3 marks

Question 13 Marks

Team A wins 26 matches out of 52 matches. Team B wins three-fourth of 52 matches played. Which team has a better winning record?

Answer

Matches won by Team $A=26$ out of 52
Matches won by team $B=\frac{3}{4} \times 52=39$ out of 52
$\therefore$ Team B won 39 out of 52 and therefore team B has the better record.

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Question 23 Marks

Thirumagal's mother wears a bracelet made of 35 red beads and 30 blue beads. Thirumagal wants to make smaller bracelets using the same two coloured beads in the same ratio. In how many different ways can she make the bracelets?

Answer

Red : blue = 35 : 30 = 7 : 6Different ways(i) 7 : 6(ii) 14 : 12(iii) 21 : 18(iv) 28 : 24

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Question 33 Marks

Antony brushes his teeth in the morning and night on all days in a week. Shabeen brushes her teeth only in the morning. What is the ratio of the number of times they brush their teeth in a week?

Answer

Number of times Antony brushes a day = 2
Number of times Antony brushes a week = 2 × 7 = 14
Number of times Shabeen brushes a day = 1
Number of times Shabeen brushes a week = 1 × 7 = 7
Number of times Antony brushes : Number of times Shabeen brushes
= 14 : 7
= 2 : 1
The required ratio = 2 : 1

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Question 43 Marks

The ingredients required for the preparation of Ragi Kali, a healthy dish of Tamilnadu is given below.

Ingredients	Quantity
Ragi flour	4 cups
Raw rice broken	1 cup
Water	8 cups
Sesame oil	15 ml
Salt	10 mg

(a) If one cup of ragi flour is used then, what would be the amount of raw rice required?
(b) If 16 cups of water is used, then how much of ragi flour should be used?
(c) Which of these ingredients cannot be expressed as a ratio? Why?

Answer

(a) $\frac{1}{4}$ cups
(b) 8 cups
(c) Ragi flour, Raw rice and water are in one unit.Sesame oil and salt are in different units.These different units cannot be compared and cannot be expressed as a ratio because the two quantities of a ratio should be in the same unit.

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Question 53 Marks

A gets double of what B gets and B gets double of what C gets. Find A : B and B : C and verify whether the result is in proportion or not

Answer

Let x be the part owned by C thenA : B : C = 2(2x) : 2x : x = 4x : 2x : xA : B = 4x : 2x = 2 : 1B : C = 2x : x = 2 : 1A : B : : B : Ci.e, They are in proportion.

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Question 63 Marks

I have a box which has 3 green, 9 blue, 4 yellow, 8 orange coloured cubes in it.
(a) What is the ratio of orange to yellow cubes?
(b) What is the ratio of green to blue cubes?
(c) How many different ratios can be formed, when you compare each colour to anyone of the other colours?

Answer

(i) orange : Yellow = 8 : 4 = 2 : 1
(ii) green : blue = 3 : 9 = 1 : 3
(iii) green : orange = 3 : 8
orange : green = 8 : 3
blue : orange = 9 : 8
orange : blue = 8 : 9
green : yellow = 3 : 4
yellow : green = 4 : 3
blue : yellow = 9 : 4
yellow : blue = 4 : 9
green : blue = 3 : 9 = 1 : 3
blue : green = 9 : 3 = 3 : 1
yellow : orange = 4 : 8 = 1 : 2
orange : yellow = 8 : 4 = 2 : 1

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Question 73 Marks

A particular high school has 1500 students 50 teachers and 5 administrators. If the school grows to 1800 students and the ratios are maintained, then find the number of teachers and administrators

Answer

Administrators : teachers : students
$=5: 50: 1500$
$=1: 10: 300$If the school grows to 1800 students then 10 parts = teachers
1 part $=$ administrators
300 parts $=1800$
1 part $=\frac{1800}{300}=6$
10 parts $=6 \times 10=60$So, if the school grows to 1800 students the new ratio is
administrators : teachers : students
$6: 60: 1800$

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Question 83 Marks

The maximum speed of some of the animals are given below:
the Elephant $= 20$ km/h;
the Lion $= 80$ km/h;
the Cheetah $= 100$ km/h
Find the following ratios of their speeds in simplified form and find which ratio is the least?
(i) the Elephant and the Lion
(ii) the Lion and the Cheetah
(iii) the Elephant and the Cheetah

Answer

$ \text { (i) the Elephant: the Lion }$
$=20: 80$
$=\frac{20}{80}$
$=\frac{1}{4}$
$=1: 4$
$\text { (ii) the Lion : the Cheetah }$
$=80: 100$
$=\frac{80}{100}$
$=\frac{4}{5}$
$=4: 5$
$\text { (iii) the Elephant: the Cheetah }$
$=20: 100$
$=\frac{20}{100}$
$=\frac{1}{5}$
$=1: 5$
$\text { The ratio of Elephant to Cheetah is the least. }$

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Question 93 Marks

From your school diary, write the ratio of the number of holidays to the number of working days in the current academic year

Answer

Number of holidays $=145$Number of working days $=220$Holidays $:$ working days $=145: 220$
$ =\frac{145}{220}$
$=\frac{29}{44}$
$=29: 44 $

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Question 103 Marks

\text { Fill the boxes using any set of suitable numbers } 6: \square:: \square: 15

Answer

Product of extremes = 6 × 15 = 90Product of means = 90 = 1 × 90The required sets are 1 and 90, 2 and 45, 3 and 30, 5 and 18, 6 and 15, 9 and 10= 1 × 90= 2 × 45= 3 × 30= 5 × 18= 6 × 15= 9 × 10

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Question 113 Marks

Cholan walks 6 km in 1 hour at constant speed. Find the distance covered by him in 20 minutes at the same speed

Answer

Distance covered in 1 hour i.e 60 minutes $=6 km$Distance covered in 1 minutes $=\frac{6}{60} km$
Distance covered in 20 minutes $=\frac{6}{60} \times 20=2 km$Cholan cover $2 km$ in 20 minutes.

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Question 123 Marks

The America’s famous Golden Gate bridge is 6480 ft long with 756 ft tall towers. A model of this bridge exhibited in a fair is 60 ft long with 7 ft tall towers. Is the model, in proportion to the original bridge?

Answer

6480 : 756, 60 : 7Product of the means = 756 × 60= 45360Product of the extremes = 6480 × 7= 45360ad = bc∴ They are in proportion

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Question 133 Marks

Write the mean and extreme terms in the following ratios and check whether they are in proportion.
78 litre is to 130 litre and 12 bottles is to 20 bottles

Answer

78 : 130, 12 : 20Product of the means = 78 × 20= 1560Product of the extremes = 130 × 12= 1560a × d = b × c∴ They are in proportion

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Question 143 Marks

Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees

Answer

400 : 50, 25 : 625Product of the extremes = 400 × 625= 250000Product of the means = 50 × 25 = 1250a × d ≠ b × c∴ They are not in proportion

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Question 153 Marks

You purchase 6 apples for ₹ 90 and your friend purchases 5 apples for ₹ 70. Whose purchase is better?

Answer

MyselfCost of 6 apples $=₹ 90$Cost of 1 apple $=\frac{90}{6}=₹ 15$Friend's purchaseCost of 5 apples $=₹ 70$Cost of 1 apple $=\frac{70}{5}=₹ 14$
$\therefore$ Friend's purchase is better than myself..

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Question 163 Marks

A line segment 63 cm long is to be divided into two parts in the ratio 3 : 4. Find the length of each part.

Answer

Total length $63 cm$, on dividing $3+4=7$ equal parts, we get the line segments with lengths $\frac{3}{7} \times 63=27 cm$ $\frac{4}{7} \times 63=36 cm$Length of each line segment is $27 cm$ and $36 cm$

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Question 173 Marks

Divide the numbers given below in the required ratio.
20 in the ratio 3 : 2

Answer

20 in the ratio $3: 2$.Dividing 20 into $3+2=5$ equal parts, then $20 \times \frac{3}{5}=12,20 \times \frac{2}{5}=8$The required answer is 12,8

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Question 183 Marks

Divide the numbers given below in the required ratio.
27 in the ratio 4 : 5

Answer

27 in the ratio $4: 5$Dividing 27 into $4+5=9$ equal parts, and $27 \times \frac{4}{9}=12,27 \times \frac{5}{9}=15$The numbers are 12,15

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Question 193 Marks

Divide the numbers given below in the required ratio.
40 in the ratio 6 : 14

Answer

40 in the ratio $6: 14$Dividing 40 into $6+14=20$ equal parts and $40 \times \frac{6}{20}=12,40 \times \frac{14}{20}=28$The numbers are 12, 28 .

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Question 203 Marks

Identify of the two ratios is larger?
$4 : 5$ or $8 : 15$

Answer

$ 4: 5 \text { or } 8: 15$
$4: 5=\frac{4}{5}$
$8: 15=\frac{8}{15}$
$\frac{4 \times 15}{5 \times 15}=\frac{60}{75}$
$\frac{8 \times 5}{15 \times 5}=\frac{40}{75}$
$\frac{60}{75}>\frac{40}{75}$
$\frac{4}{7}>\frac{8}{15}$
$4: 5>8: 15 $

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Question 213 Marks

Identify of the two ratios is larger?
$3 : 4$ or $7 : 8$

Answer

$ 3: 4 \text { or } 7: 8$
$3: 4=\frac{3}{4}$
$7: 8=\frac{7}{8}$
$\frac{3 \times 8}{4 \times 8}=\frac{24}{32}$
$\frac{7 \times 4}{8 \times 4}=\frac{28}{32}$
$\frac{28}{32}>\frac{24}{32}$
$\frac{7}{8}>\frac{3}{4}$
$7: 8>3: 4 $

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Question 223 Marks

Identify of the two ratios is larger?
$1 : 2$ or $2 : 1$

Answer

$1: 2 \text { or } 2: 1$
$1: 2=\frac{1}{2}$
$2: 1=\frac{2}{1}$
$=2$
$\frac{2}{1}>\frac{1}{2}$
$2: 1>1: 2$

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Question 233 Marks

Give two equivalent ratios of the following.
$3 : 2$

Answer

$3: 2$
$ \frac{3}{2}=\frac{3 \times 2}{2 \times 2}=\frac{3 \times 3}{2 \times 3}$
$\frac{3}{2}=\frac{6}{4}=\frac{9}{6} $
$3: 2=6: 4=9: 6$

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Question 243 Marks

Give two equivalent ratios of the following.
$1 : 6$

Answer

$1: 6$
$ \frac{1}{6}=\frac{1 \times 2}{6 \times 2}=\frac{1 \times 3}{6 \times 3}$
$\frac{1}{6}=\frac{2}{12}=\frac{3}{18}$
$1: 6=2: 12=3: 18 $

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Question 253 Marks

Give two equivalent ratios of the following.
$5 : 4$

Answer

$5: 4$
$ \frac{5}{4}=\frac{5 \times 2}{4 \times 2}=\frac{5 \times 3}{4 \times 3}$
$\frac{5}{4}=\frac{10}{8}=\frac{15}{12} $
$5: 4=10: 8=15: 12$

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Question 263 Marks

Complete the table.

Days	28	21	?	63
Weeks	4	3	2	?

Answer

1 week = 7 days2 weeks = 2 × 7 days = 14 days63 days = 9 × 7 days = 9 weeks

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Question 273 Marks

Out of $50$ students in a class, $30$ are boys. Find the ratio of number of boys to the number of girls

Answer

Total no of students $=50$No of boys $=30$No of girls $=50-30=20$Ratio of boys to girls $=30: 20$
$ =\frac{30}{20}$
$=\frac{3}{2}$
$=3: 2 $

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Question 283 Marks

Out of $50$ students in a class, $30$ are boys. Find the ratio of number of girls to the total number of students

Answer

Total no of students $=50$No of boys $=30$No of girls $=50-30=20$ Ratio of girls to the total number of students $=20: 50$
$ =\frac{20}{50}$
$=\frac{2}{5}$
$=2: 5 $

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Question 293 Marks

Out of $50$ students in a class, $30$ are boys. Find the ratio of number of boys to the total number of students

Answer

Total no of students $=50$No of boys $=30$No of girls $=50-30=20$Ratio of boys to the total no of students $=30: 50$
$ =\frac{30}{50}$
$=\frac{3}{5}$
$=3: 5 $

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Question 303 Marks

The cost of parking a bicycle is ₹ $5$ and the cost of parking a scooter is ₹ $15.$ Find the simplest ratio of the parking cost of a bicycle to that of a scooter

Answer

$\text { Ratio of the parking cost of a bicycle to that of a scooter }=$
$₹ 5: ₹ 15$
$=\frac{5}{15}$
$=\frac{1}{3}$
$=1: 3 $

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