MCQ 11 Mark
A rectangular field has its length and breadth in the ratio $5 : 3$ Its area is $3.75$ hectares The cost of fending it at $Rs. 5$ per metre is.
- A
$Rs. 400$
- ✓
$Rs. 4000$
- C
$Rs. 1000$
- D
$Rs. 500$
AnswerCorrect option: B. $Rs. 4000$
B. $Rs. 4000$
Solution:
Let the length and breadth of rectangle field is $5x$ and $3x$ respt and area $= 3.75$ hectars
We know that $1$ hectare $= 10000$ sq metes
Then area 37500 sq m Then Area $5x × 3x = 37500$
$⇒ 15x^2 = 37500$
$⇒ x^2 = 2500$
$⇒ x = 50$ Then length $5 × 50 = 250m$ and breadth $= 3 × 50 = 150m$
Than perimeter of rectangle field $=2(L + B) = 2(250 + 150) = 800m$
Then cost of fending $800 × 5 = 4000 Rs$
View full question & answer→MCQ 21 Mark
In a cricket team the ratio of total number of players to the number of wicket keepers is
- A
$1 : 11$
- ✓
$11 : 1$
- C
$16 : 1$
- D
$10 : 1$
AnswerCorrect option: B. $11 : 1$
Number of players in a cricket
(playing) $= 11$
Wicketkeeper $= 1$
Ratio $11 : 1$
p : wk
View full question & answer→MCQ 31 Mark
The ratio of $0.12\ kg$ and $180\ g$ is.
- A
$0.01 : 1.8$
- B
$1 : 15$
- ✓
$2 : 3$
- D
AnswerCorrect option: C. $2 : 3$
$0.12\ kg : 180\ g = 120\ g : 180\ g = 2 : 3$
View full question & answer→MCQ 41 Mark
Mark $(\checkmark)$ against the correct answer in the following:
The ratio $92 : 115$ in simplest form is:
- A
$23 : 25$
- B
$18 : 23$
- C
$3 : 5$
- ✓
$4 : 5$
AnswerCorrect option: D. $4 : 5$
$92 : 115$
$\frac{92}{115}=\frac{92\div23}{115\div23}=\frac{4}{5}$ ($H.C.F$ of $92$ and $115$ is $23$)
View full question & answer→MCQ 51 Mark
$A, B, C$ earn $Rs. 1,980$ in total. They earn it in the ratio of $2 : 1$ and $3 : 2$ respectively, then $B$ earned
- A
$Rs. 500$
- B
$Rs. 520$
- ✓
$Rs. 540$
- D
$Rs. 560$
AnswerCorrect option: C. $Rs. 540$
$A : B = 2 : 1 B : C = 3 : 2$
$\Rightarrow A : B : C = 6 : 3 : 2$
$\therefore\text{Bs share}=\frac{3}{11}\times1980=540.$
View full question & answer→MCQ 61 Mark
Kiran scored $80$ marks in his Science test which is $\frac{5}{6}$ of the total marks.What are the total marks for the test?
AnswerLet total marks achieved by Kiran be $x$
Given, Kiran scored $80$ marks in his Science test which is $\frac{5}{6}$ of the total marks
$\therefore\frac{5}{6}\times\text{x}=80$
$\therefore\text{x}=\frac{80\times6}{5}$
$\therefore\text{x}=96$
$\therefore$ total marks achieved by Kiran $=96$
View full question & answer→MCQ 71 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 81 Mark
The sum of two numbers is $100$ and their difference is $50.$ Then the ratio of the two numbers is.
- A
$2 : 1$
- ✓
$3 : 1$
- C
$4 : 1$
- D
$5 : 1$
AnswerCorrect option: B. $3 : 1$
Let the two numbers be $x$ and yas per problem sum of two numbers is
$100x + y = 100.........................eq1$
their difference is $50x - y = 50.................................eq2$
on adding both equations we get $x + y = 100$
$x - y = 50$
_______________________$2x = 150x = 75$putting
value of $x = 75$ we get
$y = 2575 + y = 100y = 25$ ratio of two numbers will be $75 : 25 = 3 : 1$
View full question & answer→MCQ 91 Mark
Two numbers are in the ratio $2 : 7$. If the second number is $378$, find the first.
AnswerLet the first number be $= 2a$ and second number $= 7a$
Given, $7a = 378$
$a = 54$
Hence, first number $= 2a = 108$
View full question & answer→MCQ 101 Mark
Neelam’s annual income is $Rs. 288000$. Her annual saving amount is $Rs. 36000$. The ratio of her savings to her expenditure is:
- A
$1 : 8$
- ✓
$1 : 7$
- C
$1 : 6$
- D
$1 : 5$
AnswerCorrect option: B. $1 : 7$
Given,
Neelam’s annual income $= Rs. 2,88,000$
Her annual saving $= Rs. 36,000$
Her expenditure = Income - Savings $= Rs. 2,88,000 - Rs. 36,000 = Rs. 2,520$
$\therefore$ Ratio of her savings to her expenditure $=\frac{36000}{252000}$
$=\frac{1}{7}$ [On dividing numerator and denominator by $36000$]
$= 1 : 7$
Hence, $(b)$ is the correct option.
View full question & answer→MCQ 111 Mark
The three numbers are in the ratio $1 : 2 : 3$ and the sum of their cubes is $98784.$ The numbers are _____
- ✓
$(14, 28, 42)$
- B
$(6, 12, 18)$
- C
$(7, 14, 21)$
- D
$(8, 16, 24)$
AnswerCorrect option: A. $(14, 28, 42)$
Ratio of three numbers $= 1 : 2 : 3$
Let the numbers be $x, 2x, 3x$
Given that $x^3 + (2x)^3 + (3x)^3 = 98784$
$\Rightarrow x^3 + (2x)^3 + (3x)^3 = 98784$
$x^3 + 8x^3 + 27x^3 = 98784$
$\Rightarrow x^3 + 8x^3 + 27x^3 = 98784$
View full question & answer→MCQ 121 Mark
$42$ men take $25$ days to dig a pond If the pond would have to be dug in $14$ days then what is the number of men to be employed?
AnswerIn $25$ days $42$ men dig a pond Then in $14$ days the man required =
$\frac{42\times25}{14}=75$ man dig a pond
View full question & answer→MCQ 131 Mark
Ratio is a method of comparing two quantities by__
AnswerAs per definition, Ratio is a method of comparing two quantities by division.
View full question & answer→MCQ 141 Mark
The ratio $2$ to $\frac{1}{3}$ is equal to the ratio.
- ✓
$\frac{6}{1}$
- B
$\frac{5}{1}$
- C
$\frac{3}{2}$
- D
$\frac{2}{3}$
AnswerCorrect option: A. $\frac{6}{1}$
The ratio $=2:\frac{1}{3}\rightarrow\frac{2}{1}=\frac{6}{1}$
or ratio $= 6 : 1$
View full question & answer→MCQ 151 Mark
$A$ began business with $Rs. 4,500$ and was joined afterwards by $B$ with $Rs. 5,400$. If the profit at the end of the year was divided in the ratio of $2 : 1$, then the time of joining $B$ was after
- A
$5$ months
- ✓
$7$ months
- C
$8$ months
- D
$9$ months
AnswerCorrect option: B. $7$ months
Let $B$ join after $x$ months
$A$ joins for $12$ months with $Rs. 4,500$
$B$ joins for $(12 - x)$ months with $Rs. 5,400$
$\Rightarrow\frac{4500\times12}{5400\times(12-\text{x})}=\frac{2}{1}$
$\Rightarrow\text{x}=7$
View full question & answer→MCQ 161 Mark
On a shelf, books with green cover and that with brown cover are in the ratio $2 : 3$. If there are $18$ books with green cover, then the number of books with brown cover is:
AnswerGiven,
Ratio of books with green cover to books with brown cover $= 2 : 3$ Books with green cover $= 18$
Let the books with green cover and brown cover are $2x$ and $3x$ respectively.
According to the question,
$2\text{x} = 18$
$\Rightarrow\text{x}=\frac{18}{2}$
$\therefore\ \text{x} = 9$
Thus, the books with brown cover $= 3x$
$= 3 \times 9 = 27$
Hence, $(c)$ is the correct option.
View full question & answer→MCQ 171 Mark
Mark $(\checkmark)$ against the correct answer in the following.
If the cost of $5$ bars of soap is $Rs. 82.50$, then the cost of one dozen such bars is
- A
$Rs. 208$
- B
$Rs. 192$
- ✓
$Rs. 198$
- D
$Rs. 204$
AnswerCorrect option: C. $Rs. 198$
$1$ dozen $= 12$ bars
Cost of 5 bars of soap $= Rs. 82.50$
Then cost of $1$ bar $=\text{Rs. }\frac{82.50}{5}$
And cost of $12$ bars $=\text{Rs. }\frac{8250\times12}{100\times5}$
$=\text{Rs. }66\times3=\text{Rs. }198$
View full question & answer→MCQ 181 Mark
Mark $(\checkmark)$ against the correct answer in the following.
If a bus covers $195\ km$ in $3$ hours and a train covers $300\ km$ in $4$ hours, then the ratio of their speeds is:
- ✓
$13 : 15$
- B
$15 : 13$
- C
$13 : 12$
- D
$12 : 13$
AnswerCorrect option: A. $13 : 15$
Bus covers in $3$ hours $= 195\ km$
It will cover in $1$ hour $=\frac{195}{3}=65\text{km}$
Train cover in $4$ hours $=300\text{km}$
It will cover in $1$ hour $=\frac{300}{4}=75\text{km}$
$\therefore$ Ratio in thier speeds $=65:75$
$=13:15$
View full question & answer→MCQ 191 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 201 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 211 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 221 Mark
In a cricket team the ratio of total number of players to the number of wicket keepers is
- A
$\frac{1}{11}$
- ✓
$\frac{11}{1}$
- C
$\frac{16}{1}$
- D
$\frac{10}{1}$
AnswerCorrect option: B. $\frac{11}{1}$
The number of total players are $11$ and total wicket keeper $= 1$
therefore the $\text{Ratio}=\frac{11}{1}$
View full question & answer→MCQ 231 Mark
In a school the total number of studentsare $3200$ out of which $1800$ are boys. Remaining are girls. Ratio of girls to boys is
- A
$1400 : 1800$
- B
$9 : 7$
- ✓
$7 : 9$
- D
$1 : 3$
AnswerCorrect option: C. $7 : 9$
Total students $= 3200$
Boys $= 1800$
Girls $= 1400$
Ratio of girls to boys $= 1400 : 1800$
$=7 : 9$
View full question & answer→MCQ 241 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. $a : b : : b : c$
$\Rightarrow ac = b^2$
View full question & answer→MCQ 251 Mark
Reema has $24$ notebook and $18$ books find the ratio of notebooks to books?
- A
$5 : 3$
- B
$6 : 3$
- C
$3 : 3$
- ✓
$4 : 3$
AnswerCorrect option: D. $4 : 3$
no. of notebooks $= 24$ no. of books $= 18$ ratio of notebooks to books
$=\frac{24}{18}=\frac{4}{3}=4:3$
View full question & answer→MCQ 261 Mark
If $\Box$ represents one tenth then $\Box\Box\Box\Box\Box\Box\Box\Box\Box$ represents
AnswerIf $\Box$ represents $\frac{1}{10}=0.1$ then $9$ $\Box=9\times0.1=0.9$
View full question & answer→MCQ 271 Mark
If $yz : zx : xy = 2 : 3 : 4$ then $\sqrt{\frac{\text{x}}{\text{yz}}}:\sqrt\frac{\text{y}}{\text{zx}}$ is equal to.
- ✓
$3 : 2$
- B
$1 : 4$
- C
$2 : 1$
- D
$2 : 3$
AnswerCorrect option: A. $3 : 2$
Given, $yz : zx : xy = 2 : 3 : 4$
or $\frac{\text{yz}}{\text{zx}}=\frac{2}{3}$
$⇒ x : y = 3 : 2$ and $\frac{\text{zx}}{\text{xy}}=\frac{3}{4}$
$⇒ y : z = 4 : 3$
$\therefore$ $x : y : z = 6 : 4 : 3$ and
$\sqrt{\frac{\text{x}}{\text{yz}}}:\sqrt\frac{\text{y}}{\text{zx}}=\sqrt{\frac{6}{12}}:\sqrt{\frac{42}{189}}=\frac{1}{\sqrt{2}}:\frac{\sqrt{2}}{3}=\frac{3}{2}$
View full question & answer→MCQ 281 Mark
The cost of one pencil is $Rs. 1.50$ then the cost of $10$ pencils is -
- ✓
$Rs. 15$
- B
$Rs. 150$
- C
$Rs. 1.5$
- D
AnswerCorrect option: A. $Rs. 15$
Cost of $11$ pencil $= Rs. 1.50$ cost of $10$ pencils $= Rs.10 \times 1.50 = 15 Rs.$
View full question & answer→MCQ 291 Mark
If a bus travels $160\ km$ in $4h$ and a train travels $320\ km$ in $5h$ at uniform speeds, then the ratio of the distances travelled by them in one hour is:
- A
$1 : 2$
- B
$4 : 5$
- ✓
$5 : 8$
- D
$8 : 5$
AnswerCorrect option: C. $5 : 8$
Given,
Bus travels in $4h = 160\ km$ and Train travels in $5h = 320\ km$.
Ratio of the distance travelled and time is Distance
$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
$\text{Speed of bus}=\frac{160}{40}$
$\text{Speed of train} = \frac{320}{5}$
Ratio of speed of bus to train = $\frac{40}{64}$
$=\frac{5}{8}$ [On dividing numerator and denominator by $8$]
$= 5 : 8$
Hence, $(c)$ is the correct option.
View full question & answer→MCQ 301 Mark
The profits of a firm are to be distributed in a suitable ratio. Suitable ratio is the ratio whose terms differ by $40$ and the measure of which is $\frac{2}{7}$ Which of the following shows suitable ratio?
- A
$280 : 2$
- ✓
$16 : 56$
- C
$80 : 7$
- D
$40 : 14$
AnswerCorrect option: B. $16 : 56$
Let the ratio is $x : (x + 40)$
Then $\frac{\text{x}}{\text{x}+40}=\frac{2}{7}$
$\Rightarrow 7x = 2x + 80$
$\Rightarrow 7x - 5x = 80$
$\Rightarrow 2x = 80$
$\Rightarrow x = 40$
Required ratio $= 16 : (40 + 16) = 16 : 56$
View full question & answer→MCQ 311 Mark
The antecedent and consequent of a ratio ..........interchanged unless there is a change in the given statements.
AnswerThe antecedent and consequent of a ratio cannot be interchanged unless there is a change in the given statements.
View full question & answer→MCQ 321 Mark
In the word $34 \ \text{MATHEMATICS} \ 34$ the ratio of number of consonants to the number of vowels is:
- A
$4 : 7$
- ✓
$7 : 4$
- C
$5 : 6$
- D
$6 : 5$
AnswerCorrect option: B. $7 : 4$
$7 : 4$
View full question & answer→MCQ 331 Mark
Shyam wants to make a sold brick shape structure from $400$ wooden cubes of unit volume each. If the sides of the solid brick have the ratio $1 : 2 : 3,$ then the maximum number of cubes, which can be used will be
AnswerLet 4he side are $x, 2x, 3x$
$v = (x) (2x) (3x) = 6x^3$
$\text{A T Q }6\text{x}^3\leq400$
$\Rightarrow\text{x}^3\leq66\frac{2}{3}$
$\Rightarrow\text{x}=64$
$\therefore\text{x}=64$
maximum number of cubes $= 6x^3 = 6 \times 64 = 384$
View full question & answer→MCQ 341 Mark
The coordinates of the points $P$ which divides $(1, 0)$ and $(0, 0)$ in $1 : 2$ ratio are ____
- A
$(2,3)$
- B
$\big(\frac{2}{3},3)$
- C
$(3,2)$
- ✓
$\big(\frac{2}{3},0)$
AnswerCorrect option: D. $\big(\frac{2}{3},0)$
Using the section formula, if a point $(x, y)$ divides the line joining the
points $(x_1, y_1)$ and $(x_2, y_2)$ internally in the ratio $m : n,$ then $(x, y)$ $\Big( \frac{\text{mx}_2 + \text{nx}_{ 1 } }{ \text{m + n}} ,\frac { \text{my}_{ 2 } + \text{ny}_1 }{ \text{m + n}}\Big)$
Substituting $(x_1, y_1) = (1, 0)$ and $(x_2, y_2) = (0, 0)$ and $m = 1, n = 2$ in the section formula,
we get the point $\text{P}=\Big(\frac{1(10)+2(1)}{1+2},\frac{1(10)+2(1)}{1+2}\Big)=\Big(\frac{2}{3},0\Big)$
View full question & answer→MCQ 351 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 361 Mark
A planet of volume $V$ and mass m has gravitational acceleration $g$ on its surface. If it expands to $8$ times its original volume, what will be the acceleration due to gravity.
- A
$4\text{g}$
- B
$2\text{g}$
- ✓
$\frac{\text{g}}{4}$
- D
$\frac{\text{g}}{8}$
AnswerCorrect option: C. $\frac{\text{g}}{4}$
$\therefore \frac{4}{3}\pi\text{r}^3\times8=\frac{4}{3}\pi\text{R}^3$
$\Rightarrow\text{R}=2\text{r}$
$\text{g}=\frac{\text{GM}}{\text{r}^2},\text{g}'=\frac{\text{GM}}{\text{R}^2}$
$\Rightarrow\Big(\frac{\text{g}'}{\text{g}}\Big)=\frac{\text{r}^2}{\text{R}^2}$
$\therefore\text{g}'=\frac{\text{g}}{4}.$
View full question & answer→MCQ 371 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 381 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 391 Mark
A train travelling at a speed of $75\ mph$ enters a tunnel $3\frac{1}{2}$ miles long. The train is $\frac{1}{4}$ mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
- A
$2.5$ min
- ✓
$3$ min
- C
$3.2$ min
- D
$3.5$ min
AnswerCorrect option: B. $3$ min
Total distance covered $=\Big(\frac{7}{2}+\frac{1}{4}\Big)\text{miles}$
$=\frac{15}{4}\text{miles}$
$\therefore$ Time taken $=\Big(\frac{15}{4\times75}\Big)\text{hrs}$
$=\frac{15}{4}\text{hrs}$
$=\Big(\frac{15}{20}\times60\Big)\text{min}$
$=3\text{ min}$
View full question & answer→MCQ 401 Mark
If the given ratio of $\frac{1}{6}$ add $4$ to the antecedent and $2$ to the consequent. Then the new ratio is.
- A
$\frac{5}{6}$
- B
$\frac{1}{8}$
- ✓
$\frac{5}{8}$
- D
$\frac{8}{5}$
AnswerCorrect option: C. $\frac{5}{8}$
Given ratio $=\frac{1}{6}$
Now we add 4 to Antecedent or Numerator and $2$ to Consequentor Denominator as shown
$\Rightarrow\frac{1+4}{6+2}$
$\Rightarrow\frac{5}{8}$
View full question & answer→MCQ 411 Mark
Express $64\ cm$ divided by $4.8m$ in the simplest form.
- ✓
$\frac{2}{15}$
- B
$\frac{4}{3}$
- C
$\frac{3}{4}$
- D
$\frac{1}{15}$
AnswerCorrect option: A. $\frac{2}{15}$
$\text{Required ratio}=\frac{64\text{cm}}{4.8\text{m}}$
$=\frac{64\text{cm}}{4.8\times100\text{cm}}=\frac{64}{480}=\frac{2}{15}$
View full question & answer→MCQ 421 Mark
The ratio between the number of passengers travelling by $I^{st}$ $II^{nd}$class between the tworailwaystations is $1 : 50$ where as the ratio of $I^{st}$ $II^{nd}$ class fares between the same stationsis $3 : 1$ If on a particular day, $Rs. 1325$ were collected from the passengers travelling between these stations by theseclasses, then what was the amount collected from the $II^{nd}$ classpassengers?
- A
$Rs. 750$
- B
$Rs. 850$
- C
$Rs. 1000$
- ✓
$Rs. 1250$
AnswerCorrect option: D. $Rs. 1250$
The ratio between the number of passengers travelling byIstandIIndclass between the tworailwaystations is $1 : 50$
Where as the ratio ofIstandIIndclass fares between the same stations is $3 : 1$
Then ratio of the amount collected from the $1^{st}$ class and $2^{nd}$ class passengers $3 : 50$
$\therefore$ amount collated from the $2^{nd}$ class passengers $=\frac{50}{53}\times1325=1250\text{ Rs.}$
View full question & answer→MCQ 431 Mark
If $\frac{\text{x}}{2\text{y}+\text{z}-\text{x}}=\frac{\text{y}}{2\text{z}+\text{x}-\text{y}}=\frac{\text{y}}{2\text{z}+\text{y}-\text{z}}$ and $\text{x}+\text{y}+\text{z}\neq0$ then what is each ratio equal to.
- ✓
$\frac{1}{2}$
- B
$\frac{1}{3}$
- C
$3$
- D
$\frac{2}{3}$
AnswerCorrect option: A. $\frac{1}{2}$
Suppose,$\frac{\text{x}}{2\text{y}+\text{z}-\text{x}}=\frac{\text{y}}{2\text{z}+\text{x}-\text{y}}=\frac{\text{y}}{2\text{z}+\text{y}-\text{z}}=\frac{1}{\text{k}}$
$\Rightarrow\frac{\text{x}}{2\text{y }+\text{ z}-\text{x}}=\frac{1}{\text{k}},\frac{\text{y}}{2\text{z }+\text{ x}-\text{y}}=\frac{1}{\text{k}},\text{and }\frac{\text{y}}{2\text{z }+\text{ y}-\text{z}}=\frac{1}{\text{k}}$
$⟹ xk = 2y + z - x...................(1) yk = 2z + x - y .............. (2)$ and
$zk = 2x + y - z .............. (3)$ Adding $(1), (2)$ and $(3)$ we get $xk + yk + zk = 2x + 2y + 2z$
$⟹ (x + y + z) k = (x + y + z)$
$\therefore$ $k = 2$ Hence, each ratio is equal to $\frac{1}{2}$
View full question & answer→MCQ 441 Mark
A group of $24$ students was polled as to whether they enjoy biology class, chemistry class, both, or neither. The results are shown in the table.
Given the data, Mark the correct statement.
|
|
Biology
|
Chemistry
|
|
Enjoy
|
$14$
|
$18$
|
|
Dont Enjoy
|
$10$
|
$6$
|
- A
The ratio of those who enjoy biology class to those who enjoy chemistry class is $7 : 8$
- B
The ratio of those who enjoy chemistry class to those who dont enjoy chemistry class is $9 : 4$
- C
The ratio of those who enjoy biology class to those who dont enjoy chemistry class is $7 : 2$
- ✓
The ratio of those who dont enjoy biology class to those who enjoy chemistry class is $5 : 9$
AnswerCorrect option: D. The ratio of those who dont enjoy biology class to those who enjoy chemistry class is $5 : 9$
The ratio of those who dont enjoy biology class to those who enjoy chemistry class is $5 : 9$
View full question & answer→MCQ 451 Mark
Mark $(\checkmark)$ against the correct answer in the following.
If the cost of $30$ packets of $8$ pencils each is $Rs. 600$, what is the cost of $25$ packets of $12$ pencils each?
- A
$Rs. 725$
- ✓
$Rs. 750$
- C
$Rs. 480$
- D
$Rs. 720$
AnswerCorrect option: B. $Rs. 750$
Total pencils in $30$ packets of $8$ pencils
$= 30 \times 8 = 240$
And total pencils of $25$ packets of $12$
Pencils $= 25 \times 12 = 300$
Now cost of $240$ pencils $= Rs. 600$
Then cost of $1$ percent $=\text{Rs. }\frac{600}{24}$
And cost of $300$ pencils $=\text{Rs. }\frac{600\times300}{240}$
$=\text{Rs. }750$
View full question & answer→MCQ 461 Mark
If $391$ is divided into three parts proportional to $\frac{1}{2}:\frac{2}{3}:3$ then the first part is.
Answer$3$ parts are $\frac{1}{2}:\frac{2}{3}:3$
Making denimenator equal
$1$st part $=\frac{1}{2}\times\frac{3}{3}=\frac{3}{6}$
$2$nd part $=\frac{2}{3}\times\frac{2}{2}=\frac{4}{6}$
$3$rd part $=\frac{3}{1}\times\frac{6}{6}=\frac{18}{6}$
Therefore first part will be $391\times\frac{3}{6}=195.5$
Answer will be none of these as the above answers are not matching
View full question & answer→MCQ 471 Mark
The ratio of $8$ books to $20$ books is:
- ✓
$2 : 5$
- B
$5 : 2$
- C
$4 : 5$
- D
$5 : 4$
AnswerCorrect option: A. $2 : 5$
$= \frac{8 \text{ books}}{20 \text{ books}}= \frac{8}{20}$
$= 2:5$
[On dividing numerator and denominator by $4$]
Hence, $(a)$ is the correct option.
View full question & answer→MCQ 481 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 491 Mark
The ratio of $Re. 1$ to $60$ paise is
- A
$5 : 4$
- B
$5 : 2$
- ✓
$5 : 3$
- D
$1 : 6$
AnswerCorrect option: C. $5 : 3$
$Re\ 1 = 100$paise
$\therefore$ Ratio of $Re\ 1$ $60$ paise
$= 100 : 60 = 5 : 3$
View full question & answer→MCQ 501 Mark
If $a : b = 2 : 5,$ then $(3a + 4b) : (5a + 6b)$ is equal to.
- ✓
$13 : 20$
- B
$26 : 33$
- C
$16 : 27$
- D
$18 : 35$
AnswerCorrect option: A. $13 : 20$
$13 : 20$
View full question & answer→