Tag: proportion

Quizzes (5) Questions (52)

Questions Related to proportion

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

 The third proportion between : $2$ and $8$

  1. $4$
  2. $3$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a : b :: b : c, then we say that a, b, c are in continued proportion, and c is the third proportional of a and b.

Here, $ {b}^{2} = ac $ or $ b = \sqrt {ac} $

So, for $ 2, 8 $, the third proportional is $ b = \sqrt {ac} = \sqrt {2 \times 8} = \sqrt {16} = 4 $

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

 The third proportion between $12$ and $192$

  1. $48$
  2. $18$
  3. $68$
  4. $58$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a : b :: b : c, then we say that a, b, c are in continued

proportion, and c is the third proportional of a and b.





Here, $ {b}^{2} = ac $ or $ b = \sqrt {ac} $





So, for $ 12, 192 $, the third proportional is $ b = \sqrt {12 \times 192} = \sqrt {4

\times 3 \times 64 \times 3} = 2 \times 3 \times 8 = 48 $

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

The third proportional to $(x^2\, -\, y^2)$ and $(x - y)$ is

  1. $(x+y)$
  2. $\displaystyle \frac {x + y}{x - y}$
  3. $\displaystyle \frac {x - y}{x + y}$
  4. $(x^2\, -\, y^2)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let third proportional is x
$\left ( x^{2}-y^{2} \right ):\left ( x-y \right )=\left ( x-y \right ):x$
$\Rightarrow x=\frac{\left (x-y  \right )\left (x-y  \right )}{\left ( x^{2}-y^{2} \right )}$
$\Rightarrow x=\frac{\left (x-y  \right )\left (x-y  \right )}{\left (x+y  \right )\left (x-y  \right )}$
$\Rightarrow x=\frac{\left ( x-y \right )}{\left (x+y  \right )}$
 

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

Find the third proportional to $\displaystyle (x^{2}-y^{2}): and: (x+y)$.

  1. $\displaystyle \frac{x+y}{x-y}$
  2. $x-y$
  3. $\displaystyle \frac{x-y}{x+y}$

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the third proportional to $\displaystyle (x^{2}-y^{2}): and: (x+y)$ be A.

Then,
$\displaystyle \left ( x^{2}-y^{2} \right ):\left ( x+y \right )::\left ( x+y \right ):A$
$\displaystyle \Rightarrow (x^{2}-y^{2})\times A=(x+y)^{2}$

$\Rightarrow A=\cfrac{(x+y)^{2}}{x^{2}-y^{2}}$
$\Rightarrow A=\cfrac{(x+y)^{2}}{(x+y)(x-y)}=\cfrac{x+y}{x-y}$

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

By mistake instead of dividing Rs. $117$ among $A,B$ and $C$ into the ratio $\displaystyle \frac{1}{2}: \frac{1}{3}: \frac{1}{4}$ , it was divided in the ratio of $2:3:4$ . Who gains the most and by how much?

  1. $A, Rs. 28$
  2. $B, Rs. 3$
  3. $C, Rs. 20$
  4. $C, Rs. 25$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To convert $\displaystyle \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ into normal ratio, multiply each fraction by the LCM$(2,3,4) = 12$

$\displaystyle= 12\times \frac{1}{2}:12\times\frac{1}{3}:12\times\frac{1}{4}$
= $\displaystyle 6:4:3 $
Thus, A would have got $\displaystyle \frac{6}{6+4+3} \times 117 = 54$

B would have got $\displaystyle \frac{4}{6+4+3} \times 117 = 36$

And C would have got $\displaystyle \frac{3}{6+4+3} \times 117 = 27$

Instead Rs. $117$ have been divided in the ratio of $2:3:4$

A gets $\displaystyle \frac {2}{2+3+4} \times 117 = 26$

B gets $\displaystyle \frac {3}{2+3+4} \times 117 = 39$

C gets $\displaystyle \frac {4}{2+3+4} \times 117 = 52$

Thus, by changing the ratio,
A gained $26 - 54$ = -$28$
B gained $39 - 36$ = $3$
And C gained $52 - 27 = 25$
Thus, C's gain of $25$ is the most.

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

Divide Rs 7053 into three parts so that the amount after 2, 3 and 4 years respectively may be equal, the rates of interest being 4% per annum. 

  1. Rs 2500, Rs 3500, Rs 1053

  2. Rs 2436, Rs 2349, Rs 2268

  3. Rs 2568, Rs 3200, Rs1285

  4. Rs 2360, Rs 2289, Rs 2404
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Take the parts as x, y & z.

Then x+y+z=7053.
Obtain the the respective amounts for x,y & z, which are equal, for the 
given years.
Now solve for x, y & z.

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

The third proportional to 8 and 10 correct to two places of decimal is 12.50

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a : b :: b : c, then we say that a, b, c are in continued

proportion, and c is the third proportional of a and b.





Here, $ {b}^{2} = ac $ or $ c = \frac{{b}^{2}}{a} $





So, for $ 8, 10 $, the third proportional is $ c = \frac{{b}^{2}}{a} = \frac {{10}^{2}}{8} = 12.50 $

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

If 150 is the third proportional to 6 and x; find the value of x.

  1. 30

  2. 60

  3. 63

  4. 34
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If a : b :: b : c, then we say that a, b, c are in continued proportion, and

c is the third proportional of a and b.





Here, $ {b}^{2} = ac $ 





Given  the third proportional of $ 6, x $ is 150 

$ => {x}^{2} = 6 \times 150 = 6 \times 6 \times 25 $

$ => x = \sqrt { 6 \times 6 \times 25 } $

$ x = 6 \times 5 = 30 $