Practice Ratio and Proportion

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\[\frac{50}{100}\] is same as

\[1:2\]

\[1:3\]

\[1:4\]

\[1:5\]

\[\frac{50}{100}\]

\[=\frac{5}{10}\]

\[=\frac{1}{2}\]

\[=1:2\]

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Find \[x\], if

\[x:5=2:5\].

\[1\]

\[2\]

\[3\]

\[4\]

\[x:5=2:5\]

\[\Rightarrow \frac{x}{5}=\frac{2}{5}\]

\[\Rightarrow x=\frac{2}{5}\times5\]

\[\Rightarrow x=2\]

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Two numbers are in the ratio \[4:5\] and the sum of these numbers is \[27\]. Find the two numbers.

\[25,15\]

\[25,20\]

\[25,30\]

\[25,40\]

Let the two numbers be \[4x\] and \[5x\]

According to the question,

\[4x+5x=27\]

\[\implies 9x=27\]

\[\implies x=3\]

\[\therefore\] the two numbers are

\[4x=4\times3=25\]
\[5x=5\times3=15\]

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Two numbers are in the ratio \[5:3\] and the difference of these numbers is \[20\]. Find the smaller number.

\[20\]

\[30\]

\[40\]

\[50\]

Let the two numbers be \[5x\] and \[3x\]

According to the question,

\[5x-3x=20\]

\[\implies 2x=20\]

\[\implies x=10\]

\[\therefore\] the two numbers are

Larger number \[=5x=5\times10=50\]
Smaller number \[=3x=3\times10=30\]

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Find a fourth proportional to the numbers \[2, 5, 4\].

\[2\]

\[6\]

\[8\]

\[10\]

Let \[x\] be the fourth proportional, then

\[2:5::4:x\]

\[\Rightarrow\frac{2}{5}=\frac{4}{x}\]

\[\Rightarrow x=\frac{4\times5}{2}\]

\[=2\times5\]

\[=10\]

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Find the mean proportional between \[48\] and \[12\]

\[22\]

\[24\]

\[26\]

\[28\]

Let \[x\] be the mean proportional, then

\[48:x::x:12\]

\[\Rightarrow\frac{48}{x}=\frac{x}{12}\]

\[\Rightarrow x^2=48\times12\]

\[\Rightarrow x=\sqrt{48\times12}\]

\[\Rightarrow x=\sqrt{576}\]

\[\Rightarrow x=24\]

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If \[a : b = 7 : 9\] and \[b : c =15 : 7\], then what is \[a : c\]?

\[3:5\]

\[5:3\]

\[5:7\]

\[7:5\]

\[a:c=(a:b)\times(b:c)\]

\[=\frac{7}{9}\times\frac{15}{7}\]

\[=\frac{15}{9}\]

\[=\frac{5}{3}\]

\[=5:3\]

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\[A : B = 3 : 4\]
\[B : C = 5 : 7\]
\[C : D = 8 : 9\]

then \[A : D\] is equal to

\[7:18\]

\[11:19\]

\[11:20\]

\[10:21\]

\[A:D=\frac{A}{D}=\frac{A}{B}\times\frac{B}{C}\times\frac{C}{D}\]

\[=\frac{3}{4}\times\frac{5}{7}\times\frac{8}{9}\]

\[=\frac{10}{21}\]

\[=10:21\]

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The ratio of \[A \ to\ B\] is \[4 : 5\] and that of \[B \ to \ C\] is \[2 : 3\]. If \[A\] equals \[800, C\] equals

\[1100\]

\[1300\]

\[1500\]

\[1700\]

\[A : B = 4 : 5\]

\[B : C = 2 : 3\]

\[\therefore A : B : C = 4 × 2 : 5 × 2 : 5 × 3\]

\[= 8 : 10 : 15\]

If \[A\] equals \[800\], then \[C\] equals

\[\frac{800}{8}\times15=100\times15=1500\]

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If \[A : B = 2 : 3\] and \[B : C = 4 : 5\], then \[A : B : C\] is

\[1:2:3\]

\[3:4:15\]

\[5:9:10\]

\[8:12:15\]

\[A : B = 2 : 3\]

\[B : C = 4 : 5\]

\[\therefore A : B : C = 2 × 4 : 3 × 4 : 3 × 5\]

\[= 8 : 12 : 15\]

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If \[A : B = 3 : 2\] and \[B : C = 3 : 4\] then \[A : C\] is equal to

\[8:9\]

\[9:8\]

\[7:8\]

\[8:7\]

\[A : B = 3 : 2\]

\[B : C = 3 : 4\]

\[\therefore A : B : C = 3 × 3 : 2 × 3 : 2 × 4\]

\[= 9 : 6 : 8\]

\[\therefore A : C = 9 : 8\]

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If two-third of \[A\] is four-fifth of \[B\], then \[A : B = ?\]

\[2:1\]

\[4:3\]

\[5:4\]

\[6:5\]

\[A\times\frac{2}{3}=B\times\frac{4}{5}\]

\[\Rightarrow\frac{A}{B}=\frac{4}{5}\times\frac{3}{2}\]

\[=6:5\]

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If \[\frac{a}{b}=\frac{2}{3}\] and \[\frac{b}{c}=\frac{4}{5}\], then

\[(a+b):(b+c)=?\]

\[17:19\]

\[20:21\]

\[27:31\]

\[20:27\]

\[a:b=2:3\]

\[b:c=4:5\]

\[\therefore a:b:c=2\times4:3\times4:3\times5\]

\[=8:12:15\]

\[\therefore\frac{a+b}{b+c}\]

\[=\frac{8+12}{12+15}\]

\[=\frac{20}{27}\]

\[=20:27\]

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\[Rs.40,000\] are divided among \[A\] and \[B\] in such a manner that the ratio of the amount of \[A\] to that of \[B\] is \[3 : 5\]. The amount of money received by \[A\] is

\[Rs.10000/-\]

\[Rs.12000/-\]

\[Rs.14000/-\]

\[Rs.15000/-\]

\[A : B = 3:5\]

Sum of the ratios

\[= 3+5=8\]

\[\therefore A’s\] share

\[Rs.\left(\frac{3}{8}\times40000\right)\]

\[=Rs.15000\]

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\[Rs.33,630\] are divided among \[A, B\] and \[C\] in such a manner that the ratio of the amount of \[A\] to that of \[B\] is \[3 : 7\] and the ratio of the amount of \[B\] to that of \[C\] is \[6 : 5\]. The amount of money received by \[B\] is

\[Rs.12866/-\]

\[Rs.14868/-\]

\[Rs.17854/-\]

\[Rs.18890/-\]

\[A : B = 3 : 7\]

\[B : C = 6 : 5\]

\[A : B : C = 3×6 : 7×6 : 7×5\]

\[= 18 : 42 : 35\]

Sum of the ratios

\[= 18 + 42 + 35 = 95\]

\[\therefore B’s\] share

\[Rs.\left(\frac{42}{95}\times33630\right)\]

\[=Rs.14868\]

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If \[\frac{3x+5}{5x-2}=\frac{2}{3}\],then the value of \[x\] is

\[11\]

\[13\]

\[17\]

\[19\]

\[\frac{3x+5}{5x-2}=\frac{2}{3}\]

\[\implies 10 x – 4 = 9 x + 15\]

\[\implies 10 x – 9 x = 15 + 4 = 19\]

\[\implies x = 19\]

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Which of the following represents a correct proportion ?

\[12 : 9 = 16 : 12\]

\[13 : 11 = 5 : 4\]

\[30 : 45 = 13 : 24\]

\[3 : 5 = 2 : 5\]

\[\frac{12}{9}=\frac{16}{12}\]

\[\implies 12 × 12 = 9 × 16\]

\[\implies 144 = 144.\]

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If \[18, x\] and \[50\] are in continued proportion, then the value of \[x\] is

\[\frac{18}{x}=\frac{x}{40}\]

\[x^2 = 18 × 50 = 900\]

\[\implies x = \sqrt{900}\]

\[= 30\]

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The number of pupils of a class is \[55\]. The ratio of the number of male pupils to the number of female pupils is \[5: 6\]. The number of female pupils is

Boys : Girls \[= 5 : 6\]

Sum of the terms of ratio

\[= 5 + 6 = 11\]

\[\therefore\] Number of girls

\[= \frac{6}{11} × 55 = 30\]

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The ratio of ages of two students is \[3 : 2\]. One is older to the other by \[5\] years. What is the age of the younger student ?

\[10\] years

\[12\] years

\[14\] years

\[16\] years

Let their age be \[3 x\] and \[2 x\] years.

\[\therefore 3 x – 2 x = 5 \]

\[\implies x = 5\]

\[\therefore\] Younger student’s age

\[= 2 x = 2 × 5 = 10\] years