Ratio And Proportion - Class 6 - Mathematics
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Examples - Ratio And Proportion | NCERT | Mathematics | Class 6
Length and breadth of a rectangular field are $50 \mathrm{~m}$ and $15 \mathrm{~m}$ respectively. Find the ratio of the length to the breadth of the field.
To find the ratio of the length to the breadth of the rectangular field, we simply divide the length by the breadth.
Given, the length (L = 50 , \text{m}) and the breadth (B = 15 , \text{m}).
The ratio of the length to the breadth is: $$\frac{L}{B} = \frac{50}{15}$$
Simplifying the fraction gives us: $$\frac{10}{3}$$
Therefore, the ratio of the length to the breadth of the field is (10:3).
Find the ratio of $90 \mathrm{~cm}$ to $1.5 \mathrm{~m}$.
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Sign up nowThere are 45 persons working in an office. If the number of females is 25 and the remaining are males, find the ratio of:
(a) The number of females to number of males.
(b) The number of males to number of females.
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Sign up nowGive two equivalent ratios of $6: 4$.
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Sign up nowFill in the missing numbers :
$\frac{14}{21}=\frac{\square}{3}=\frac{6}{\square}$
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Sign up nowRatio of distance of the school from Mary's home to the distance of the school from John's home is $2: 1$.
(a) Who lives nearer to the school?
(b) Complete the following table which shows some possible distances that Mary and John could live from the school.
Distance from Mary's home to school (in km.) | 10 | 4 | |||
---|---|---|---|---|---|
Distance from John's home to school (in km.) | 5 | 4 | 3 | 1 |
(c) If the ratio of distance of Mary's home to the distance of Kalam's home from school is $1: 2$, then who lives nearer to the school?
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Sign up nowDivide ₹ 60 in the ratio $1: 2$ between Kriti and Kiran.
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Sign up nowAre the ratios $25 \mathrm{~g}: 30 \mathrm{~g}$ and $40 \mathrm{~kg}: 48 \mathrm{~kg}$ in proportion?
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Sign up nowAre 30, 40, 45 and 60 in proportion?
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Sign up nowDo the ratios $15 \mathrm{~cm}$ to $2 \mathrm{~m}$ and $10 \mathrm{sec}$ to 3 minutes form a proportion?
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Sign up nowIf the cost of 6 cans of juice is ₹ 210 , then what will be the cost of 4 cans of juice?
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Sign up nowA motorbike travels $220 \mathrm{~km}$ in 5 litres of petrol. How much distance will it cover in 1.5 litres of petrol?
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Sign up nowIf the cost of a dozen soaps is ₹ 153.60 , what will be the cost of 15 such soaps?
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Sign up nowCost of 105 envelopes is ₹ 350 . How many envelopes can be purchased for ₹ 100 ?
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Sign up nowA car travels $90 \mathrm{~km}$ in $2 \frac{1}{2}$ hours.
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Sign up nowExercise 12.1 - Ratio And Proportion | NCERT | Mathematics | Class 6
There are 20 girls and 15 boys in a class.
(a) What is the ratio of number of girls to the number of boys?
(b) What is the ratio of number of girls to the total number of students in the class?
Let's solve both parts of your question step-by-step:
(a) Ratio of number of girls to the number of boys
The number of girls is 20 and the number of boys is 15.
The ratio of the number of girls to the number of boys is given by dividing the number of girls by the number of boys:
$$ \text{Ratio of girls to boys} = \frac{\text{Number of girls}}{\text{Number of boys}} = \frac{20}{15} $$
This can be simplified to:
$$ \frac{20}{15} = \frac{4}{3} $$
So, the ratio of the number of girls to the number of boys is 4:3.
(b) Ratio of number of girls to the total number of students in the class
To determine this ratio, we first need to find the total number of students in the class.
The total number of students is the sum of the number of girls and the number of boys:
$$ \text{Total number of students} = \text{Number of girls} + \text{Number of boys} = 20 + 15 = 35 $$
Now, the ratio of the number of girls to the total number of students is given by dividing the number of girls by the total number of students:
$$ \text{Ratio of girls to total students} = \frac{\text{Number of girls}}{\text{Total number of students}} = \frac{20}{35} $$
This can be simplified to:
$$ \frac{20}{35} = \frac{4}{7} $$
Therefore, the ratio of the number of girls to the total number of students in the class is 4:7.
Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
(a) Number of students liking football to number of students liking tennis.
(b) Number of students liking cricket to total number of students.
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Sign up nowSee the figure (Inside a rectangle there are 3 triangle, 2 circles and 2 squares) and find the ratio of
(a) Number of triangles to the number of circles inside the rectangle.
(b) Number of squares to all the figures inside the rectangle.
(c) Number of circles to all the figures inside the rectangle.
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Sign up nowDistances travelled by Hamid and Akhtar in an hour are $9 \mathrm{~km}$ and $12 \mathrm{~km}$. Find the ratio of speed of Hamid to the speed of Akhtar.
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Sign up nowFill in the following blanks:
$\frac{15}{18}=\frac{\square}{6}=\frac{10}{\square}=\frac{\square}{30}$ [Are these equivalent ratios?]
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Sign up nowFind the ratio of the following :
(a) 81 to 108
(b) 98 to 63
(c) $33 \mathrm{~km}$ to $121 \mathrm{~km}$
(d) 30 minutes to 45 minutes
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Sign up nowFind the ratio of the following:
(a) 30 minutes to 1.5 hours
(b) $40 \mathrm{~cm}$ to $1.5 \mathrm{~m}$
(c) 55 paise to ₹ 1
(d) $500 \mathrm{~mL}$ to 2 litres
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Sign up nowIn a year, Seema earns $₹ 1,50,000$ and saves $₹ 50,000$. Find the ratio of
(a) Money that Seema earns to the money she saves.
(b) Money that she saves to the money she spends.
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Sign up nowThere are 102 teachers in a school of 3300 students. Find the ratio of the number of teachers to the number of students.
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Sign up nowIn a college, out of 4320 students, 2300 are girls. Find the ratio of
(a) Number of girls to the total number of students.
(b) Number of boys to the number of girls.
(c) Number of boys to the total number of students.
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Sign up nowOut of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of
(a) Number of students who opted basketball to the number of students who opted table tennis.
(b) Number of students who opted cricket to the number of students opting basketball.
(c) Number of students who opted basketball to the total number of students.
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Sign up nowCost of a dozen pens is $₹ 180$ and cost of 8 ball pens is $₹ 56$. Find the ratio of the cost of a pen to the cost of a ball pen.
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Sign up nowConsider the statement: Ratio of breadth and length of a hall is $2: 5$. Complete the following table that shows some possible breadths and lengths of the hall.
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Sign up nowDivide 20 pens between Sheela and Sangeeta in the ratio of $3: 2$.
Breadth of the hall (in metres) | 10 | 40 | ||
Length of the hall (in metres) | 25 | 50 |
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Sign up nowMother wants to divide $₹ 36$ between her daughters Shreya and Bhoomika in the ratio of their ages. If age of Shreya is 15 years and age of Bhoomika is 12 years, find how much Shreya and Bhoomika will get.
16. Present age of father is 42 years and that of his son is 14 years. Find the ratio of
(a) Present age of father to the present age of son.
(b) Age of the father to the age of son, when son was 12 years old.
(c) Age of father after 10 years to the age of son after 10 years.
(d) Age of father to the age of son when father was 30 years old.
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Sign up nowExercise 12.2 - Ratio And Proportion | NCERT | Mathematics | Class 6
Determine if the following are in proportion. with steps
(a) $15,45,40,120$
(b) $33,121,9,96$
(c) $24,28,36,48$
(d) $32,48,70,210$
(e) $4,6,8,12$
(f) $33,44,75,100$
To determine if the given numbers are in proportion, we compare the ratios of the first two numbers to the ratio of the last two numbers for each set. If these ratios are equal, then the numbers are in proportion.
For a set of numbers $a, b, c, d$, they are in proportion if $\frac{a}{b} = \frac{c}{d}$ or equivalently $a \cdot d = b \cdot c$.
Let's evaluate each of the given sets:
(a) $15, 45, 40, 120$
For $15, 45, 40, 120$, we check if $\frac{15}{45} = \frac{40}{120} \longleftrightarrow 15 \cdot 120 = 45 \cdot 40$.
(b) $33, 121, 9, 96$
For $33, 121, 9, 96$, we check if $\frac{33}{121} = \frac{9}{96} \longleftrightarrow 33 \cdot 96 = 121 \cdot 9$.
(c) $24, 28, 36, 48$
For $24, 28, 36, 48$, we check if $\frac{24}{28} = \frac{36}{48} \longleftrightarrow 24 \cdot 48 = 28 \cdot 36$.
(d) $32, 48, 70, 210$
For $32, 48, 70, 210$, we check if $\frac{32}{48} = \frac{70}{210} \longleftrightarrow 32 \cdot 210 = 48 \cdot 70$.
(e) $4, 6, 8, 12$
For $4, 6, 8, 12$, we check if $\frac{4}{6} = \frac{8}{12} \longleftrightarrow 4 \cdot 12 = 6 \cdot 8$.
(f) $33, 44, 75, 100$
For $33, 44, 75, 100$, we check if $\frac{33}{44} = \frac{75}{100} \longleftrightarrow 33 \cdot 100 = 44 \cdot 75$.
Let us calculate each and see if they result in true proportions. Here are the results for each set of numbers:
(a) $15, 45, 40, 120$
These numbers are in proportion.
(b) $33, 121, 9, 96$
These numbers are not in proportion.
(c) $24, 28, 36, 48$
These numbers are not in proportion.
(d) $32, 48, 70, 210$
These numbers are not in proportion.
(e) $4, 6, 8, 12$
These numbers are in proportion.
(f) $33, 44, 75, 100$
These numbers are in proportion.
Sets (a), (e), and (f) are in proportion, while sets (b), (c), and (d) are not.
Write True ( $\mathrm{T}$ ) or False ( $\mathrm{F}$ ) against each of the following statements :
(a) $16: 24:: 20: 30$
(b) $21: 6:: 35: 10$
(c) $12: 18:: 28: 12$
(d) $8: 9:: 24: 27$
(e) $5.2: 3.9:: 3: 4$
(f) $0.9: 0.36:: 10: 4$
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Sign up nowAre the following statements true?
(a) 40 persons : 200 persons $=₹ 15: ₹ 75$
(b) 7.5 litres : 15 litres $=5 \mathrm{~kg}: 10 \mathrm{~kg}$
(c) $99 \mathrm{~kg}: 45 \mathrm{~kg}=₹ 44: ₹ 20$
(d) $32 \mathrm{~m}: 64 \mathrm{~m}=6 \mathrm{sec}: 12 \mathrm{sec}$
(e) $45 \mathrm{~km}: 60 \mathrm{~km}=12$ hours : 15 hours
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Sign up nowDetermine if the following ratios form a proportion. Also, write the middle terms and extreme terms where the ratios form a proportion.
(a) $25 \mathrm{~cm}: 1 \mathrm{~m}$ and ₹ $40: ₹ 160$
(b) 39 litres : 65 litres and 6 bottles : 10 bottles
(c) $2 \mathrm{~kg}: 80 \mathrm{~kg}$ and $25 \mathrm{~g}: 625 \mathrm{~g}$
(d) $200 \mathrm{~mL}: 2.5$ litre and ₹$4: ₹ 50$
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Sign up nowExercise 12.3 - Ratio And Proportion | NCERT | Mathematics | Class 6
If the cost of $7 \mathrm{~m}$ of cloth is ₹ 1470 , find the cost of $5 \mathrm{~m}$ of cloth.
To solve this, we will first find the cost of 1 meter of cloth and then multiply that by 5 to find the cost of 5 meters of cloth.
If the cost of 7 meters of cloth is ₹1470, the cost of 1 meter of cloth will be: $$ \text{Cost of 1 meter} = \frac{1470}{7} $$
Then, to find the cost of 5 meters of cloth, we'll multiply the cost of 1 meter by 5: $$ \text{Cost of 5 meters} = \text{Cost of 1 meter} \times 5 $$
Let's calculate this. The cost of 5 meters of cloth is ₹1050.
Ekta earns $₹ 3000$ in 10 days. How much will she earn in 30 days?
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Sign up nowIf it has rained $276 \mathrm{~mm}$ in the last 3 days, how many $\mathrm{cm}$ of rain will fall in one full week (7 days)? Assume that the rain continues to fall at the same rate.
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Sign up nowCost of $5 \mathrm{~kg}$ of wheat is ₹ 91.50 .
(a) What will be the cost of $8 \mathrm{~kg}$ of wheat?
(b) What quantity of wheat can be purchased in ₹ 183?
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Sign up nowThe temperature dropped 15 degree celsius in the last 30 days. If the rate of temperature drop remains the same, how many degrees will the temperature drop in the next ten days?
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Sign up nowShaina pays $₹ 15000$ as rent for 3 months. How much does she has to pay for a whole year, if the rent per month remains same?
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Sign up nowCost of 4 dozen bananas is ₹ 180 . How many bananas can be purchased for $₹ 90$ ?
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Sign up nowThe weight of 72 books is $9 \mathrm{~kg}$. What is the weight of 40 such books?
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Sign up nowA truck requires 108 litres of diesel for covering a distance of $594 \mathrm{~km}$. How much diesel will be required by the truck to cover a distance of $1650 \mathrm{~km}$ ?
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Sign up nowRaju purchases 10 pens for $₹ 150$ and Manish buys 7 pens for $₹ 84$. Can you say who got the pens cheaper?
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Sign up nowAnish made 42 runs in 6 overs and Anup made 63 runs in 7 overs. Who made more runs per over?
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Sign up nowExtra Questions - Ratio And Proportion | NCERT | Mathematics | Class 6
Are the ratios 2:5 and 10:15 equivalent?
To determine if the ratios $2:5$ and $10:15$ are equivalent, we compare the fractions $\frac{2}{5}$ and $\frac{10}{15}$.
Simplifying the second fraction, we find:
$$ \frac{10}{15} = \frac{2 \times 5}{3 \times 5} = \frac{2}{3} $$
Comparing $\frac{2}{5}$ and $\frac{2}{3}$, it's evident that they are not equal. Hence, the ratios 2:5 and 10:15 are not equivalent.
Suhas ate 5 fruits out of 11 fruits. This can be expressed as a
A. rate
B. ratio
C. fraction
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Sign up nowTwo numbers $A$ and $B$ are such that the sum of $8%$ of $A$ and $6%$ of $B$ is two-fifths of the sum of $10%$ of $A$ and $20%$ of $B$. Find the ratio of $A$ : $B$.
(A) $2:1$ (B) $1:2$ (C) $4:1$ (D) $1:4$
E None of These
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State whether the given statement is true or false. The interest on ₹350 at 5% per annum for 73 days is ₹35.
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Sign up nowWhat is the ratio $\frac{AC}{BC}$ for the following construction:
A line segment $AB$ is drawn. A single ray is extended from $A$ and divided into 12 equal arcs, cutting the ray at $A_{1}$, $A_{2}$, ..., $A_{12}$. A line is drawn from $A_{12}$ to $B$, and a line parallel to $A_{12}B$ is drawn, passing through the point $A_{6}$ and intersecting $AB$ at $C$.
(A) $1:2$ (B) $1:1$ (C) $2:1$ (D) $3:1$
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Sign up nowIf $x:y = 2:5$, then find $3x:5y$.
(A) $6:5$ (B) $6:25$ (C) $2:3$ (D) $12:20$
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Sign up nowSimplify the ratio:
$$ \frac{1}{5} : \frac{1}{20} : \frac{1}{35} $$
(A) $28 : 7 : 4$
(B) $4 : 28 : 7$
(C) $28 : 4 : 7$
(D) $7 : 4 : 28$
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