Sample QuestionsRatio and Proportion questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Find the reciprocal ratio of 3: 5
Find the sub-triplicate ratio of 216: 343
Find the sub-duplicate ratio of $9x^2a^4: 25y^6b^2$
View full solution →Find the triplicate ratio of 2a: 3b
Find the duplicate ratio of $2 \sqrt{2}: 3 \sqrt{5}$
View full solution →Find the mean proportional to $(x – y)$ and $(x^3 – x^2y).$
View full solution →Find the third proportional to $a^2 – b^2$ and $a + b.$
View full solution →Find the fourth proportional to $2xy, x^2$ and $y^2.$
View full solution →A woman reduces her weight in the ratio $7 : 5.$ What does her weight become if originally it was $84\ kg?$
View full solution →What quantity must be added to each term of the ratio x: y so that it may become equal to c: d?
If $(3x – 4y): (2x – 3y) = (5x – 6y): (4x – 5y),$ find $x: y.$
View full solution →If $\frac{x^2+y^2}{x^2-y^2}=2 \frac{1}{8}$ find $\frac{x^3+y^3}{x^3-y^3}$
View full solution →If x, y, z are in continued proportion prove that $\frac{(x+y)^2}{(y+z)^2}=\frac{x}{z}$
View full solution →If $\frac{4 m+3 n}{4 m-3 n}=\frac{7}{4}$ use properties of proportion to find $\frac{2 m^2-11 n^2}{2 m^2+11 n^2}$
View full solution →If 7x – 15y = 4x + y, find the value of x: y. Hence, use componendo and dividend to find the values of:
$\frac{3 x^2+2 y^2}{3 x^2-2 y^2}$
View full solution →If $x$ and $y$ both are positive and $(2x^2- 5y^2): xy = 1: 3,$ find $x: y.$
View full solution →Given $\frac{x^3+12 x}{6 x^2+8}=\frac{y^3+27 y}{9 y^2+27}$
using componendo and dividendo, find $x : y$
View full solution →If $x=\frac{2 a b}{a+b}$ find the value of $\frac{x+a}{x-a}+\frac{x+b}{x-b}$
View full solution →If $15(2x^2 – y^2) = 7xy,$ find $x: y;$ if $x$ and $y$ both are positive.
View full solution →Find x, if $16\left(\frac{a-x}{a+x}\right)^3=\frac{a+x}{a-x}$
View full solution →If $\frac{7 m+2 n}{7 m-2 n}=\frac{5}{3}$ use properties of proportion to find:
(i) $m : n$
(ii) $\frac{ m ^2+ n ^2}{ m ^2- n ^2}$
View full solution →If $b$ is the mean proportion between $a$ and $c,$ show that:
$\frac{a^4+a^2 b^2+b^4}{b^4+b^2 c^2+c^4}=\frac{a^2}{c^2}$
View full solution →If $\frac{ x }{ a }=\frac{ y }{ b }=\frac{ z }{ c }$ show that:
$\frac{x^3}{a^3}+\frac{y^3}{b^3}+\frac{z^3}{c^3}=\frac{3 x y z}{a b c}$
View full solution →The mean proportional between 4 and 9 is:
Answer: B.
View full solution →The given table shows the distance covered and the time taken by a train moving at a uniform speed along a straight track:| Distance (in m) | 60 | 90 | y |
| Time(in sec) | 2 | X | 5 |
The values of $x$ and $y$ are: - A
$x=4, y=150$
- B
$x=3, y=100$
- C
$x=4, y=100$
- ✓
$x=3, y=150$
Answer: D.
View full solution →Statement (A): In alternendo, if $a: b:: c: d$ then $a: c:: b: d$
Statement (B): In componendo, if $a: b:: c: d$ then $(a+b): b::(c+d): d$.
Which of the statement is valid?
Answer: C.
View full solution →Statement (A): If $6: x:: 2: 13$, then $x$ is 39
Statement (B): The third proportional to 9 and 15 is 35 .
Which of the statement is valid?
Answer: A.
View full solution →Statement (A): If $a, b, c$ and d are in proportion then $\frac{d}{b}=\frac{c}{d} \Rightarrow a d=b c$
Statement (B): If $a, b$ and $c$ are in continued proportion, then, $b=\sqrt{a c}$
Which of the statement is valid?
Answer: C.
View full solution →Assertion : If $a: b=c: d$, then $b: a=d: c$ by invertendo
Reason (R): Invertendo property allows us to invert the terms of a proportion of form another true proportion.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
View full solution →Assertion : Let $a: b$ be the duplicate ratio of $a+c$ and $b+c$. Then $b$ is the third proportion between $a$ and $c$.
Reason : If $y$ is the third proportion between $x$ and $z$, then $\frac{x}{y}-\frac{y}{z}$.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
View full solution →Assertion : If $(4 a+5 b)(4 c-5 d)(4 a-5 b)(4 c+5 d)$, then $a, c, b, d$ are in proportion.
Reason: If $\frac{x}{y}=\frac{m}{n}$, then $x, y, m, n$ are in proportion.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- ✓
Assertion is incorrect but reason is correct.
Answer: D.
View full solution →Assertion : If $y$ is the mean proportion between $x$ and $z$, then $x y z(x+y+z)^3=(x y+y z+z x)^3$.
Reason : If $y$ is the mean proportion between $x$ and $z$, then $y=\frac{x+z}{2}$.
- A
Both assertion and reason are correct and reason is the correct explanation of assertion.
- B
Both assertion and reason are correct but reason is not the correct explanation of assertion.
- C
Assertion is correct but reason is incorrect.
- D
Assertion is incorrect but reason is correct.
View full solution →