MCQ 11 Mark
Mark against the correct answer in the following: What least number must be subtracted from each term of the ratio $15 : 19$ to make the ratio $3 : 4?$
AnswerLet us assume that the number to be subtracted is $x$
Then, $(15 - x) : (19 - x) = 15 : 3$
$\Rightarrow\frac{15-\text{x}}{19-\text{x}}=\frac{3}{4}$
$\Rightarrow 60 - 4x = 57 - 3x$
$\Rightarrow x = 3$
View full question & answer→MCQ 21 Mark
Mark against the correct answer in the following:
The mean proportional between $9$ and $16$ is:
AnswerMean proportional of $9$ and $16 = \sqrt{(9 \times 16)} = \sqrt{144} = 12$
View full question & answer→MCQ 31 Mark
Mark against the correct answer in the following: If $Rs. 420$ is divided between $A$ and $B$ in the ratio $3 : 4,$ then $A’s$ share is:
- ✓
$Rs. 180$
- B
$Rs. 240$
- C
$Rs. 270$
- D
$Rs. 210$
AnswerCorrect option: A. $Rs. 180$
Amount $= Rs. 420$
And ratio $= 3 : 4$
Sum of ratios $= 3 + 4 = 7$
A’s share $=\frac{420\times3}{7}=\text{Rs. }60\times3=\text{Rs. }180$
View full question & answer→MCQ 41 Mark
Mark against the correct answer in the following: The boys and girls in a school are in the ratio $9 : 5.$ If the number of girls is $320,$ then the total strength of the school is:
AnswerSuppose that the number of boys in the school is $x$
Then, $x : 320 = 9 : 5$
$\Rightarrow 5x = 2880$
$\Rightarrow x = 576$
Hence, total strength of the school $= 576 + 320 = 896$
View full question & answer→MCQ 51 Mark
Mark against the correct answer in the following: If $15\%$ of $A = 20\%$ of $B,$ then $A : B = ?$
- A
$3 : 4$
- ✓
$4 : 3$
- C
$17 : 16$
- D
$16 : 17$
AnswerCorrect option: B. $4 : 3$
$15\%$ of $A = 20\%$ of $B$
$\Rightarrow\text{A}\times\frac{15}{100}=\frac{20}{100}\times\text{B}$
$\Rightarrow\frac{\text{A}}{\text{B}}=\frac{20}{100}\times\frac{100}{15}=\frac{4}{3}$
$\therefore\text{A : B}=4:3$
View full question & answer→MCQ 61 Mark
Mark against the correct answer in the following: If $2A = 3B = 4C,$ then $A : B : C = ?$
- A
$2 : 3 : 4$
- B
$4 : 3 : 2$
- ✓
$6 : 4 : 3$
- D
$3 : 4 : 6$
AnswerCorrect option: C. $6 : 4 : 3$
$2\text{A}=3\text{B}=4\text{C}=\text{x}$
$\therefore\text{A}=\frac{\text{x}}{2},\text{B}=\frac{\text{x}}{3},\text{C}=\frac{\text{x}}{4}$
$\therefore\text{A : B : C}=\frac{\text{x}}{2}:\frac{\text{x}}{3}:\frac{\text{x}}{4}=\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$
$\frac{6\ :\ 4\ :\ 3}{12}=6:4:3$
View full question & answer→MCQ 71 Mark
Mark against the correct answer in the following: If $Rs. 840$ is divided between $A$ and $B$ in the ratio $4 : 3,$ then $B’s$ share is:
- A
$Rs. 480$
- ✓
$Rs. 360$
- C
$Rs. 320$
- D
$Rs. 540$
AnswerCorrect option: B. $Rs. 360$
Sum of the ratio terms $= 4 + 3 = 7$
$B’s$ share $840\times\frac{3}{7}=360$
View full question & answer→MCQ 81 Mark
Mark against the correct answer in the following:
If $2A = 3B$ and $4B = 5C,$ then $A : C = ?$
- A
$4 : 3$
- B
$8 : 15$
- C
$3 : 4$
- ✓
$15 : 8$
AnswerCorrect option: D. $15 : 8$
$2\text{A}=3\text{B}$
$\Rightarrow\frac{\text{A}}{\text{B}}=\frac{3}{2}$
$4\text{B}=5\text{C}$
$\Rightarrow\frac{\text{B}}{\text{C}}=\frac{5}{4}$
Multiplying, We get
$\frac{\text{A}}{\text{B}}\times\frac{\text{B}}{\text{C}}=\frac{3}{2}\times\frac{5}{4}$
$\Rightarrow\frac{\text{A}}{\text{C}}=\frac{15}{8}$
$\therefore\text{A : C}=15:8$
View full question & answer→MCQ 91 Mark
Mark against the correct answer in the following: If $\frac{\text{A}}{3}=\frac{\text{B}}{4}=\frac{\text{C}}{5}$ then $A : B : C = ?$
- ✓
$3 : 4 : 5$
- B
$4 : 3 : 5$
- C
$5 : 4 : 3$
- D
$20 : 15 : 12$
AnswerCorrect option: A. $3 : 4 : 5$
$\frac{\text{A}}{3}=\frac{\text{B}}{4}=\frac{\text{C}}{5}=1$ (Suppose)
$\text{A}=3,\text{B}=4,\text{C} =5$
$\text{A : B : C}=3:4:5$
View full question & answer→MCQ 101 Mark
Mark against the correct answer in the following: Two number are in the ratio $3 : 5.$ If each number is increased by $10,$ the ratio becomes $5: 7.$ The sum of the numbers is:
AnswerRatio in two numbers $= 3 : 5$
Let first number $= 3x$
Then second number $= 5x$
According to the condition,
$\frac{3\text{x}+10}{5\text{x}+10}=\frac{5}{7}$
(By cross multiplication)
$25x + 50 = 21x + 70$
$25x - 21x = 70 - 50$
$4x = 20$
$x = 5$
First number $= 3 \times 5 = 15$
and second number $= 5 \times 5 = 25$
Sum of numbers $= 15 + 25 = 40$
View full question & answer→MCQ 111 Mark
Mark against the correct answer in the following: What number has to be added to each term of $3 : 5$ to make the ratio $5 : 6 ?$
AnswerLet $x$ to be added to each term of $3 : 5$
Then $\frac{3+\text{x}}{5+\text{x}}=\frac{5}{6}$
By cross multiplication
$18 + 6x = 25 + 5x$
$6x - 5x = 25 - 18$
$x = 7$
$7$ is to be added
View full question & answer→MCQ 121 Mark
Mark against the correct answer in the following:
The ages of $A$ and $B$ are in the ratio $5 : 2.$ After $5$ years, their ages will be in the ratio $15: 7.$ The present age of $A$ is:
- A
$48$ years
- B
$36$ years
- ✓
$40$ years
- D
$35$ years
AnswerCorrect option: C. $40$ years
Suppose that the present ages of $A$ and $B$ are $5x\ yrs$ and $2x\ yrs,$ respectively.
After $5$ years, the ages of $A$ and $B$ will be $(5x + 5)\ yrs$ and $(2x + 5)\ yrs,$ respectively
Then, $(5x+ 5) : (2x + 5) = 15 : 7$
$\Rightarrow\frac{5\text{x}+5}{2\text{x}+5}=\frac{15}{7}$
Cross multiplying; we get:
$\Rightarrow 35x + 35 = 30x + 75$
$\Rightarrow 5x = 40$
$\Rightarrow x = 8$
Then, the present age of $A$ is $5 \times 8 = 40$ years.
View full question & answer→MCQ 131 Mark
Mark against the correct answer in the following: If $(3a + 5b): (3a - 5b) = 5 : 1,$ then $a : b = ?$
- A
$2: 1$
- B
$3 : 2$
- ✓
$5 : 2$
- D
$5 : 3$
AnswerCorrect option: C. $5 : 2$
$(3\text{a}+5\text{b}):(3\text{a}-5\text{b})=5:1$
$\Rightarrow\frac{3\text{a}+5\text{b}}{3\text{a}-5\text{b}}=\frac{5}{1}$
$3\text{a}+5\text{b}=5(3\text{a}-5\text{b})$
$\Rightarrow3\text{a}+5\text{b}=15\text{a}-25\text{b}$
$\Rightarrow3\text{a}-15\text{a}=-25\text{b}-5\text{b}$
$-12\text{a}=-30\text{b}$
$\Rightarrow\frac{\text{a}}{\text{b}}=\frac{-30}{-12}=\frac{5}{2}$
$\therefore\text{a : b}=5:2$
View full question & answer→MCQ 141 Mark
Mark against the correct answer in the following: What least number must be subtracted from each term of the ratio $15 : 19$ to make the ratio $3 : 4?$
AnswerLet $x$ be subtracted from each of the term
$\frac{15-\text{x}}{19-\text{x}}=\frac{3}{4}$
$\Rightarrow 4 (15 - x) = 3 (19 - x)$
$\Rightarrow 60 - 4x = 57 - 3x$
$\Rightarrow -4x + 3x = 57 - 60$
$\Rightarrow -x = -3$
$x = 3$
Required number $= 3$
View full question & answer→MCQ 151 Mark
Mark against the correct answer in the following: If $\frac{\text{A}}{2}=\frac{\text{B}}{3}=\frac{\text{C}}{4}$ then $A : B : C = ?$
- ✓
$2 : 3 : 4$
- B
$4 : 3 : 2$
- C
$3 : 2 : 4$
- D
AnswerCorrect option: A. $2 : 3 : 4$
$\text{A}=\frac{2}{3}\text{B}$
$\text{C}=\frac{4}{3}\text{B}$
$\therefore\text{A : B : C}=\frac{2}{3}\text{ B : B : }\frac{4}{3}\text{ B}$
$=2 : 3 : 4$
View full question & answer→MCQ 161 Mark
Mark against the correct answer in the following:
The boys and girls in a school are in the ratio $8 : 5.$ If the number of girls is $160,$ what is the total strength of the school$?$
AnswerLet $x$ be the number of bosy.
Then, $8 : 5 = x : 160$
$\Rightarrow\frac{8}{5}=\frac{\text{x}}{160}$
$\Rightarrow\text{x}=\frac{8\times160}{5}=256$
$\therefore$ Total strength of the school $= 256 + 160 = 416$
View full question & answer→MCQ 171 Mark
Mark against the correct answer in the following: The third proportional to $9$ and $12$ is:
AnswerLet $x$ be the third proportional to $9$ and $12$ then
$9 : 12 :: x : 12$
$\Rightarrow 9 \times x = 12 \times 12$
$\Rightarrow\text{x}=\frac{12\times12}{9}=\frac{144}{9}=16$
Third proportional $= 16$
View full question & answer→MCQ 181 Mark
Mark against the correct answer in the following: If $a : b = 3 : 4$ and $b : c = 8 : 9$, then $a : c = ?$
- A
$1 : 2$
- B
$3 : 2$
- C
$1 : 3$
- ✓
$2 : 3$
AnswerCorrect option: D. $2 : 3$
$\text{a : b}=3:4,\text{b : c}=8:9$
Or $\frac{\text{a}}{\text{b}}=\frac{3}{4}$ and $\frac{\text{b}}{\text{c}}=\frac{8}{9}$
Multiplying,
$\frac{\text{a}}{\text{b}}\times\frac{\text{b}}{\text{c}}=\frac{3}{4}\times\frac{8}{9}$
$\Rightarrow\frac{\text{a}}{\text{c}}=\frac{2}{3}$
$\therefore\text{a : c}=2:3$
View full question & answer→MCQ 191 Mark
Mark against the correct answer in the following: If $2A = 3B = 4C$ then $A : B : C = ?$
- A
$2 : 3 : 4$
- B
$3 : 4 : 6$
- C
$4 : 3 : 2$
- ✓
$6 : 4 : 3$
AnswerCorrect option: D. $6 : 4 : 3$
$\text{A}=\frac{3}{2}\text{B}$
$\text{C}=\frac{3}{4}\text{B}$
$\text{A : B : C}=\frac{3}{2}\text{B : B : }\frac{3}{4}\text{B}$
$=6:4:3$
View full question & answer→MCQ 201 Mark
Mark against the correct answer in the following: Which one is greater out of $(2 : 3)$ and $(4 : 7)?$
AnswerCorrect option: A. $2 : 3$
$\frac{2}{3}$ and $\frac{4}{7}$
$\text{LCM}$ of $3$ and $7 = 21$
$\therefore\frac{2}{3}=\frac{2\times7}{3\times7}=\frac{14}{21}$
$\frac{4}{7}=\frac{4\times3}{7\times3}=\frac{12}{21}$
It is clear that $\frac{14}{21}$ or $\frac{2}{3}$ is greater.
$2 : 3$
View full question & answer→MCQ 211 Mark
Mark against the correct answer in the following:
The ages of $A$ and $B$ are in the ratio $3 : 8.$ Six years hence, their ages will be in the ratio $4 : 9$. The present age of $A$ is:
- ✓
$18$ years
- B
$15$ years
- C
$12$ years
- D
$21$ years
AnswerCorrect option: A. $18$ years
Let age of $A = 3x$
And age of $B = 8x$
$6$ years hence, their ages will be $3x + 6$ and $8x + 6$
$\frac{3\text{x}+6}{8\text{x}+6}=\frac{4}{9}$
$\Rightarrow 9(3x + 6) = 4(8x + 6)$
$\Rightarrow 27x + 54 = 32x + 24$
$\Rightarrow 32x - 27x = 54 - 24$
$\Rightarrow 5x = 30$
$\Rightarrow x = 6$
$A’s$ age $= 3x = 3 \times 6 = 18$ years
View full question & answer→MCQ 221 Mark
Mark against the correct answer in the following: If $\frac{1}{\text{x}}:\frac{1}{\text{y}}:\frac{1}{\text{z}}=2:3:5$ then, $x : y : z = ?$
- A
$2 : 3 : 5$
- ✓
$15 : 10 : 6$
- C
$5 : 3 : 2$
- D
$6 : 10 : 15$
AnswerCorrect option: B. $15 : 10 : 6$
$\frac{1}{\text{x}}:\frac{1}{\text{y}}:\frac{1}{\text{z}}=2:3:5$
Let $\frac{1}{\text{x}}=2\text{k},\frac{1}{\text{y}}=3\text{k},\frac{1}{\text{z}}=5\text{k}$
$\Rightarrow\text{x}=\frac{1}{2\text{k}},\text{y}=\frac{1}{3\text{k}},\text{z}=\frac{1}{5\text{z}}$
$\therefore\text{x : y : z}=\frac{1}{2\text{k}}:\frac{1}{3\text{k}}:\frac{1}{5\text{k}}$
$=\frac{15\ :\ 10\ :\ 6}{30\text{k}}$
$\therefore$ Ratio of $x : y : z = 15 : 10 : 6$
View full question & answer→MCQ 231 Mark
Mark against the correct answer in the following: If $x : y = 3 : 4,$ then $(7x + 3y) : (7x - 3y) = ?$
- A
$4 : 3$
- B
$5 : 2$
- ✓
$11 : 3$
- D
$37 : 39$
AnswerCorrect option: C. $11 : 3$
$\frac{\text{x}}{\text{y}}=\frac{3}{4}$
$\text{x}=\frac{3\text{y}}{4}$
$\therefore\frac{7\text{x}+3\text{y}}{7\text{x}-3\text{y}}=\frac{7\frac{3\text{y}}{4}+3\text{y}}{7\frac{3\text{y}}{4}-3\text{y}}$
$=\frac{21\text{y}+12\text{y}}{21\text{y}-12\text{y}}=\frac{33\text{y}}{9\text{y}}=\frac{11}{3}$
Hence, $(7x + 3y) : (7x - 3y) = 11 : 3$
The correct option is $(C).$
View full question & answer→MCQ 241 Mark
Mark against the correct answer in the following:
If $(x : y) = 3 : 4,$ then $(7x + 3y) : (7x - 3y) = ?$
- A
$7 : 3$
- B
$5 : 2$
- ✓
$11 : 3$
- D
$14 : 9$
AnswerCorrect option: C. $11 : 3$
We have $\text{x}=\frac{3}{4}\text{y}$
Now, $\frac{7\text{x}+3\text{y}}{7\text{x}-3\text{y}}$
$=\frac{7\times\frac{3}{4}\text{y}+3\text{y}}{7\times\frac{3}{4}\text{y}-3\text{y}}=\frac{21\text{y}+12\text{y}}{21\text{y}-12\text{y}}$
$\frac{33\text{y}}{9\text{y}}=\frac{11}{3}$
View full question & answer→MCQ 251 Mark
Mark against the correct answer in the following: If $A: B = 5 : 7$ and $B : C = 6 : 11,$ then $A : B : C = ?$
- A
$30 : 42 : 55$
- ✓
$30 : 42 : 77$
- C
$35 : 49 : 66$
- D
AnswerCorrect option: B. $30 : 42 : 77$
$A : B = 5 : 7, B : C = 6 : 11$
$LCM$ of $7, 6 = 42$
$\therefore\frac{\text{A}}{\text{B}}=\frac{5}{7}=\frac{5\times6}{7\times6}=\frac{30}{42}$
And $\frac{\text{B}}{\text{C}}=\frac{6}{11}=\frac{6\times7}{11\times7}=\frac{42}{77}$
$\therefore\text{A : B}=30:42$
And $\text{B : C}=42:77$
$\therefore\text{A : B : C}=30:42:77$
View full question & answer→MCQ 261 Mark
Mark against the correct answer in the following: If $7 : x :: 35 : 45,$ then $x = ?$
Answer$7:\text{x}::35:45$
$\Rightarrow\frac{7}{\text{x}}=\frac{35}{45}$
$\Rightarrow\text{x}\times35=7\times45$
$\text{x}=\frac{7\times45}{35}=9$
$\text{x}=9$
View full question & answer→MCQ 271 Mark
The ages of A and B are in the ratio 3 : 8. Six years hence, their ages will be in the ratio 4 : 9.
The present age of A is
MCQ 281 Mark
The mean proportional between 9 and 16 is
MCQ 291 Mark
The third proportional to 9 and 12 is
MCQ 301 Mark
Which one is greater out of (2 : 3) and (4: 7)?
MCQ 311 Mark
The boys and girls in a school are in the ratio 8 : 5. If the number of girls is 160, what is the total strength of the school?
MCQ 321 Mark
If ₹ 420 is divided between A and B in the ratio 3: 4, then A's share is
MCQ 331 Mark
What least number is to be subtracted from each term of the ratio 15 : 19 to make the ratio 3 : 4?
MCQ 341 Mark
Two numbers are in the ratio 3 : 5. If each number is increased by 10, the ratio becomes 5: 7. The sum of the numbers is
MCQ 351 Mark
What number has to be added to each term of 3 : 5 to make the ratio 5 : 6?
MCQ 361 Mark
If 7 : x :: 35 : 45, then x = ?
MCQ 371 Mark
If $(3 a+5 b):(3 a-5 b)=5: 1$, then $a: b=$ ?
View full question & answer→MCQ 381 Mark
If x: y = 3 : 4, then (7x +3y): (7x-3y) = ?
MCQ 391 Mark
If $\frac{1}{x}: \frac{1}{y}: \frac{1}{z}=2: 3: 5$, then, $x: y: z=$ ?
View full question & answer→MCQ 401 Mark
If $\frac{A}{3}=\frac{B}{4}=\frac{C}{5}$, then $A: B: C=$ ?
View full question & answer→MCQ 411 Mark
if 2А = 3B = 4C, then A : B : C =?
MCQ 421 Mark
If A : B =5 : 7 and B : C = 6 :11, then A : B : C=?
MCQ 431 Mark
If $A=\frac{1}{3} B$ and $B=\frac{1}{2} C$, then $A: B: C=$ ?
View full question & answer→MCQ 441 Mark
If 15% of A = 20% of B, then A : B =?
MCQ 451 Mark
If 2A = 3B and 4B = 5C, then A : C = ?
MCQ 461 Mark
If A: B=2 : 3 and B : C = 4 : 5, then C : A = ?
MCQ 471 Mark
If a: b = 3 : 4 and b : c = 8 : 9, then a : c =?