MATHS M.C.Q. [1 Marks Each]

$SP$ of stool $= Rs. 630$
Loss$\% = 10\%$
$\text{C.P.}=\frac{\text{S.P}\times100}{100-\text{loss%}}$
$=\frac{630\times100}{100-10}$
$=\text{Rs. }\frac{630\times100}{90}$
$=\text{Rs. }700$

Given number is multiplied by $100$ and then divided by $100.$

Rs. $10 : 50$ paise $= 10 \times 100$ paise: $50$ paise
$= 1000 : 50 = 20 : 1$

$25\%=\frac{25}{100}$
$=\frac{25\div25}{100\div25}$
$=\frac{1}{4}$
Hence, the correct option is $(a).$

Number of students who like to watch $T.V.$
$= 30\%$ of $100$
$=\frac{30}{100}\times100$
$=30$

$27$ days $- 3$ days $= 24$ days
Men $= 500 + 300 = 800$
For $500$ men, provision is sufficient $= 24$ days
For $1$ man, provision will be $= 24 \times 500$ (less man, more days)
and for $500 + 300 = 800$ men provision
will be sufficient $=\frac{24\times500}{800}=15\text{ days}$
(more men, less days)

Weight of $4.5\ m$ rod $= 17.1\ kg$
Wight of $1\ m$ rod $=\frac{17.1}{4.5}\text{kg}$
And wight of $12\ m$ rod
$=\frac{17.1\times12}{4.5}=\frac{171\times12\times100}{100\times45}\text{kg}$
$=\frac{19\times12}{5}=\frac{228}{5}=45.6\text{kg}$

Let the original salary of the man be $x$.
According to the question,
$\text{x}+25\%\ \text{of x}=20000$
$\Rightarrow\text{x}+\frac{25}{100}\times\text{x}=20000$
$\Rightarrow\text{x}+\frac{\text{x}}{4}=20000$
$\Rightarrow\frac{4\text{x}+4}{4}=20000$
$\Rightarrow\frac{5\text{x}}{4}\times4=20000\times4$
$\Rightarrow5\text{x}=80000$
$\Rightarrow\text{x}=\frac{80000}{5}$
$\Rightarrow\text{x}=16000$
Therefore, Original salary of the man is $Rs. 16000.$
Hence, the correct option is $(b).$

Let the $CP$ of a pen be $x.$
SP of a pen $= Rs. 48$
Loss $= 20\%$
Therefore, $CP$ is more than $SP.$
Now, Loss $= CP - SP$ and Loss = Loss percent $\times CP$
Thus, $CP - SP =$ Loss percent $\times CP$
$\Rightarrow\text{x}-48=\frac{20}{100}\times\text{x}$
$\Rightarrow100\text{x}-4800=20\text{x}$
$\Rightarrow100\text{x}-20\text{x}=4800$
$\Rightarrow80\text{x}=4800$
$\Rightarrow\text{x}=\frac{4800}{80}$
$\Rightarrow\text{x}=60$
Therefore, $CP$ of the pen $= Rs. 60$
Now, in order to gain $20\%$, let the new $SP$ be $y.$
Gain = Gain percent $\times CP$
$=\frac{20}{100}\times60$
$= Rs.12$
$SP = CP + Gain$
$= Rs. 60 + Rs. 12$
$= Rs. 72$
Hence, the correct option is ($d).$

Times $= 5$ years
Simple interest $=\frac25\text{P}$
$\Rightarrow\frac{\text{P}\times\text{Rate}\times\text{time}}{100}=\frac{2}{5}\text{P}$
$\Rightarrow\frac{\text{Rate}\times5}{100}=\frac25$
$\Rightarrow\text{Rate}=\frac{2\times100}{5\times5}$
$\Rightarrow\text{Rate}=8\%$

Let the number that must be added to each term of the ratio $9 : 16$ be $x.$
Then,
$(9+\text{x}):(16+\text{x})=2:3$
$\Rightarrow\frac{(9+\text{x})}{(16+\text{x})}=\frac{2}{3}$
$\Rightarrow3(9+\text{x})=2(16+\text{x})$
$\Rightarrow27+\text{3x}=32+\text{x}$
$\Rightarrow3\text{x}-2\text{x}=32-27$
$\therefore\text{x}=5$
So, $5$ must be added to each term of the ratio $9 : 16$ to make the ratio $2 : 3.$
Hence, the correct alternative is option $(a).$

Let the $CP$ be $x.$
$SP = Rs. 924$
Gain $= 10\%$
Therfore, $SP$ is more than $CP.$
Now,
Gain$=10\%$ of $CP$ and $SP = CP +$ gain
So, $SP = CP + 10\%$ of $CP$
$\Rightarrow924=\text{x}+\frac{10}{100}\times\text{x}$
$\Rightarrow924=\Big(1+\frac{1}{10}\Big)\text{x}$
$\Rightarrow924=\Big(\frac{11}{10}\Big)\text{x}$
$\Rightarrow\text{x}=\Big(\frac{9240}{11}\Big)$
$\Rightarrow\text{x}=840$
Thus, $CP = Rs. 840$
Hence, the correct option is $(d).$

It is given that,
Sum ($P_1$) $= Rs. 1000$
Rate ($R_1$) $= 12%$
Time ($T_1$) $= 3 years$
$\text{I}_1=\frac{\text{P}_1\ \times\ \text{R}_1\ \times\ \text{T}_1}{100}$
$=\frac{1000\ \times\ 12\ \times\ 3}{100}$
$=\text{Rs. }360\ ...(\text{i})$
Sum ($P_2$​​​​​​​) $= Rs. 1500$
Rate ($R_2$​​​​​​​) $= 8%$
Time ($T_2$) $=1\frac{1}{2}\ \text{year}=\frac{3}{2}\ \text{year}$
$\text{I}_2=\frac{\text{P}_2\ \times\ \text{R}_2\ \times\ \text{T}_2}{100}$
$=\frac{1500\ \times\ 8\ \times\ 3}{100\ \times\ 2}$
$=\text{Rs. }180\ ...(\text{ii})$
Subtracting $(ii)$ from $(i)$, we get
$I_2 - I_1 = Rs. 360 - Rs. 180$
$= Rs. 180$
Hence, the correct option is $(c).$

Let $P$'s share be $Rs. x.$
Then $Q$'s share $= Rs. (840 - x)$
As, $P'$s share : $Q$'s share $= 3 : 4$
$\Rightarrow\frac{\text{P's share}}{\text{Q's share}}=\frac34$
$\Rightarrow\frac{\text{x}}{(840-\text{x})}=\frac{3}{4}$
$\Rightarrow\text{4x}=3(840-\text{x})$
$\Rightarrow\text{4x}=3\times840-\text{3x}$
$\Rightarrow\text{4x}+\text{3x}=3\times840$
$\Rightarrow7\text{x}=3\times840$
$\text{x}=\frac{3\times840}{7}$
$\Rightarrow\text{x}=3\times120$
$\therefore\text{x}=360$
So, $P$'s share is Rs. $360.$
Hence, the correct alternative is option $(c).$

First decimal is removed and then multiplied by $100.$

Let the rate of popukation be $p, q, r$ respectively.
Therefore, population after $3$ years is
$=\text{P}(1+\frac{\text{P}}{100})(1+\frac{\text{q}}{100})(1+\frac{\text{r}}{100})$
$=2500\times(1+\frac{4}{100})(1+\frac{5}{100})(1+\frac{8}{100})$
$=25000\times\frac{26}{25}\times\frac{21}{20}\times\frac{27}{25}$
$=29,484$

$\text{A}=\frac{1}{3}\text{B, B}=\frac{1}{2}\text{C}$
$\frac{\text{A}}{\text{B}}=\frac{1}{3},\frac{\text{B}}{\text{C}}=\frac{1}{2}$
$\Rightarrow\text{A : B}=1:3$
$\text{B : C}=1:2=3:6$
(Multiplying by $3)$
$\therefore\text{A : B : C}=1 : 3 : 6$

Amount that Meenu gets
$= (100\% - 60\%) × 100$
$=\frac{40}{100}\times100=\text{Rs. }40$

$50\%\ \text{of}\ 150=\frac{50}{100}\times150$
$=75$
$70\%\ \text{of}\ 300=\frac{70}{100}\times300$
$=210$
Therefore, $50\%$ of $150 + 70\%$ of $300 = 75 + 210 = 285.$
Hence, the correct option is $(b).$

$3 : 5 = 15 : x$
$\frac{3}{5}=\frac{15}{\text{x}}$
$x = 25$

$100\% - 40\% = 60\%.$

Let the rate be $R \%$
$S.I. = A - P$
$= 720 - 600$
$= Rs. 120$
Time $= 4$ years
$\text{R}=\frac{10\times\text{S.I.}}{\text{P}\times\text{T}}$
$\text{R}=\frac{100\times120}{600\times4}$
$=5$
Rate of interest $= 5\%$
Now,
$\text{R}=(5+2)\%=7\%$
$\text{S.I.}=\frac{\text{P}\times\text{R}\times\text{T}}{100}$
$=\frac{600\times7\times4}{100}$
$\text{Rs. }168$
Amount $= S.I. + P$
$= 600 + 168$
$= Rs. 768$

Let the $SP$ be $x.$
$CP = Rs. 3300$
Loss $= 10\%$
Therfore, $CP$ is more than $SP.$
Now,
Loss $= 10\%$ of $CP$ and $SP = CP$ - loss
So, $SP = CP - 10\%$ of $CP$
$\Rightarrow\text{x}=3300-\frac{10}{100}\times3300$
$\Rightarrow\text{x}=\Big(1-\frac{1}{10}\Big)3300$
$\Rightarrow\text{x}=\Big(\frac{9}{10}\Big)3300$
$\Rightarrow\text{x}=2970$
Thus, $SP = Rs. 2970$
Hence, the correct option is $(d).$

$2\text{A}=3\text{B}=4\text{C}=\text{x}$
$\therefore\text{A}=\frac{\text{x}}{2},\text{B}=\frac{\text{x}}{3},\text{C}=\frac{\text{x}}{4}$
$\therefore\text{A : B : C}=\frac{\text{x}}{2}:\frac{\text{x}}{3}:\frac{\text{x}}{4}=\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$
$\frac{6\ :\ 4\ :\ 3}{12}=6:4:3$

As, $\frac{1}{\text{a}}:\frac{1}{\text{b}}:\frac{1}{\text{c}}=3:4:5$
$\Rightarrow\frac{1}{\text{a}}:\frac{1}{\text{b}}=3:4$ and $\frac{1}{\text{b}}:\frac{1}{\text{c}}=4:5$
$\Rightarrow\frac{1}{\text{a}}\div\frac{1}{\text{b}}=\frac{3}{4}$ and $\frac{1}{\text{b}}\div\frac{1}{\text{c}}=\frac45$
$\Rightarrow\frac{1}{\text{a}}\times\frac{\text{b}}{1}=\frac{3}{4}$ and $\frac{1}{\text{b}}\times\frac{\text{c}}{1}=\frac{4}{5}$
$\Rightarrow\frac{\text{b}}{\text{a}}=\frac{3}{4}$ and $\frac{\text{c}}{\text{b}}=\frac{4}{5}$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{4}{3}$ and $\frac{\text{b}}{\text{c}}=\frac{5}{4}$ (Reciprocal of both sides)
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{4\times5}{3\times5}$ and $\frac{\text{b}}{\text{c}}=\frac{5\times3}{4\times3}$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{20}{15}$ and $\frac{\text{b}}{c}=\frac{15}{12}$
$\Rightarrow\text{a}:\text{b}=20:15$ and $\text{b}:\text{c}=15:12$
$\therefore\text{a}:\text{b}:\text{c}=20:15:12$
Hence, the correct alternative is option $(b).$

For bufalo, $CP = Rs. = 44000$
Loss$\% = 5\%$
$\therefore\text{Loss}\%=\frac{\text{Loss}}{\text{CP}}\times100\%$
$\Rightarrow5=\frac{\text{Loss}}{44000}\times100$
$\Rightarrow\text{Loss}=5\times440=\text{Rs.}2200$
So, $SP = CP -$ Loss $= 44000 - 2200 = Rs. 41800$
For cow, $CP = Rs. 18000$
Profit$\% = 10\%$
$\therefore\text{Profit}\%=\frac{\text{Profit}}{\text{CP}}\times100\%$
$\Rightarrow10=\frac{\text{Profit}}{18000}\times100$
Profit $= Rs. 1800$
So, $SP = CP +$ Profit $= 18000 + 1800 = Rs. 19800$
Total $CP$ of buffalo and cow $= 44000 + 18000 = Rs. 62000$
Total $SP$ of buffalo and cow $= 41800 + 19800 = Rs. 61600$
Net loss $= CP - SP = 62000 - 61600 = Rs. 400$

$120 : 600 = 3 : x$
$\Rightarrow\frac{120}{600}=\frac{3}{\text{x}}$
$\Rightarrow\text{x}$

$C.P$. of $12$ pencils
$= S.P$. of $15$ pencils
$=$ Re $1$ (suppose)
$\therefore$ $C.P$ Of $1$ pencil $= \text{Rs. }\frac{1}{12}$
And $S.P$ of $1$ pencil $=\text{Rs. }\frac{1}{15}$
$\therefore$ Loss $= C.P - S.P$
$=\frac{1}{12}-\frac{1}{15}$
$=\frac{5-4}{60}$
$=\text{Rs. }\frac{1}{60}$
$\therefore\text{Loss%}=\frac{\text{Loss}\times100}{\text{C.P.}}$
$=\frac{\frac{1}{60}\times100}{\frac{1}{12}}$
$=\frac{1\times100\times12}{60\times1}$
$=20\%$