Ratio and Proportion – basics, definition, formula, problems

Ratio : விகிதம்

Proportion : விகித சமம்

Ratio a:b (or) \frac{a}{b} \\

Proportion a:b::c:d (or) \frac{a}{b}=\frac{c}{d} \\

ratio and proportion definition

Types Of Proportion

First Proportion

Second Proportion

Third Proportion

Fourth Proportion

Mean Proportion

QUESTION 01

Find the missing term ___:2=3:6 ?

(or)

If x:2 :: 3:6 Then x is equal to

(or)

Find the value of first proportion ?:2 :: 3:6

(or)

Find the value of \frac{?}{2}=\frac{3}{6} \\

(or)

If the ratio formed using the number x,2,3,6 in the same order are in proportion then x is

(or)

Find the missing number in the proportion ___:2 :: 3:6

ANSWER

\frac{x}{2}=\frac{3}{6} \\ x=\frac{{3}\times{2}}{6} \\ x=\frac{6}{6}

x=1

QUESTION 02

Find the missing term 4:___=6:3 ?

(or)

If 4:x :: 6:3 Then x is equal to

(or)

Find the value of second proportion 4:? :: 6:3

(or)

Find the value of \frac{4}{?}=\frac{6}{3} \\

(or)

If the ratio formed using the number 4,x,6,3 in the same order are in proportion then x is

(or)

Find the missing number in the proportion 4:__ :: 6:3

ANSWER

\frac{4}{x}=\frac{6}{3} \\ x=\frac{{4}\times{3}}{6} \\ x=\frac{12}{6}

x=2

QUESTION 03

Find the missing term 4:2=__:3 ?

(or)

If 4:2 :: x:3 Then x is equal to

(or)

Find the value of third proportion 4:2 :: ?:3

(or)

Find the value of \frac{4}{2}=\frac{?}{3} \\

(or)

If the ratio formed using the number 4,2,?,3 in the same order are in proportion then x is

(or)

Find the missing number in the proportion 4:2 :: ?:3

ANSWER

\frac{4}{2}=\frac{x}{3} \\ x=\frac{{4}\times{3}}{2} \\ x=\frac{12}{2}

x=6

QUESTION 04

Find the missing term 2:4=2:__ ?

(or)

If 2:4 :: 2:x Then x is equal to

(or)

Find the value of fourth proportion 2:4 :: 2:?

(or)

Find the value of \frac{2}{4}=\frac{2}{?} \\

(or)

If the ratio formed using the number 2,4,2,x in the same order are in proportion then x is

(or)

Find the missing number in the proportion 2:4 :: 2:__

ANSWER

\frac{2}{4}=\frac{2}{x} \\ x=\frac{{2}\times{4}}{2} \\ x=\frac{8}{2}

x=4

Mean Proportion
\sqrt{ab} \\
QUESTION 05

Mean Proportion between 2 and 8

ANSWER

Formula \sqrt{ab} \\

= \sqrt{2\times8} \\

= \sqrt{16} \\

=4

Types Of Ratio

DUPLICATE RATIO a^2 : b^2 \\

SUB-DUPLICATE RATIO \sqrt{a} : \sqrt{b} \\

TRIPLICATE RATIO a^3 : b^3 \\

SUB TRIPLICATE RATIO \sqrt[3]{a} : \sqrt[3]{b} \\

INVERSE OR RECIPROCAL RATIO \frac{1}{a} : \frac{1}{b} \\

COMPOUND RATIO a:b, c:d, e:f, is \frac{a\times c\times e}{b\times d\times f} \\

QUESTION 06

If a:b is 4:9

FIND THE VALUE OF

(i) DUPLICATE RATIO

(ii) SUB-DUPLICATE RATIO

(iii) TRIPLICATE RATIO

(iv) SUB-TRIPLICATE RATIO

(v) INVERSE OR RECIPROCAL RATIO

ANSWER

DUPLICATE RATIO

=4^2:9^2 \\ =\frac{16}{81}\\

=16:81

SUB-DUPLICATE RATIO

=\sqrt{4}:\sqrt{9} \\ =\frac{2}{3} \\

=2:3

TRIPLICATE RATIO

=4^3:9^3 \\ =\frac{64}{729} \\

=64:729

SUB-TRIPLICATE RATIO

=\sqrt[3]{4}:\sqrt[3]{9} \\ =\frac{\sqrt[3]{4}}{\sqrt[3]{9}} \\ =\sqrt[3]{4}:\sqrt[3]{9} \\

INVERSE OR RECIPROCAL RATIO

=\frac{1}{4}:\frac{1}{9} \\
QUESTION 07

Find the compound ratio 2:4, 6:8, 4:2

=\frac{2\times 6\times 4}{4\times 8\times 2} \\ =\frac{48}{64} \\ =\frac{3}{4} \\

=3:4

QUESTION 07

If a:b = 2:3, b:c = 4:5, c:d = 6:7, then

Find the value of

(i) a

(ii) b

(iii) c

(iv) d

(v) a:b

(vi) b:c

(vii) c:d

(viii) a:b:c

(ix) a:b:c:d

ANSWER
Ratio and proportion problem

(i) a

=48

(ii) b

=72

(iii) c

=90

(iv) d

=105

(v) a:b

=48:72

(vi) b:c

=72:90

(vii) c:d

=90:105

(viii) a:b:c

=48:72:90

(ix) a:b:c:d

=48:72:90:105

QUESTION 08

If A:B = 3:1, B:C = 5:2, C:D = 4:7, then A:B:C:D is

ANSWER
Ratio and proportion tricks

A:B:C:D = 60:20:8:14

QUESTION 09

Find the ratio of 4 years to 8 months

ANSWER

1 year = 12 months

4 years = 48 months

=\frac{48}{8} \\ =\frac{6}{1} \\

=6:1

QUESTION 10

Find the ratio of 9 months to 1 year

ANSWER

1 year=12 months

=\frac{9}{12} \\ =\frac{3}{4} \\

=3:4

QUESTION 11

What is the ratio of 2\frac{1}{2} hrs to 20 minutes ?

ANSWER

1 hour = 60 minutes

=2\frac{1}{2} hours = 150 minutes

=\frac{150}{20} \\

=\frac{15}{2} \\

=15:2

QUESTION 12

If x:y=2:3 then find (6x-y):(3x+2y)

ANSWER

x=2

y=3

(6x-y):(3x+2y)

=(6(2)-3):(3(2)+2(3))

=(12-3):(6+6)

=9:12

=\frac{9}{12} \\

=3:4

QUESTION 13

If x:y=2:3, y:z=4:6, then find x:z

ANSWER
Ratio and proportion

X:Z = 8:18

QUESTION 14

Ratio 2:3,4:15,6:32 and 8:42

(i) Greatest Ratio (or) Biggest Ratio

(ii) Smallest Ratio

(iii) Ascending order

(iv) Descending order

(v) Lesser than

(vi) Greater than

ANSWER

2:3 =\frac{2}{3} \\ =0.666

4:15 =\frac{4}{15} \\ =0.266

6:32 =\frac{6}{32} \\ =0.187

8:42=\frac{8}{42} \\ =0.190

(i) Greatest Ratio (or) Biggest Ratio

2:3

(ii) Smallest Ratio

6:32

(iii) Ascending order

6:32, 8:42, 4:15 ,2:3

(iv) Descending order

2:3, 4:15, 8:42, 6:32

(v) Lesser than

6:32<8:42<4:15<2:3

(vi) Greater than

2:3>4:15>8:42>6:32

QUESTION 15

Divide Rs. 672 in the ratio 5:3

ANSWER

First Step =5+3 =8

=\frac{5}{8} \times 672 \\

= 5\times 84 \\

=420

Second Step =5+3 =8

=\frac{3}{8} \times 672 \\

= 3 \times 84 \\

=252

Ratio is 420 and 252

QUESTION 16

Divide Rs.675 among a, b, c, in the proportion of 4:5:6

ANSWER

First Step =4+5+6 =15

=\frac{4}{15} \times 675 : \frac{5}{15} \times 675 : \frac{6}{15} \times 675 \\ =4 \times 45 : 5 \times 45 : 6\times 45 \\

=180:225:270

QUANTITATIVE APTITUDE STUDY MATERIAL

Ration and proportional

Simplification

Percentage

Number series

L.C.M and H.C.F

Simple Interest

Compound Interest

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