Question 11 Mark
If $A$ is increased by $20\%,$ it equals $B.$ If $B$ is decreased by $50\%,$ it equals $C.$ Then, _____$\%$ of $A$ is equal to $C.$
AnswerGiven, if $A$ is increased by $20\%,$ then it is equal to $B.$
$\therefore\text{A}+20\%\text{ of}\text{ A}=\text{B}$
$\Rightarrow\text{A}\Big(1+\frac{20}{100}\Big)=\text{B}$
$\Rightarrow\frac{120}{100}\text{ A}=\text{B}$
$\Rightarrow\text{B}=\frac{6}{5}\text{ A} \ ...(\text{i} )$
If $B$ is decreased by $50\%,$ then it is equal to $C.$
$\therefore\text{B}-50\%\text{ of}\text { B}= \text{C}$
$\Rightarrow\text{B}\Big(1-\frac{50}{100}\Big)=\text{C}$
$\Rightarrow\text{B}\times\frac{50}{100}=\text{C}$
$\Rightarrow\frac{1}{2}\text{B}=\text{C}$
$\Rightarrow\text{B}=2\text{C}\ ... (\text{ii})$
On comparing Eqs. $(i)$ and $(ii),$ We get $\frac{6}{5}\text{A}=2\text{C}$
$\Rightarrow\frac{\text{A}}{\text{C}}=\frac{10}{6}$
$\Rightarrow\text{C}=\frac{6}{10}$
$\Rightarrow\text{C}=\frac{3}{5}\text{A}$
$\therefore$ In percentage,
$\frac{\text{C}}{\text{A}}\times100=\frac{\frac{3}{5}\text{A}}{\text{A}}\times100\%$
$=\frac{3}{5}\times100\%$
$=60\%$
Hence, $80\%$ of $A$ is equal to $C.$
View full question & answer→Question 21 Mark
A vendor purchased $720$ lemons at $Rs. 120$ per hundred. $10\%$ of the lemons were found rotten, which he sold at $Rs. 50$ per hundred. If he sells the remaining lemons at $Rs. 125$ per hundred, then his profit will be $16\%.$
AnswerGiven, cost pricr of $100$ lemons $= Rs. 120$
Cost price of $1$ lemon $=\text{Rs.}\frac{120}{100}$
and cost price of $720$ lemons $=\frac{120}{100}\times720=\text{Rs.}864$
According to the question, $10\%$ of the lemons were rotten.
$\therefore 10\%$ of $720$ lemons $=\frac{10}{100}\times720=72\text{ lemons}$
Also, given, selling price of $100$ rotten lemons $= Rs. 50$
Selling price of $1$ rotten lenom $=\text{Rs.}\frac{50}{100}$
and selling price of $72$ rotten lemons $=\frac{50}{100}\times72=\text{Rs.}36.$
and selling price of $(720 - 72)$ good lemons
$=\frac{125}{100}\times(720-72)=\frac{125}{100}\times648=\text{Rs.}810$
Now, total selling price of $720$ lemons $= 36 + 810 = Rs. 846$
Clearly, selling price $ < $ cost price.
Therefore, vendor will bear loss.
View full question & answer→Question 31 Mark
Out of a total deposit of $Rs. 1500$ in her bank account, Abida withdrew $40\%$ of the deposit. Now, the balance in her account is _____.
AnswerTotal deposit $= Rs. 1500$
$\therefore$ Amount withdrawn $= 40\%$ of $\text{Rs. }1500=\frac{40}{100}\times1500=\text{Rs. }900$
View full question & answer→Question 41 Mark
Express $\frac{9}{40}$ as a per cent.
AnswerWe have, $\frac{9}{40}.$ In percentage, $\frac{9}{40}\times100\%=22\frac{1}{2}\%.$
View full question & answer→Question 51 Mark
In a class of $50$ students $8\%$ were absent on one day. The number of students present on that day, was ______.
AnswerWe have, total number of students $= 50$
Absent on one day $= 8\%$
Percentage of present students on that day $= 100 - 8 = 92\%$
$\therefore$ Number of students present on that day $= 92\%$ of $50=\frac{92}{100}\times50=\frac{92}{2}=46$
So, the number of students present on that day, was $46.$
View full question & answer→Question 61 Mark
If a bicycle was bought for $Rs. 650$ and sold for $Rs. 585$, then the percentage of profit is $10\%.$
AnswerGiven, $CP = Rs. 650$ and $SP = 585$
Since, $CP > SP$
Loss $= CP - SP = 650 - 585 = Rs. 65$
Now, $\text{Loss}\%=\frac{\text{Loss}}{\text{CP}}\times100=\frac{65}{650}\times100=10\%$
Hence, the percentage of loss is $10\%$
View full question & answer→Question 71 Mark
Express $16\frac{2}{3}\%$ as a ratio in the lowest form.
AnswerWe have, $16\frac{2}{3}\%=\frac{50}{3}\%$ For ration, $\frac{50}{3}\%:1$ $=\frac{50}{3}\times\frac{1}{100}:1$ $=\frac{1}{6}:1$ $=\frac{1}{6}\times6:1\times6$ $=1:6$
View full question & answer→Question 81 Mark
$50\%$ of $Rs. 50$ is $Rs. 25.$
AnswerSince, $50\%$ of $Rs. 50$
$=\frac{50}{100}\times50=\text{Rs.}25$
Hence, $50\%$ of $Rs. 50$ is $Rs. 25.$
View full question & answer→Question 91 Mark
Express $80\%$ as a fraction in its lowest form.
AnswerWe have, $80\%$ For fraction,
$80\times\frac{1}{100}=\frac{80}{100}=\frac{4}{5}$
$\Big[\text{to convet in fraction, multiply by}\frac{1}{100}\Big]$
View full question & answer→Question 101 Mark
What is $15\%$ of $20?$
AnswerWe have, $15\%$ of $20$
$=\frac{15}{100}\times20=3$
View full question & answer→Question 111 Mark
Express $150\%$ as a ratio in the lowest form.
AnswerWe have, $150\%$ For ration, $150\% : 1$
$=\frac{150}{100}:1$
$=\frac{3}{2}:1$
$\frac{3}{2}\times2:1\times2$
$=3:2$
View full question & answer→Question 121 Mark
When converted into percentage, the value of $6.5$ is ______ than $100\%.$
AnswerWe have, $6.5$
In percentage, $6.5 × 100\% = 650\%$
Hence, when converted into percentage, the value of $6.5$ is more than $100\%.$
View full question & answer→Question 131 Mark
Find out $8\%$ of $25\ kg.$
AnswerWe have, $8\%$ of $25\ kg$
$=\frac{8}{100}\times25=2\text{kg}$
View full question & answer→Question 141 Mark
A _______ with its denominator $100$ is called a percent.
AnswerA fraction with its denominator $100$ is called a percent.
View full question & answer→Question 151 Mark
Amount obtained by depositing $Rs. 20000$ at $8\%$ per annum for six months, is _____.
AnswerDeposited amount $= Rs. 20000$
Rate of interest $= 8\%$
Time period $6\text{ months}=\frac{6}{12}\text{ year}=\frac{1}{2}\text{ year}$
$\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{20000\times8\times\frac{1}{2}}{100}$
$=\frac{20000\times8}{200}=100\times8=\text{Rs. }800$
$\therefore$ Amount received $=$ Principal $+$ Interest $= 20000 + 800 = Rs. 20800$
View full question & answer→Question 161 Mark
Interest on $Rs. 1200$ for $1\frac{1}{2}\text{ year}$ at the rate of $15\%$ per annum is $Rs. 180.$
AnswerGiven, $P = Rs. 1200,$
$\text{T}=1\frac{1}{2}\text{ year}=\frac{3}{2}\text{ year}\text{ and R}=15\%$
$\therefore\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{1200\times15\times3}{2\times100}=\text{Rs.}270$
So, the interest is $Rs. 270.$
View full question & answer→Question 171 Mark
$120\%$ of $50\ km =$___________.
AnswerWe have, $120\%$ of $50\text{km}=\frac{120}{100}\times50\text{km}=60\text{km}$
View full question & answer→Question 181 Mark
By selling a book for $Rs. 50,$ a shopkeeper suffers a loss of $10\%.$ The cost price of the book is $Rs. 60.$
AnswerGiven, $SP = Rs. 50$ and loss percent $= 10\%$
We know that, $\text{Loss}\%=\frac{\text{Loss}}{\text{CP}}\times100\% [\therefore$ Loss $= CP - SP]$
$\Rightarrow\text{Loss}\%=\frac{\text{CP}-\text{}\text{S}\text{P}}{\text{CP}}\times100\%$
$\Rightarrow10=\frac{(\text{CP}-\text{SP})}{\text{CP}}\times100$
$\Rightarrow10\text{CP}=100\text{CP}-5000$
$\Rightarrow90\text{CP}=5000$
$\Rightarrow\text{CP}=\frac{5000}{90}$
$\therefore\text{CP}=\text{Rs.}55.55$
Hence, the cost price of the book is $Rs. 55.55$
View full question & answer→Question 191 Mark
Interest $=\frac{\text{P}\times\text{R}\times\text{T}}{100},$ where $T$ is _____, $R\%$ is ____ and $P$ is ____.
AnswerHere, $T$ is time period, $R\%$ is rate of interest and $P$ is Principal.
View full question & answer→Question 201 Mark
$2 : 3 = $________$\%$
AnswerGiven ratio $= 2 : 3$ In percentage $=\frac{2}{3}\times100\%=66\frac{2}{3}\%$
View full question & answer→Question 211 Mark
When an improper fraction is converted into percentage, then the answer can also be less than $100.$
AnswerConsider, an improper fraction $=\frac{12}{5}(\text{N}>\text{D} )$
In percentage, $\frac{12}{4}\times100\%=240\%$
Hence, when an improper fraction is converted into percentage,
then the answer is always greater than $100.$
View full question & answer→Question 221 Mark
What is $800\%$ of $800?$
AnswerWe have, $800\%$ of $800$
$=\frac{800}{100}\times800=6400$
View full question & answer→Question 231 Mark
AnswerWe know, Percentage $=$ Fraction $×\ 100$
$\text{Fraction}=\frac{\text{Percentage}}{100}$ $\text{Decimal}=\frac{\text{Percentage}}{100}$
Now, according to these formulae, we have.
| Percentage |
Fraction |
Decimal |
| $0\%$ |
$0$ |
$0$ |
| $12.5\%$ |
$\frac{1}{8}$ |
$0.1$ |
| $25\%$ |
$\frac{1}{4}$ |
$0.2$ |
| $37.5\%$ |
$\frac{3}{8}$ |
$0.3$ |
| $50\%$ |
$\frac{1}{2}$ |
$0.4$ |
| $62.5\%$ |
$\frac{5}{8}$ |
$0.5$ |
| $75\%$ |
$\frac{3}{4} $ |
$0.6$ |
| $87.5\%$ |
$\frac{7}{8}$ |
$0.7$ |
| $100\%$ |
$1$ |
$0.8$ |
View full question & answer→Question 241 Mark
$2.5 = $_____$\%$
AnswerWe have, $2.5$ In percentage, $2.5 × 100\% = 250\%$
View full question & answer→Question 251 Mark
$15\ kg$ is _______$\%$ of $50\ kg.$
AnswerLet $x\%$ of $50\ kg$ be $15\ kg.$
Then, $\frac{\text{x}}{100}\times50=15$
$\Rightarrow\frac{\text{x}}{2}=15$
$\Rightarrow\text{x}=15\times2$
$\therefore\text{x}=30\%$
Hence, $15\ kg$ is $30\%$ of $50\ kg.$
View full question & answer→Question 261 Mark
If the price of sugar is decreased by $20\%,$ then the new price of $3\ kg$ sugar originally costing $Rs. 120,$ will be ______.
AnswerOriginal price of $3\ kg$ sugar $= Rs. 120$
Given that, price of sugar is decreased by $20\%.$
So, new price of sugar $=$ Original price $-\ 20\%$ of original price $= 120 - 20\%$ of $120$
$=120-\frac{20}{100}\times120=120-24=\text{Rs. }96100$
View full question & answer→Question 271 Mark
Weight of Nikhil increased from $60\ kg$ to $66\ kg$. Then, the increase in weight is _____$\%$
AnswerWe have, initial weight of Nikhil $= 60\ kg$
After increase in weight, weight became $=66\ kg$
Increase in weight $= 66 - 60 = 6\ kg$
$\therefore$ Increase percentage of weight.
$\frac{\text{Increase}}{\text{Initialweight}}\times100\%=\frac{6}{60}\times100\%=\frac{60}{6}\%=10\%$
So, the number of students present on that day, was $46.$
View full question & answer→Question 281 Mark
The _____ of interests on a sum of $Rs. 2000$ at the rate of $6\%$ per annum for $1\frac{1}{2} \text{ year}$ and $2$ year is $Rs. 420.$
AnswerGiven, $p = Rs. 2000$ and $R = 6\%$
$\text{For }1\frac{ 1}{2}\text{ year},$
$\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{2000\times6\times3}{100\times2}$
$=\text{Rs.}180$
For $2$ year, $\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{2000\times6\times2}{100}$
$=\text{Rs.}240$
$\therefore$ The aum or interests is $Rs. (180 + 240),$ i.e. $Rs. 420$
View full question & answer→Question 291 Mark
Mohini bought a cow for $Rs. 9000$ and Sold it at a loss of $Rs. 900.$ The selling price of the cow is _______.
AnswerGiven, $CP$ of cow $= Rs. 9000$ and loss $= Rs. 900$
We know that, $SP = CP \ - $Loss $= 9000 - 900 = Rs. 8100$
Hence, the selling price of the cow is $Rs. 8100.$
View full question & answer→Question 301 Mark
If $20$ lemons are bought for $Rs. 10$ and sold at $5$ for three rupees, then ______ in the transaction is _____$\%.$
Answer$CP$ of $20$ lemons $= Rs. 10$
By unitary method, If $SP$ of $5$ lemons $= Rs. 3$
Then, $SP$ of $1$ lemon $=\text{Rs. }\frac{3}{5}$
$\therefore SP$ of $20$ lemons $=\frac{3}{5}\times20=\text{Rs. }12$
Now, $CP = Rs. 10$ and $SP = Rs. 2$
We know that, $\text{Profit}\%=\frac{\text{Profit}}{\text{CP}}\times100\%=\frac{2}{10}\times100\%=20\%$
Hence, Profit in the transaction is $20\%$
View full question & answer→Question 311 Mark
Match each of the entries in Column $I$ with the appropriate entries in Column $II:$
|
|
Column $I$
|
|
Column $II$
|
|
$(i)$
|
$3:5$
|
$(A)$
|
$Rs. 54$
|
|
$(ii)$
|
$2.5$
|
$(B)$
|
$Rs. 47$
|
|
$(iii)$
|
$100\%$
|
$(C)$
|
$Rs. 53$
|
|
$(iv)$
|
$\frac{2}{3}$
|
$(D)$
|
$Rs. 160$
|
|
$(v)$
|
$6\frac{1}{4}\%$
|
$(E)$
|
$60\%$
|
|
$(vi)$
|
$12.5 \%$
|
$(F)$
|
$25\%$
|
|
$(vii)$
|
$SP$ when $CP = Rs. 50$ and loss $= 6\%$
|
$(G)$
|
$\frac{1}{16}$
|
|
$(viii)$
|
$SP$ when $CP = Rs. 50$ and profit $= Rs. 4$
|
$(H)$
|
$250\%$
|
|
$(ix)$
|
Profit$\%$ when $CP = Rs. 40$ and $SP = Rs. 50$
|
$(I)$
|
$Rs. 159$
|
| $(x)$ |
Profit$\%$ when $CP = Rs. 50$ and $SP = Rs. 60$ |
$(J)$ |
$66\frac{2}{3}\%$ |
| $(xi)$ |
Interest when principal $= Rs. 800$, Rate of interest $= 10\%$ per annum and period $= 2$ years |
$(K)$ |
$20 \%$ |
| $(xii)$ |
Amount when principal $= Rs. 150$ Rate of interest $= 6\%$ per annum and period $= 1$ year |
$(L)$ |
$0.125$ |
| |
|
$(M)$ |
$3 : 2$ |
| |
|
$(N)$ |
$164$ |
| |
|
$(O)$ |
$3 : 3$ |
Answer$i. \rightarrow (E)$
Given, ratio $= 3 : 5$
In percentage, $\frac{3}{5}\times100\%=60\%$
$ii.\rightarrow (H)$
We have, $2.5$
In percentage, $2.5 \times 100\% = 250\%$
$iii. \rightarrow (O)$
We have, $100\%$
Ratio $= 100\% : 1$
$=\frac{100}{100}:1$
$\therefore$ Ration $= 1 : 1$
$= 1 \times 3 : 1 \times 3$
$= 3 : 3$
$iv. \rightarrow (J)$
We have, $\frac{2}{3}$
In percentaqge, $\frac{2}{3}\times100\%=66\frac{2}{3}\%$
$v. \rightarrow (G)$
We have, $6\frac{1}{4}\%=\frac{25}{4}\%$
For fraction, $\frac{25}{4}\times\frac{1}{100}=\frac{1}{16}$
$vi. \rightarrow (L)$
We have, $\frac{125}{10}\times\frac{1}{100}=\frac{125}{1000}$
For decimal, $\frac{125}{1000}=0.125$
$vii. \rightarrow (B)$
Given, $CP = Rs. 50,$ Loss $\% = 6\%, SP = ?$
We know that,
$\text{Loss}\%=\frac{\text{Loss}}{\text{CP}}\times100\%$
$\Rightarrow\text{Loss}\%=\frac{\text{CP}-\text{SP}}{\text{CP}}\times100\%$
$\Rightarrow6=\frac{(50-\text{SP})}{50}\times100$
$\Rightarrow\frac{6\times50}{100}=50-\text{SP}$
$\text{SP} =\text{Rs. }47$
$viii. \rightarrow (A)$
Given, $CP = Rs. 50,$ Profit $= 4, SP = ?$
We know that, Profit $= SP - CP$
$\Rightarrow SP =$ Profit $+\ CP$
$\therefore SP = 4 + 50 = Rs. 54$
$ix. \rightarrow (F)$
Given, $CP = Rs. 40, SP = Rs. 50,$ Profit$\% = ?$
We know that, Profit $= SP - CP = 50 - 40 = Rs. 10$
Now, $\text{Profit}\%=\frac{\text{Profit}}{\text{CP}}\times100\%$
$=\frac{10}{40}\times100\%$
$\therefore\text{Profit}\%=25\%$
$x. \rightarrow (K)$
Given, $CP = Rs. 50, SP = Rs. 60,$ Profit$\% = ?$
We know that,
Profit $= SP - CP$
Profit $= 60 - 50 = Rs. 10$
Now, $\text{Profit}\% =\frac{\text{Profit}}{\text{CP}}\times100\%=\frac{10}{50}\times100\%$
$xi. \rightarrow (D)$
Given, $P = Rs. 800, R = 10\%, T = 2$ year, $I = ?$
$\therefore\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{800\times10\times2}{100}=160$
$=\text{Rs. }160$
$xii. \rightarrow (I)$
Given, $P = Rs. 150, R = 6\%, T = 1$ year,$ A =?$
$\because\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$\therefore\text{I}=\frac{150\times6\times1}{100}=\text{Rs. }9$
Now, $A = P + I$
$= 150 + 9$
$= Rs. 159$
View full question & answer→Question 321 Mark
$8h$ is $50\%$ of $4$ days.
AnswerLet $8h$ be $x\%$ of $4$ days.
Then, $8h = x\%$ of $4$ days.
$\Rightarrow8=\frac{\text{x}}{100}\times4\times24$
$\Rightarrow\frac{8\times100}{4\times24}=\text{x}$
$\Rightarrow\text{x}=\frac{25}{3}=8\frac{1}{3}$
Hence, $8h$ is $8\frac{1}{3}\%$ of $4$ days.
View full question & answer→Question 331 Mark
The interest on $Rs. 350$ at $5\%$ per annum for $73$ days is $Rs. 35.$
AnswerGiven, $P = Rs. 350. R = 5\%$ and $\text{T}=73\text{ days}=\frac{73}{365}\text{ year}$
$\therefore\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$\text{I}=\frac{350\times5\times73}{100\times365}=\frac{127750}{36500}$
$\text{I}=\text{Rs.}3.5$
View full question & answer→Question 341 Mark
$\frac{2}{3}=66\frac{2}{3}\%.$
AnswerTrue. Solution: Given, $\text{fraction}=\frac{2}{3}$ In percentage, $\frac{2}{3}\times100\%=\frac{200}{3}\%=66\frac{2}{3}\%$
View full question & answer→Question 351 Mark
Write $1.56$ as a per cent.
AnswerWe have, $1.56$ In percentage, $1.56 \times 100\% = 156\%$
View full question & answer→Question 361 Mark
If Ankita obtains $336$ marks out of $600,$ then percentage of marks obtained by her is $33.6\%.$
AnswerMarks obtained by Ankita out of $600 = 336$ Percentage,
$\frac{336}{600}\times100\%=56\%$
Hence, Ankita got $56\%$ marks.
View full question & answer→Question 371 Mark
John sells a bat for $Rs. 75$ and suffers a loss of $Rs. 8.$ The cost price of the batis ___.
AnswerGiven, $SP$ of bat $= Rs.75$ and loss $= Rs. 8$
We know that,$ CP = SP\ +$ Loss $= 75 + 8 = Rs. 83$
Hence, cost price of the bat is $Rs. 83.$
View full question & answer→Question 381 Mark
Out of $600$ students of a school, $126$ go for a picnic. The percentage of students that did not go for the picnic, is $75.$
AnswerTotal students $=600 $
Students went for picnic $= 126$
$\therefore$ Students did not go for picnic $= 600 - 126 = 474$
In percentage, $\frac{471}{600}\times100\%=79\%$
Hence, $79\%$ of students did not go for picnic.
View full question & answer→Question 391 Mark
$25ml$ is _____$\%$ of $5$ literes.
AnswerLet $25\ ml$ be $x\%$ of $5L.$
Then, $25\ ml = x\%$ of $5L.$
$\Rightarrow25=\frac{\text{x}}{100}\times5\times1000$
$\Rightarrow\frac{25\times100}{5\times1000}=\text{x}$
$\Rightarrow\text{x}=0.5$
Hence, $25\ mL$ is $0.5\%$ of $5L.$
View full question & answer→Question 401 Mark
Express $33\frac{1}{3}\%$ as a ratio in the lowest form.
AnswerWe have, $33\frac{1}{3}\%$ For ratio, $33\frac{1}{3}\%.$
$\text{t}=\frac{100}{3}\times\frac{1}{100}:\text{t}$
$=\frac{1}{3}:1$
$=\frac{1}{3}\times3:1\times3$
$=1:3$
View full question & answer→Question 411 Mark
Narain bought $120$ oranges at $Rs. 4$ each. He sold $60\%$ of the oranges at $Rs. 5$ each and the remaining at $Rs. 3.50$ each. His _____ is _____$\%.$
AnswerGiven, $CP$ of $1$ orange $= Rs. 4$
$CP$ of $120$ oranges $= 4 \times 120 = Rs. 480$
Now,$60\%$ of $120$ oranges $=\frac{60}{100}\times120=72$
$\therefore SP$ of $72$ oranges $= 72 \times 5 = Rs. 360$
and $SP$ of remainig oranges $= (120 - 72) \times 350 = 48 \times 350 = Rs. 168$
$\therefore$ Total $SP$ of $120$ oranges $= 360 + 168 = Rs. 528$
Sice, $SP > CP$
Profit $= SP - CP = 528 - 480 = Rs. 48$
We know that, Profit% $=\frac{\text{Profit}}{\text{CP}}\times100\%=\frac{48}{480}\times100\%=10\%$
View full question & answer→Question 421 Mark
Interest on $Rs. 3000$ at $10\%$ per annum for a period of $3$ years is ________.
AnswerGiven, $P = Rs. 3000, R = 10\%$ and $T = 3$ year.
We know that, $\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{3000\times10\times3}{100}=\text{Rs. }900$
Hence, interest is $Rs. 900$
View full question & answer→Question 431 Mark
Mohini bought a cow for $Rs. 9000$ and Sold it at a loss of $Rs. 900.$ The selling price of the cow is _______.
AnswerGiven, $CP$ of cow $= Rs. 9000$ and loss $= Rs. 900$
We know that, $SP = CP -$ Loss $= 9000 - 900 = Rs. 8100$
Hence, the selling price of the cow is $Rs. 8100.$
View full question & answer→Question 441 Mark
If a chair is bought for $Rs. 2000$ and is sold at a gain of $10\%,$ then selling price of the chair is $Rs. 2010.$
AnswerGiven, $CP = Rs.2000$ and profit$\% = 10\%$
We know that, $\text{Profit}\%=\frac{\text{Profit}}{\text{CP}}\times100\%$
$\Rightarrow\text{Profit}\%=\frac{\text{SP}-\text{CP}}{\text{CP}}\times100\%$
$\Rightarrow10=\frac{\text{SP}-\text{CP}}{\text{CP}}\times100$
$\Rightarrow\frac{10\times2000}{100}=\text{SP}-2000$
$\therefore\text{SP}=\text{Rs.}2200$
Hence, the $SP$ of chair is $Rs. 2200$
View full question & answer→Question 451 Mark
Sushma sold her watch for $Rs. 3320$ at a gain of $Rs. 320.$ For earning a gain of $10\%,$ she should have sold the watch for $Rs. 3300.$
AnswerGiven that, $SP = Rs. 3320$ and profit $= Rs. 320$
$CP = SP\ -$ Profit $= 3320 - 320 = Rs. 3000$
Now, for earning profit $10\%$ we have to find new $SP$
$\therefore\text{Profit}\%=\frac{\text{Profit}}{\text{CP}}\times100\%$
$=\frac{\text{SP}-\text{CP}}{\text{CP}}\times100\%[\therefore$ Profit $= SP - CP]$
$10=\frac{\text{SP}-3000}{3000}\times100$
$300=\text{SP}-300$
$\text{SP}=\text{Rs.}3300$
View full question & answer→Question 461 Mark
The difference of interests for $2$ year and $3$ year on a sum of $Rs. 2100$ at $8\%$ per annum is _______.
AnswerGiven, $P = Rs. 2100$ and $R = 8\%$
For $T = 2$ year, $\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{2100\times8\times2}{100}=\text{Rs. }336$
For $3$ year, $\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{2100\times8\times3}{100}=\text{Rs. }504$
$\therefore$ Difference between both interests $= 504 - 336 = Rs. 168$
View full question & answer→Question 471 Mark
The simple interest on a sum of $Rs.P$ for $T$ year at $R\%$ per annum is given by the formula.
Simple Interest $=\frac{\text{T}\times\text{P}\times\text{R}}{100}$
AnswerSimple Interest $=\frac{\text{T}\times\text{P}\times\text{R}}{100}$
We can also write it as, $=\frac{\text{T}\times\text{P}\times\text{R}}{100}$
[since, multiplication is commutative]
View full question & answer→Question 481 Mark
Savitri obtained $440$ marks out of $500$ in an examination. She secured _____$\%$ marks in the examination.
AnswerMarks obtained by Savitri out of $500 = 440$
Percentage of marks obtained $=\frac{440}{500}\times100\%=88\%$
Hence, Savitri secured $88\%$ marks in the examination.
View full question & answer→Question 491 Mark
Aahuti purchased a house for $Rs. 5059700$ and spent $Rs. 40300$ on its repairing. To make a profit of $5\%,$ she should sell the house for $Rs.$_______.
AnswerGiven, $CP$ of house $= Rs. 5059700$ and amount spent on repairing $= Rs. 40300$
So, total $CP$ of house $= 5059700 + 40300 = Rs. 5100000$
We know that, profit$\% =\frac{\text{Profit}}{\text{CP}}\times100\%$
$\Rightarrow5=\frac{\text{SP}-\text{CP}}{\text{CP}}\times100$
$\Rightarrow5=\frac{\text{SP}-5100000}{5100000}\times100$
$\Rightarrow\frac{5\times5100000}{100}=\text{SP}-5100000$
$\Rightarrow255000=\text{SP}-5100000$
$\Rightarrow\text{SP}=5100000+255000$
$\therefore\text{SP}=\text{Rs. }5355000$
View full question & answer→Question 501 Mark
$18\frac{3}{4}\%=$______ : ___
AnswerGiven, pecentage $=18\frac{3}{4}\%=\frac{75}{4}\%$
$\Big[\therefore$ mixed fraction = improper fraction $=\frac{\text{whole number}\times\text{denominator}+\text{numerator}}{\text{denominator}}\Big]$
in fraction, $\frac{75}{4}\times\frac{1}{100}=\frac{3}{16}$
$\therefore$ Ration $= 3 : 16$
View full question & answer→Question 511 Mark
What is $100\%$ of $500?$
AnswerWe have, $100\%$ of $500$
$=\frac{100}{100}\times500=500$
View full question & answer→Question 521 Mark
AnswerWe know, Percentage $=$ Fraction $×\ 100$
$\text{Fraction}=\frac{\text{Percentage}}{100}$
$\text{Decimal}=\frac{\text{Percentage}}{100}$
Now, according to these formulae, we have.
| Percentage |
Fraction |
Decimal |
| $0\%$ |
$0$ |
$0$ |
| $10\%$ |
$\frac{1}{10}$ |
$0.1$ |
| $20\%$ |
$\frac{1}{5}$ |
$0.2$ |
| $30\%$ |
$\frac{3}{10}$ |
$0.3$ |
| $40\%$ |
$\frac{2}{5}$ |
$0.4$ |
| $50\%$ |
$\frac{1}{2}$ |
$0.5$ |
| $60\%$ |
$\frac{3}{5}$ |
$0.6$ |
| $70\%$ |
$\frac{7}{10}$ |
$0.7$ |
| $80\%$ |
$\frac{4}{5}$ |
$0.8$ |
| $90\%$ |
$\frac{9}{10}$ |
$0.9$ |
| $100\%$ |
$1$ |
$1$ |
View full question & answer→Question 531 Mark
Sonal bought a bed sheet for $Rs. 400$ and sold it for $Rs. 440.$ Her ____$ \%$ is ___$\%$.
AnswerGiven, $CP$ of a bed sheet $= Rs. 400$ and $SP$ of a ned sheet $= Rs. 440$
Since, $CP > SP$
$\therefore$ Profit $= SP - CP = 440 - 400 = Rs. 40$
Now, $\text{Profit}\%=\frac{\text{Profit}}{\text{CP}}\times100\%=\frac{40}{400}\times100\%=10\%$
Hence, Sonal's Profit$\%$ is $10\%$
View full question & answer→Question 541 Mark
$30\%$ of $Rs. 360 =$ ________.
AnswerWe have, $30\%$ of $\text{Rs. }360=\frac{30}{100}\times360 = \text{Rs. }108$
View full question & answer→Question 551 Mark
$0.018$ is equivalent to $8\%.$
AnswerGiven, decimal $= 0.018.$
In percentage, $0.018 \times 100= 1.8\%$
Hence, $0.018$ is equivalent to $1.8\%.$
View full question & answer→Question 561 Mark
Express $\frac{1}{6}$ as a per cent.
AnswerWe have, $\frac{1}{6}$ In percentage,
$\frac{1}{6}\times100\%=\frac{50}{3}=16.6\% [$to convert in per cent, mulitply by $100]$
View full question & answer→Question 571 Mark
Write $0.089$ as a per cent.
AnswerWe have, $0.089$
In percentage, $0.089 \times 100\% = 8.9\% [$to convert in per cent, multiply by $100]$
View full question & answer→Question 581 Mark
$Rs. 6400$ were lent to Feroz and Rashmi at $15\%$ per annum for $3\frac{1}{2}$ and $5$ year, respectively. The difference in the interests paid by them is $Rs. 150.$
AnswerGiven, Feroz borrowed $Rs. 6400$ for $3 \frac{1}{2}$ year at $15 \%$
Here, $P_1=$ Rs. $6400, T_1=3 \frac{1}{2}=\frac{7}{2}$ year and $R_1=15 \%$
$\therefore \mathrm{I}=\frac{\mathrm{P}_1 \times \mathrm{R}_1 \times \mathrm{T}_1}{100}$
$=\frac{6400 \times 15 \times 7}{100 \times 2}=\text { Rs. } 3360$
Rasmi borrowed $Rs. 6400$ for $5$ year at $15 \%$
Here, $P_2=$ Rs. $6400, R_2=15 \%$ and $T_2=5$ year
$\therefore \mathrm{I}_2=\frac{\mathrm{P}_2 \times \mathrm{R}_2 \times \mathrm{T}_2}{100}$
$=\frac{6400 \times 15 \times 5}{100}=\text { Rs. } 4800$
$\therefore$ Difference between interests $=4800-3360= Rs. 1440$
Hence, the difference in interest, paid by them is $Rs. 1440 .$
View full question & answer→Question 591 Mark
$75\%\frac{4}{3}.$
AnswerWe have. $75\%$ In fraction,
$\frac{75}{100}=\frac{3}{4}$
$\therefore75\%=\frac{3}{4}$
View full question & answer→Question 601 Mark
A fruit seller purchased $20\ kg$ of apples at $Rs. 50$ per kg. Out of these, $5\%$ of the apples were found to be rotten. If he sells the remaining apples at $Rs. 60$ per kg, then his _____ is _____%.
AnswerWe have, price for par $kg$ apples $= Rs. 50$
Total purchased appies $= 20\ kg$
Since, $5\%$ were rotten, so good apples $= 20\ kg - 5\%$ of $20\ kg ($rotten$)$
$=20-\frac{5}{100}\times20=20-1=19\text{kg}$
Also, he sells $19\ kg$ apples at $Rs. 60$ per kg.
$\therefore$ Total seilling price $= 19 \times 60 = Rs. 1140$
$\therefore$ Cost price was $20\ kg$ appies $= 20 \times 50 = Rs. 1000$
$\therefore$ Profit $= SP - CP = 1140 - 1000 = Rs. 140$
Now, $\text{profit}\%=\frac{\text{Profit}}{\text{CP}}\times100\%=\frac{140}{10}=14\%$
So, his profit is $14\%$
View full question & answer→Question 611 Mark
$250\ cm$ is $4\%$ of $1\ km.$
Answer$\therefore250\text{cm}=\frac{250}{100}=2.5$
Now, $4\%$ of $1\ km=\frac{4}{400}\times1000\text{m}=40\text{m}$
Hence, $250\text{cm}\neq4\%\text{ of }1\text{km.}$
View full question & answer→Question 621 Mark
$\frac{8}{5} =$____$\%$
AnswerWe have, $\frac{8}{5}$
In percentage, $\frac{8}{5} \times 100\% = 250\%$
View full question & answer→Question 631 Mark
To convert a decimal into a per cent, we shift the decimal point two places to the _____.
Answer To convert a decimal into a percent, we shift the decimal point two places to the right. Solution: To convert a decimal into a percent, we shift the decimal point into places to the right.
View full question & answer→Question 641 Mark
To convert a fraction into a percent, we ______ it by $100.$
AnswerTo convert a fraction into a percent, we multiply it by $100.$
View full question & answer→Question 651 Mark
$12\%$ of $120$ is $100.$
AnswerSince, $12\%\text{ of }120=\frac{12}{100}\times120=\frac{1440}{100}=144$
Therefore, $12\%$ of $120$ is $14.4$
View full question & answer→Question 661 Mark
____ is $50\%$ more than $60.$
AnswerLet number be $x.$
It is given that $x$ is $50\%$ more than $60.$
Therefore, $x = 60 + 50\%$ of $60=60+\frac{50}{100}\times60=60+30=90$
View full question & answer→Question 671 Mark
Interest on $Rs. 12500$ at $18\%$ per annum for a period of $2$ year and $4$ months is ______.
AnswerGiven, $P = Rs. 12500$ and $R = 18\%$
$T = 2$ year $4$ months $=\Big(2+\frac{4}{12}\Big)\text{year}=\Big(2+\frac{1}{3}\Big)\text{year}=\frac{7}{3}\text{year}$
We know that, $\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{125000\times18\times7}{3\times100}\text{ Rs. }5250$
View full question & answer→Question 681 Mark
Nasim bought a pen for $Rs. 60$ and sold it for $Rs. 54.$ His _____________ $\%$ is
AnswerGiven, $CP$ of a pen $= Rs. 60$
and $SP$ of pen $= Rs. 54$
Since, $CP > SP$
$\therefore$ Loss $= CP - SP = 60 - 54 = Rs. 6$
Now, $\text{loss}\%=\frac{\text{Loss}}{\text{CP}}\times100\%=\frac{6}{60}\times100\%=10\%$
Hence, Nasim's loss$\%$ is $10\%$
View full question & answer→Question 691 Mark
Devangi buys a chair for $Rs. 700$ and sells it for $Rs. 750.$ She earns a profit of ______$\%$ in the transaction.
AnswerGiven, $CP$ of chair $= Rs. 700$
$SP$ of chair $= Rs. 750$
We know that, profit $= SP - CP = 750 - 700 = Rs. 50$
Also, profit$\%=\frac{\text{Profit}}{\text{CP}}\times100\%=\frac{50}{700}\times100\%=7\frac{1}{7}\%$
Hence, profit earned by Devangi is $7\frac{1}{7}\%$
View full question & answer→Question 701 Mark
Express $\frac{1}{100}$ as a per cent.
AnswerWe have, $\frac{1}{100}$ In percentage, $\frac{1}{100}\times100\%=1\%.$
View full question & answer→Question 711 Mark
Amount received after depositing $Rs. 800$ a period of $3$ year at the rate of $12\%$ per annum is $Rs. 896.$
AnswerGiven, $P = Rs. 800, T = 3$ year and $R = 12\%$
$\therefore\text{I}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{800\times12\times3}{100}=\text{Rs.}1088$
Also, amount, $(A) = P + I = 800 + 288 = Rs.1088$
Hence, then amount received is $Rs. 1088.$
View full question & answer→
