Ratio and Proportion Question and Answers Quiz-1

Given, x : y = 4 : 5

Let, \frac{x}{y} = \frac{4}{5} = k

\frac{x}{4} =\frac{y}{5} = k

x = 4k, y = 5k

Given expression,
(3x + y) : (5x + 3y)

\frac{3x+y}{5x+3y} = \frac{3\times 4k +5k}{5 \times 4k + 3 \times 5k}

\frac{12k+5k}{20k+15k} </span></span></span></span></span></span></span></span>= \frac{17k}{35k} <span class="math-tex"><span id="MathJax-Element-30-Frame" class="MathJax" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left" rowspacing="4pt" columnspacing="1em"><mtr><mtd><mo>=</mo><mfrac><mrow class="MJX-TeXAtom-ORD"><mn>3</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mn>5</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow class="MJX-TeXAtom-ORD"><mn>3</mn><mo>&#x00D7;</mo><mn>4</mn><mi>k</mi><mo>+</mo><mn>5</mn><mi>k</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mn>5</mn><mo>&#x00D7;</mo><mn>4</mn><mi>k</mi><mo>+</mo><mn>3</mn><mo>&#x00D7;</mo><mn>5</mn><mi>k</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mo>=</mo><mfrac><mrow class="MJX-TeXAtom-ORD"><mn>12</mn><mi>k</mi><mo>+</mo><mn>5</mn><mi>k</mi></mrow><mrow class="MJX-TeXAtom-ORD"><mn>20</mn><mi>k</mi><mo>+</mo><mn>15</mn><mi>k</mi></mrow></mfrac></mtd></mtr></mtable></math>"><span id="MathJax-Span-1154" class="math"><span id="MathJax-Span-1155" class="mrow"><span id="MathJax-Span-1156" class="mtable"><span id="MathJax-Span-1157" class="mtd"><span id="MathJax-Span-1158" class="mrow"><span id="MathJax-Span-1159" class="mo">

= \frac{17}{35}

= 17 : 35

Let the number of teachers be x.

girls : teachers = 3 : 2,

Number of girls = \frac{3}{2} \times x = 1.5x

Now, since ratio of boys : girls = 4 : 9

Number of boys = \frac{4}{9} \times 3.5x = 1.5x

Number of all students = number of boys + number of girls = 1.5x + 1.56x = 3x

∴ Ratio of student: teachers = 3x : x = 3 : 1

Hence, the ratio of all students and teachers is 3 : 1

 

Solution:
The ratio of shares of groups of men, women, and boys = 5 : 3 : 2
So share of 5 boys is = \frac{2}{10} \times 5000 = 1000
Share of one boy is = \frac{1000}{5} = 200

Let the side of a cube be 'a'

The total surface area of cube = 6a^{2}

Total surface area of 3 cubes = 3 \times 6a^{2} = 18a^{2}

After joining 3 cubes in a row,

length of Cuboid =3a

Breadth and height of cuboid = a

Total surface area of cuboid = 2 (3a^{2}+ a^{2} + 3a^{2}) = 14a^{2}

The ratio of the total surface area of a cuboid to the total surface area of 3 cubes

= \frac{14a^{2}}{18a^{2}} = \frac{7}{9}

Hence, the ratio is 7 : 9

let the salary of Raju is P
Then Ramu's salary is 3P
After 2 months Raju's salary becomes P(1 +\frac{20}{100})2 .....(1)
After 2 months Ramu's salary becomes 3P(1 - \frac{10}{100})2 ....(2)
Ratio= (1)/(2) = 12 : 27 = 4 : 9

When 5000 is shared among p,and r in the ratio of 2:3:5 then,
p = \frac{5000 \times 2}{10}=1000
q = \frac{5000 \times 3}{10}=1500
r = \frac{5000 \times 5}{10}=2500
and if upon this 500 is added to each of them then
p=1500
q=2000
r=3000
then the new ratio will be 3 : 4 : 6

According to the given information,

LCM of 7, 15 and 19 is 1995.

On dividing the given equation by 1995, we get,

\frac{7A}{1995} = \frac{15B}{1995} = \frac{19C}{1995}

\frac{A}{285} = \frac{B}{133} = \frac{C}{105}

\frac{A}{B} = \frac{285}{133}

\frac{B}{C} = \frac{133}{105}

A : B : C = 285 : 133 : 105

Let the three numbers be A,B and C respectively

$A:B=2:3$              (1)

Number of marbles in second hall = (325 \times 9 + 200 \times 6)

Number of marbles in the first hall = {(226 - 200) \times 5} = 26 \times 5

The ratio of the number of marbles in the second hall to that in the first hall = \frac{(325 \times 9 + 200 \times 6)}{26 \times 5}

\frac{4125}{1130} = \frac{825}{226} = 825 : 226

Using cross product rule, we get,

\frac{10}{3}:\frac{5}{4} = x:\frac{5}{2}

\frac{25}{6} = \frac{5x}{2}[\latex]<br /> <br /> \frac{25}{6}:\frac{2}{5} = x

\frac{5}{3} = x

x = \frac{5}{3}