}{200}\Big)^{2\times\text{Time}}$ i.e., $\text{A}=\text{P}\Big(1+\frac{\text{r}}{200}\Big)^{\text{2t}}$
View full question & answer→Question 431 Mark
If amount on the principal of $Rs. 6,000$ is written as $6000 \Big[1+\frac{5}{100}\Big]^3$and compound interest payable half yearly, then rate of interest p.a. is _______ and time in years is _______.
AnswerIf amount on the principal of $Rs. 6,000$ is written as $6000 \Big[1+\frac{5}{100}\Big]^3$and compound interest payable half yearly, then rate of interest p.a. is $10\%$ and time in years is $1\frac{1}{2}\text{yr}.$
View full question & answer→Question 441 Mark
The cost of a sewing machine is $Rs. 7,000.$ Its value depreciates at $8\%$ p.a. Then the value of the machine after $2$ years is $Rs. 5,924.80.$
AnswerPrincipal $= Rs.7000$ Rate of depreciation $= 3\%$ per annum Time period $= 2$ year$\text{A}=\text{P}\Big(1-\frac{\text{R}}{100}\Big)^{\text{n}}=7000\Big(1-\frac{8}{100}\Big)^2$
$=7000\times\frac{23}{25}\times\frac{23}{25}$
$=11.2\times23\times23=\text{Rs.} \ 5924.8$
View full question & answer→Question 451 Mark
In case of gain, $\text{S.P}=\frac{(100+\text{gain}\%)\times\text{C.P.}}{100}$
AnswerWe know that, Gain $=$ selling price $–$ cost price
$\text{Gain}\%=\frac{\text{Gain}}{\text{Cost price}}\times100$
$\text{Selling price}=\frac{100+\text{Gain}\%}{100}\times\text{Cost price}$
View full question & answer→Question 461 Mark
To calculate the growth of a bacteria if the rate of growth is known, the formula for calculation of amount in compound interest can be used.
AnswerFor calculating the growth of a bacteria of the rate of growth is known, then we can use the formula for calculation of amount in compound interest.
where, $A =$ growth after $n$ years,
$P =$ initial number of bacteria and
$R =$ rate of growth
View full question & answer→Question 471 Mark
Three times a number is $200\%$ increase in the number, then onethird of the same number is $200\%$ decrease in the number.
AnswerLet $x$ be the number.
So, three times of $x = 3x$
Difference between $3x$ and $x = 3x - x = 2x$
Percentage increase in $\text{x}=\frac{\text{2x}}{\text{x}}\times100=200\%$
If one-third of$\text{x}=\frac{1}{3}\text{x}$
Difference between $x$ and$\frac{\text{x}}{3}=\text{x}-\frac{\text{x}}{3}=\frac{\text{2x}}{3}$
Percentage decreases$=\frac{3}{\text{x}}\times100$$=\frac{2}{3}\times100=66.6\%$
View full question & answer→Question 481 Mark
The discount on an item for sale is calculated on the _________.
Answer The discount on an item for sale is calculated on the Marked price. Solution:
The discount on an item for sale is calculated on the marked price. View full question & answer→Question 491 Mark
The marked price of an article when it is sold for $Rs. 880$ after a discount of $12\%$ is ________.
AnswerThe marked price of an article when it is sold for $Rs. 880$ after a discount of $12\%$ is Marked price $Rs. 1000.$
Solution:
Selling price of an article $= Rs. 880$
Discount $\% = 12\%$
We know that, discount is calculated oh marked price.
Let the marked price be $Rs. x.$
So, $\text{x}-\text{x}\times\frac{12}{100}=880$$\frac{88\text{x}}{100}=880$
$\text{x}=\frac{880}{88}\times100=\text{Rs.}1000$
So, marked price$=\text{Rs.} \ 1000$
View full question & answer→Question 501 Mark
________ is charged on the sale of an item by the government and is added to the bill amount.
AnswerSales tax is charged on the sale of an item by the government and is added to the bill amount. Solution: Sales tax is charged on the sale of an item by the government and is added to the bill amount. Sales tax = Tax % of bill amount
View full question & answer→