MCQ 11 Mark
If $4, a, a, 36$ are in proportion, then $a =$
Answer$4, a, a, 36$ are in proportion; therefore, we get:
$4 : a : : a : 36$
$\Rightarrow 4 : a = a : 36$
$\Rightarrow 4 \times 36 = a \times a$
$\Rightarrow 144 = a2$
$\Rightarrow a = 12$
View full question & answer→MCQ 21 Mark
If the cost of $25$ packets of $12$ pencils each is $Rs. 750$, then the cost of $30$ packets of $8$ pencils each is:
- ✓
$Rs. 600$
- B
$Rs. 720$
- C
$Rs. 640$
- D
AnswerCorrect option: A. $Rs. 600$
It is given that the cost of $25$ packets of $12$ pencils each is $Rs. 750;$
Therefore, we have:
Cost of $(25 \times 12)$ pencils $= 300$ pencils $= Rs. 750$
Let the cost of $(30 \times 8)$ or $240$ pencils be $Rs. x,$
$\because 750 : 300 : : x : 240$
$\therefore$ Cost of $(30 \times 8) = 240$ pencils
$=\frac{750\times240}{300}=\text{Rs. 600}$
View full question & answer→MCQ 31 Mark
Mark the correct alternative in the following: If $343$ is the third proportional of $a$ and $b$, where $a : b = 1 : 7$, then value of $a + b$ is:
AnswerIf is given that,
$\frac{\text{a}}{\text{b}}=\frac{1}{7}\ ....(1)$
According to the question,
$a : b : : b : 343$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{\text{b}}{343}$
$\Rightarrow\frac{1}{7}=\frac{\text{b}}{343}\ ....[\text{From (1)}]$
$\Rightarrow\frac{1\times343}{7}=\frac{\text{b}\times343}{343}$
$\Rightarrow49=\text{b}$
Now,
$\frac{\text{a}}{\text{b}}=\frac{1}{7}$
$\Rightarrow\frac{\text{a}}{49}=\frac{1}{7}$
$\Rightarrow\frac{\text{a}\times49}{49}=\frac{1\times49}{7}$
$\Rightarrow\text{a}=7$
Thus, $a + b = 7 + 49 = 56$
Hence, the correct option is $(c).$
View full question & answer→MCQ 41 Mark
Mark the correct alternative in the following: The first three terms of a proportion are $12, 21$ and $8$ respectively. Then $4^{th}$ term is:
AnswerLet the $4^{th}$ term be $x.$
According to the question,
$12 : 21 : : 8 : x$
$\Rightarrow $ Product of extreme term $=$ product of mean terms
$\Rightarrow12\text{x}=8\times21$
$\Rightarrow12\text{x}=168$
$\Rightarrow\frac{12\text{x}}{12}=\frac{168}{12}$
$\Rightarrow\text{x}=14$
Hence, the correct option is $(c).$
View full question & answer→MCQ 51 Mark
If $a, b, c$ are in proportion, then
- ✓
$a : b : : b : c$
- B
$a : b : : c : a$
- C
$a : b : : c : b$
- D
$a : c : : b : c$
AnswerCorrect option: A. $a : b : : b : c$
$a : b : : b : c$
View full question & answer→MCQ 61 Mark
The first, second and fourth terms of a proportion are $16, 24$ and $54$ respectively. The third term is:
AnswerThe first, second and fourth term of a proportion are $16, 24$ and $54,$ respectively.
Let third term is be $x,$
According to the question, we have:
$16 : 24 = x : 54$
$16 : 24 = x : 54$
$\Rightarrow\frac{16\times54}{24}=\text{x}$
$\Rightarrow\text{x}=36$
View full question & answer→MCQ 71 Mark
Mark the correct alternative in the following:If $4 : 3 = x^2: 12$, then the value of $x (x > 0).$
Answer$\frac{4}{3}=\frac{\text{x}^2}{12}$
$\Rightarrow\frac{4\times4}{3\times4}=\frac{\text{x}^2}{12}$
$\Rightarrow\frac{16}{12}=\frac{\text{x}^2}{12}$
$\Rightarrow4^2=\text{x}^2\ (\because\text{x}>0)$
$\Rightarrow4=\text{x}$
Hence, the correct option is $(b).$
View full question & answer→MCQ 81 Mark
$12$ men can finish a piece of work in $25$ days. The number of days in which the same piece of work can be done by $20$ men, is:
- A
$10$ days.
- B
$12$ days.
- ✓
$15$ days.
- D
$14$ days.
AnswerCorrect option: C. $15$ days.
It is given that $12$ men can finish a piece of work in $25$ days.
Let the number of days required to do the same piece of work by $20$ men be $x$ days.
We get,
$20 : 12 = 25 : x$
$=\frac{12\times25}{20}$
$= 15$ Days.
View full question & answer→MCQ 91 Mark
If $5 : 4 : : 30 : x$, then the value of $x$ is:
Answer$5 : 4 : : 30 : x$
$\Rightarrow5:4=30:\text{x}$
$\Rightarrow\text{x}=\frac{30\times4}{5}$
$=24$
View full question & answer→MCQ 101 Mark
$14 $: If $a, b, c, d$ are in proportion, then
- A
$ab = cd$
- B
$ac = bd$
- ✓
$ad = bc$
- D
AnswerCorrect option: C. $ad = bc$
$\because a, b, c$ and $d$ are in proportion,
$\therefore a : b = c : d$
$\Rightarrow ab = cd$
$\Rightarrow ad = bc$
View full question & answer→MCQ 111 Mark
Mark the correct alternative in the following:
Two numbers are in the ration $3 : 5$ and their sum is $96$. The larger number is:
AnswerLet the larger number be $x.$
Then, the smaller number be $(96 - x).$
According to the question,
$\frac{96-\text{x}}{\text{x}}=\frac{3}{5}$
$\Rightarrow\frac{(96-\text{x})\times\text{x}\times5}{\text{x}}=\frac{3\times\text{x}\times5}{5}$
$\Rightarrow5(96-\text{x})=3\text{x}$
$\Rightarrow480-5\text{x}=3\text{x}$
$\Rightarrow3\text{x}+5\text{x}=480$
$\Rightarrow8\text{x}=480$
$\Rightarrow\frac{8\text{x}}{8}=\frac{480}{8}$
$\Rightarrow\text{x}=60$
Thus, the larger number is $60.$
Hence, the correct option is $(c).$
View full question & answer→MCQ 121 Mark
Mark the correct alternative in the following: If $80 : 60 = x : 12$, then $x =$
AnswerIt is given that,
$\frac{80}{60}=\frac{\text{x}}{12}$
$\Rightarrow\frac{80\div5}{60\div5}=\frac{\text{x}}{12}$
$\Rightarrow\frac{16}{12}=\frac{\text{x}}{12}$
$\Rightarrow\text{x}=16$
Hence, the correct option is $(a).$
View full question & answer→MCQ 131 Mark
Mark the correct alternative in the following: If $a = 2b$, then $a : b =$
- ✓
$2 : 1$
- B
$1 : 2$
- C
$3 : 4$
- D
$4 : 3$
AnswerCorrect option: A. $2 : 1$
$a = 2b$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{2}{1}$
$\Rightarrow\text{a}:\text{b}=2:1$
Hence, the correct option is $(a).$
View full question & answer→MCQ 141 Mark
Mark the correct alternative in the following: If $4 : 5 : : x : 45$, then $x =$
Answer$4 : 5 : : x : 45$
$\Rightarrow\frac{4}{5}=\frac{\text{x}}{45}$
$\Rightarrow\frac{4\times45}{5}=\frac{\text{x}\times45}{45}$
$\Rightarrow\frac{4\times6}{1}=\text{x}$
$\Rightarrow\text{x}=36$
Hence, the correct option is $(c).$
View full question & answer→MCQ 151 Mark
The ratio of boys and girls in a school is $12 : 5$. If there are $840$ girls in the school, then the number of boys is:
- A
$1190$
- B
$2380$
- C
$2856$
- ✓
$2016$
AnswerCorrect option: D. $2016$
If the number of girls in the school is $840$, let the number of boys be $x,$ It is given that the ratio of boys and girls is $12 : 5,$
Therefore, we get:
$\therefore 12 : 5 = x : 840$
$\text{x}=\frac{12\times840}{5}=2016$
View full question & answer→MCQ 161 Mark
Two ratio $384 : 480$ in its simplest form is:
- A
$3 : 5$
- B
$5 : 4$
- ✓
$4 : 5$
- D
$2 : 5$
AnswerCorrect option: C. $4 : 5$
$384 : 480 = 4 : 5$ (Dividing the denominator and numerator by $96).$
View full question & answer→MCQ 171 Mark
If $57 : x = 51 : 85$, then the value of $x$ is:
AnswerConsider
$57 : x = 51 : 85$
$\Rightarrow\frac{57\times85}{51}=\text{x}$
$\Rightarrow\text{x}=95$
View full question & answer→MCQ 181 Mark
The angles of a triangle are in the ratio $1 : 2 : 3$. The measure of the largest angle is:
- A
$30^\circ $
- B
$60^\circ$
- ✓
$90^\circ$
- D
$120^\circ$
AnswerCorrect option: C. $90^\circ$
Let x stand for the measure of angle $1.$
Then $2x$ for angle $2$ and finally $3x$ for angle $3.$
So, $x + 2x + 3x = 180$ and $6x = 180$
Therefore, $x = 30, 2x = 60$ and $3x = 90$
View full question & answer→MCQ 191 Mark
The sides of a triangle are in the ratio $2 : 3 : 5$. If its perimeter is $100\ cm$, the length of its smallest side is:
- A
$2\ cm$
- ✓
$20\ cm$
- C
$3\ cm$
- D
$5\ cm$
AnswerCorrect option: B. $20\ cm$
We have,
$= 2x + 3x + 5x = 100$
$= 10x = 100$
$= x = 10$
Now,
Length of the smallest side $= 2 \times 10 = 20$
View full question & answer→MCQ 201 Mark
Mark the correct alternative in the following: If six men can do a piece of work in $6$ days, then $3$ men can do same work in,
- A
$10$ days.
- ✓
$12$ days.
- C
$15$ days.
- D
$18$ days.
AnswerCorrect option: B. $12$ days.
Let the required number of days be $x.$
Number of days is inversaly proportional to the number of men.
According to the question,
$6 : 3 : : x : 6$
$\Rightarrow\frac{6}{3}=\frac{\text{x}}{6}$
$\Rightarrow\frac{6\times6}{3}=\frac{\text{x}\times6}{6}$
$\Rightarrow\frac{36}{3}=\text{x}$
$\Rightarrow\text{x}=12$
Thus, 3 men can do same work in $12$ days.
Hence, the correct option is $(b).$
View full question & answer→MCQ 211 Mark
Length and width of a field are in the ratio $5 : 3.$ If the width of the field is $42m$, then its length is:
- A
$50m$
- ✓
$70m$
- C
$80m$
- D
$100m$
AnswerRatio of length and width of the field $= 5 : 3$
Let the length be xm.
$\because$ Width $= 42m$
$\therefore$ Length $= 5 : 3 = x : 42$
$\Rightarrow\text{x}=\frac{5}{3\times42}=70\text{m}$
View full question & answer→MCQ 221 Mark
Mark the correct alternative in the following: If $x : y = 1 : 1$, then $\frac{3\text{x}+4\text{y}}{5\text{x}+6\text{y}}=$
- ✓
$\frac{7}{11}$
- B
$\frac{17}{11}$
- C
$\frac{17}{23}$
- D
$\frac{4}{5}$
AnswerCorrect option: A. $\frac{7}{11}$
It is given that,
$\frac{\text{x}}{\text{y}}=\frac{1}{1}=1\ ....(1)$
Now,
$\frac{3\text{x}+4\text{y}}{5\text{x}+6\text{y}}=\frac{(3\text{x}+4\text{y}\div\text{y})}{(5\text{x}+6\text{y})\div\text{y}}$
$=\frac{3\big(\frac{\text{x}}{\text{y}}\big)+4}{5\big(\frac{\text{x}}{\text{y}}\big)+6}$
$=\frac{3(1)+4}{5(1)+6}\ [\text{From (1)}]$
$=\frac{3+4}{5+6}$
$=\frac{7}{11}$
Hence, the correct option is $(a).$
View full question & answer→MCQ 231 Mark
If $A, B, C$, divide $Rs. 1200$ in the ratio $2 : 3 : 5$, then $B's$ share is:
- A
$Rs. 240$
- B
$Rs. 600$
- C
$Rs. 380$
- ✓
$Rs. 360$
AnswerCorrect option: D. $Rs. 360$
$= 2x + 3x + 5x = 1200$
$= 10x = 1200$
$x = 120$
B's share $= 3x$
$= 3 \times 120 = 360$
View full question & answer→MCQ 241 Mark
A ratio equivalent of $2 : 3$ is:
- ✓
$4 : 3$
- B
$2 : 6$
- C
$6 : 9$
- D
$10 : 9$
AnswerCorrect option: A. $4 : 3$
$2 : 3$ is equivalent to $6 : 9$ (Dividing by $3)$.
View full question & answer→MCQ 251 Mark
If the cost of $5$ bars of a soap is $Rs. 30$, then the cost of one dozen bars is:
- A
$Rs. 60$
- B
$Rs. 120$
- ✓
$Rs. 72$
- D
$Rs. 140$
AnswerCorrect option: C. $Rs. 72$
Let the cost of one dozen bars be $Rs. x$
$\therefore 30 : 5 = x : 12$
$\Rightarrow\text{x}=\frac{30}{5\times12}=\text{Rs. 72}$
Cost of one dozen ($12$) bars = $Rs. 72$
View full question & answer→MCQ 261 Mark
Mark the correct alternative in the following: If $x : y = 2 : 3$ and $y : z = 2 : 3$, then $x : x =$
- A
$2 : 3$
- B
$3 : 4$
- C
$5 : 7$
- ✓
$4 : 9$
AnswerCorrect option: D. $4 : 9$
It is given that,
$\frac{\text{x}}{\text{y}}=\frac{2}{3}\ ....(1)$
and
$\frac{\text{y}}{\text{z}}=\frac{2}{3}\ ....(2)$
Now,
$\frac{\text{x}}{\text{y}}=\frac{2}{3}$
$\Rightarrow\frac{\text{x}}{\text{y}}\times\frac{\text{y}}{\text{z}}=\frac{2}{3}\times\frac{\text{y}}{\text{z}}\ [\text{From (2)}]$
$\Rightarrow\frac{\text{x}}{\text{z}}=\frac{4}{9}$
$\Rightarrow\text{x}:\text{z}=4:9$
Hence, the correct option is $(d).$
View full question & answer→MCQ 271 Mark
If $a, b, c,$ are in proportion, then
- A
$a^2 = bc$
- ✓
$b^2= ac$
- C
$c^2= ab$
- D
AnswerCorrect option: B. $b^2= ac$
$\because a, b$ and $d$ are in proportion,
$\therefore$ $a : b : : c$
$\Rightarrow ab = bc$
$\Rightarrow b2 = ac$
View full question & answer→MCQ 281 Mark
The ratio of male and female employees in a multinational company is $5 : 3$. If there are $115$ male employees in the company, then the number of female employees is:
AnswerIf the number of male employees is $115,$ let the number of female employees be $x.$
According to the question:
$5 : 3 = 115 : x$
$\Rightarrow\text{x}=\frac{115}{5\times3}=69$
View full question & answer→MCQ 291 Mark
If a bus travels $126\ km$ in $3$ hours and a train travels $315\ km$ in $5$ hours, then the ratio of their speeds is:
- A
$2 : 5$
- ✓
$2 : 3$
- C
$5 : 2$
- D
$25 : 6$
AnswerCorrect option: B. $2 : 3$
Speed = Distance Time
Speed of the bus $=\frac{126}{3}=42\text{km/h}$
Speed of the train $=\frac{315}{5}=63\text{km/h}$
Ratio of their speeds $= 42 : 63 = 2 : 3$ (Divide by $21).$
View full question & answer→