Tag: maths

Questions Related to maths

$2:5::8:x$. Find the value of $x$.

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $15$

  2. $17$

  3. $20$

  4. $11$

Show answer
Correct Option: A

The ratio of three numbers is $6 : 7: 5$ and their sum is $108.$ The second number of the three numbers is? 

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $12$

  2. $42$

  3. $30$

  4. $36$

Show answer
Correct Option: B
Explanation:
Let the common multiple of the three numbers be $x$

$ \therefore 6x+7x+5x = 108$

$18x =108$

$x=\dfrac{108}{18}$

$x=6$

The second number is $7\times6 = 42$

Mark the correct alternative of the following.
The first, second and fourth terms of a proportion are $16, 24$ and $54$ respectively. The third term is?

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $32$

  2. $48$

  3. $28$

  4. $36$

Show answer
Correct Option: D
Explanation:

$16 : 24 = x : 54$


$16 \times 54 = 24 \times x$


$x = \dfrac{16 \times 54}{24}$

$x = \dfrac{864}{24}$

$x = 36$

Mark the correct alternative of the following.
If A, B, C divide Rs. $1200$ in the ratio $2 : 3 : 5$, then B's share is?

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. Rs. $240$

  2. Rs. $600$

  3. Rs. $380$

  4. Rs. $360$

Show answer
Correct Option: D
Explanation:

Since they divide Rs. $1200$ in the ratio $2:3:5$ then let shares of them will be $2x,3x$ and $5x$.

Then according to the problem we get,
$2x+3x+5x=1200$
or, $x=120$.
So share of B is Rs. $120\times 3=360$.

state True or False
The fourth proportion of $a^2, ab, b^2$ is $\displaystyle \frac{b^3}{a}$

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. True

  2. False

Show answer
Correct Option: A
Explanation:

In $ a:b::c:d;   d $ is the fourth proportional.

In, $ {a}^{2}:ab :: {b}^{2} :d $, product of extremes $ = $ product of means

$ {a}^{2} \times d = ab \times {b}^{2} $
$ d = \frac {{b}^{3}}{a} $

Find the fourth proportional in $14,21,4$

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $6$

  2. $7$

  3. $4$

  4. $8$

Show answer
Correct Option: A
Explanation:

In $ a:b::c:d;  d $ is the fourth proportional.

In, $ 14:21 :: 4 :d $, product of extremes $ = $ product of means

$ 14 \times d = 21 \times 4 $
$ d = 6 $

Mark the correct alternative of the following.
If $343$ is the third proportional of $a$ and $b,$ where $a : b=1 : 7$, then the values of $a+b$ is?

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $14$

  2. $24$

  3. $56$

  4. $63$

Show answer
Correct Option: C
Explanation:

$a : b = b : 343$


$\dfrac{a}{b} = \dfrac{b}{343}$


$\dfrac{1}{7} = \dfrac{b}{343}$

$b = \dfrac{343}{7}$

$b = 49$

$\dfrac{a}{b} = \dfrac{1}{7}$

$\dfrac{a}{49} = \dfrac{1}{7}$

$a = \dfrac{49}{7} = 7$

$a + b = 49 + 7 = 56$

The third proportional of $3$ and $27$ is

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $243$

  2. $256$

  3. $289$

  4. $225$

Show answer
Correct Option: A
Explanation:

$\dfrac{3}{27} = \dfrac{27}{b}$


$3 \times b = 27 \times 27$


$b = \dfrac{729}{3}$

$b = 243$

If $8:x::16:35$

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $35$

  2. $70$

  3. $\cfrac{35}{2}$

  4. $24$

Show answer
Correct Option: C
Explanation:

$8 : x :: 16 : 35$


product of means = product of Extremes 


$16 \times x = 8 \times 35$

$x = \dfrac{8 \times 35}{16}$

$x = \dfrac{35}{2}$

If the first three terms of a proportion are $3,5$ and $21$ respectively, then its fourth term is

maths ratio, proportion and unitary method more on proportion terms related to proportion proportion

  1. $21$

  2. $35$

  3. $15$

  4. None of these

Show answer
Correct Option: B
Explanation:

Given, the first three terms of a proportion are $3,5$ and $21$ respectively.

Let the fourth number be $'x'$,

So, Numbers proportion are $3, 5, 21, x$

According to proportionality,

Product of means $=$ Product of extremes

$3 : 5 :: 21 : x$

$\dfrac{3}{5} = \dfrac{21}{x}$

Cross multiply,

$3 \times x = 21 \times 5$

$3x = 105$

$x = 35$

Therefore, The required fourth number is $35$