2 Mark Question

Question 12 Marks

Express the following ratios in its simplest form:186 : 403

Answer

The given ratio is 186 : 403 $=\frac{186}{402}$
To express this ratio in the simplest form, we will have to find the H.C.F of 186 and 403, It is 31.
Dividing each term of the ratio by the H.C.F of its terms i.e. 31, we get 186 : 403 is 6 : 23.

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Question 22 Marks

Find the ratio of:25 paise to Rs. 60.

Answer

25 paise to Rs. 60 = 25 paise : Rs. 60
= 25 paise : 6000 paise
= 1 : 240
[$\because$ H.C.F = 25 paise]

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Question 32 Marks

Express the following ratios in its simplest form:85 : 391

Answer

To express this ratio in the simplest form we will have to find the H.C.F of 85 and 391, It is 17.
Dividing each term of the ratio by the H.C.F of its terms i.e. 17, we get
$\frac{85}{391}=\frac{85\div17}{391\div17}=\frac{\frac{85}{17}}{\frac{391}{17}}=\frac{5}{23}$
Hence, the simplest form of the ratio 85 : 391 is 5 : 23.

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Question 42 Marks

2 dozens of oranges cost Rs. 60. Find the cost of 120 similar oranges?

Answer

Cost of 2 dozens or 24 oranges = Rs. 60
Cost of 1 orange = Rs. 6024
Cost of 120 oranges = 6024 × 120 = Rs. 300

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Question 52 Marks

If 4, x, 9 are in continued proportion, find the value x.

Answer

$\Rightarrow\frac{4}{\text{x}}=\frac{\text{x}}{9}$
By cross multiplication we get,
$\Rightarrow4{9}=\text{x}^2$
$\Rightarrow\text{x}^2=36$
$\Rightarrow\text{x}=6$

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Question 62 Marks

Find x in the following proportions:
x : 6 = 55 : 11

Answer

x : 6 = 55 : 11$\Rightarrow\frac{\text{x}}{6}=\frac{55}{11}$
By cross multiplication we get,
$\Rightarrow\ 11\text{x}=6\times55$
$\Rightarrow\ 11\text{x}=330$
$\Rightarrow\ \text{x}=\frac{330}{11}$
$\Rightarrow\ \text{x}=30$

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Question 72 Marks

Find the ratio of:10 metres to 25cm.

Answer

10 metres to 25cm = 10 metres : 25cm= 1000cm : 25cm
= 40 : 1
[H.C.F = 25]

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Question 82 Marks

Which ratio is larger in the following pairs?
1 : 2 or 13 : 27

Answer

$1:2=\frac{1}{2}\ \text{and}\ 13:27=\frac{13}{27}$
Now, LCM of 2 and 27 is 54
$\frac{27}{54}\ \text{or}\ \frac{26}{54}$
$\therefore\frac{1}{2}>\frac{13}{27}$

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Question 92 Marks

Find x in the following proportions:
18 : x = 27 : 3

Answer

18 : x = 27 : 3
$\Rightarrow\frac{18}{\text{x}}=\frac{27}{3}$
$\Rightarrow\ 18\times3=\text{x}(27)$
$\Rightarrow\ 27\text{x}=54$
$\Rightarrow\ \text{x}=\frac{54}{27}$
$\Rightarrow\ \text{x}=2$

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Question 102 Marks

Find x in the following proportions:
16 : 18 = x : 96

Answer

16 : 18 = x : 96
$\Rightarrow\frac{16}{18}=\frac{\text{x}}{96}$
$\Rightarrow\frac{8}{9}=\frac{\text{x}}{96}$
By cross multiplication we get,
$\Rightarrow8(96)=9\text{x}$
$\Rightarrow\frac{778}{9}=\text{x}$
$\Rightarrow\text{x}=\frac{256}{3}$

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Question 112 Marks

A car travels 165km in 3 hours.
How long will it take to travel 440km?

Answer

A car travels 165km in 3 hours,
Speed of the car = Distance Time = 1653 = 55km/ h
Time taken by the car to travel 440km = 44055 = 8 hours.

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Question 122 Marks

Find which of the following are in proportion:
150, 250, 200, 300

Answer

We have,
$\frac{150}{250}=\frac{3}{5}\ \text{and}\ \frac{200}{300}=\frac{4}{6}=\frac{2}{3}$
$\therefore$ Hence, 150, 250 200, 300 are not in proportion.

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Question 132 Marks

Find which of the following are in proportion:
8, 16, 6, 12

Answer

We have,$\text{and}\ \frac{6}{12}=\frac{1}{2}$
$\therefore\frac{8}{16}=\frac{6}{12}$
Hence 8, 16, 6, 12 are in proportion.

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Question 142 Marks

Find the ratio of:10 litres to 0.25 litre.

Answer

10 litres to 0.25 litres = 10 : 0.25
= 40 : 1
[$\because$ H.C.F = 0.25]

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Question 152 Marks

Find the ratio of the following in the simplest form:2 metres to 35cm.

Answer

2 meters to 35cm = 2 met : 35cm
= 200cm : 35cm
[1m = 100cm]
= 40 : 7
[$\because$ dividing the first and second term by their H.C.F = 5].

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Question 162 Marks

Find which of the following are in proportion:
6, 2, 4, 3

Answer

We have,$\frac{6}{2}=\frac{3}{1}\ \text{and}\ \frac{4}{3}=\frac{4}{3}$
$\therefore\frac{3}{1}\neq\frac{4}{3}$
Hence, 6, 2, 4, 3 are not in proportion.

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Question 172 Marks

The weight of 45 folding chairs is 18kg. How many such chairs can be loaded on a truck having a capacity of carrying 4000kg load?

Answer

Number of folding chairs weighing 18kg = 45
Number of folding chairs weighing 1kg = 4518
Number of folding chairs weighing 4,000kg = 4518 × 4000 = 10000

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Question 182 Marks

Show that the following numbers are in continued proportion:48, 60, 75

Answer

48, 60, 75$\frac{48}{60}=\frac{60}{75}$
$\Rightarrow\frac{4}{5}=\frac{4}{5}$
$\therefore$ 48, 60, 75 are in continued proportion.

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Question 192 Marks

Find the ratio of the following in the simplest form:
48 min to 2 hours 40 min.

Answer

48 min to 2 hours 40 min = 48 min : 160 min
[$\because$ 1 hour = 60 min]
= 3 : 10
[$\because$ dividing the first and second term by their H.C.F = 3 : 10].

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Question 202 Marks

Find the ratio of the following in the simplest form:
75 paisa to Rs. 3.

Answer

75 paise to Rs 3 = 75 paise : Rs. 3
= 75 paise : 300 paise
= 1 : 4
$[\because\ \text{IRS}=100\ \text{paise}]$
[Dividing the first and second term by their H.C.F = 75].

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Question 212 Marks

Find the ratio of the following in the simplest form:
35 minutes to 45 seconds.

Answer

35 minutes to 45 seconds = 35 min : 45 sec
= 2100 sec : 45 sec
= 140 : 3 [H.C.F = 15].

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Question 222 Marks

Find the ratio of the following in the simplest form:
8kg to 400gm.

Answer

8kg to 400gm = 8kg : 400gm
= 8000gm : 400gm
= 20 : 1.
[Dividing the first and second terms by their H.C.F = 400].

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Question 232 Marks

Find the ratio of the following in the simplest form:
3m 5cm to 35cm.

Answer

3m 5cm to 35cm = 3m 5cm : 35cm
[$\because$ 1 hour = 100 min]
= 305cm : 35cm
[Dividing the first and second terms by their H.C.F = 5] = 61 : 7.

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Question 242 Marks

A rail journey of 75km costs Rs. 215. How much will a journey of 120km cost?

Answer

Cost of a rail journey of 75km = Rs. 215
Cost of a rail journey of 1km = Rs. 21575
Cost of a rail journey of 120km = 21575 × 120 = Rs. 344

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Question 252 Marks

Find the ratio of the following in the simplest form:48 minutes to 1 hour.

Answer

48 minutes to 1 hour = 48 min : 1 hour
= 48 min : 60 min
[$\because$ 1 hour = 60 min] = 4 : 5.
[Dividing the first and second term by their H.C.F = 12].

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Question 262 Marks

Express the following ratios in its simplest form:
60 : 72

Answer

To express this ratio in the simplest form, we will have to find the H.C.F of 60 and 72.
It is 12 dividing each term of the ration by the H.C.F of its terms i.e. 12 we get
$\frac{60}{12}=\frac{60\div12}{72\div12}=\frac{5}{6}\text{or}\ 5 : 6.$
Hence, the simplest form of the ratio 60 : 72 is 5 : 6.

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Question 272 Marks

The cost of 17 chairs is Rs. 19210. Find the number of such chairs that can be purchased in Rs. 113000?

Answer

Number of chairs purchased in Rs. 19,210 = 17
Number of chairs purchased in Rs. 1 = 1719210
Number of chairs purchased in Rs. 1,13,000 = 1719210 × 113000 = 100

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Question 282 Marks

Find the ratio of the following in the simplest form:
2 dozen to 3 scores.

Answer

2 dozen to 3 scores = 2 dozen : 3 scores
= 24 : 60
[$\because$ 1 dozen = 12 score = 20] = 2 : 5.
[Dividing the first and second term by their H.C.F = 12].

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Question 292 Marks

Express the following ratios in its simplest form:324 : 144

Answer

To express this ratio in the simplest form, we will have to find the H.C.F of $\frac{324}{144},$ It is 36. Dividing each term of the ration by the H.C.F of its terms i.e. 36, we get
$\frac{324}{144}=\frac{324\div36}{144\div36}=\frac{9}{4}.$
Hence, the simplest form of the ratio 324 : 144 is 9 : 4.

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Question 302 Marks

Find the ratio of the following in the simplest form:
35 minutes to 45 minutes.

Answer

35 minutes to 45 minutes
= 35 min : 45 min
= 7 : 9 [diving the first-and second term by their H.C.F = 5].

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Question 312 Marks

If the sales tax on a purchase worth Rs. 60 is Rs. 4.20. What will be the sales tax on the purchase worth Rs. 150?

Answer

Sales tax on a purchase worth Rs. 60 = Rs. 4.20
Sales tax on a purchase worth Rs. 1 = Rs. 4.2060
Sales tax on a purchase worth Rs. 150 = 4.2060 × 150 = 42060 × 100 × 150 = Rs. 10.50

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Question 322 Marks

A family of 4 members consumes 6kg of sugar in a month. What will be the monthly consumption of sugar, if the number of family members becomes 6?

Answer

Amount of sugar consumed by a family of 4 members = 6kg.

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Question 332 Marks

Find x in the following proportions:7 : 14 = 15 : x

Answer

7 : 14 = 15 : x$\frac{7}{14}=\frac{15}{\text{x}}$
$\Rightarrow\ 7\text{x}=14(15)$
$\Rightarrow\ 7\text{x}=210$
$\Rightarrow\ \text{x}=\frac{210}{7}$
$\Rightarrow\ \text{x}=30$

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Question 342 Marks

Give two equivalent ratios of 6 : 8.

Answer

i.e. have,
$\frac{6}{8}=\frac{6\div2}{8\div2}=\frac{3}{4}$
$\therefore$ 3 : 4 is an equivalent ratio of 6 : 15
$\text{Also},\ \frac{6}{8}=\frac{6\times2}{8\times2}=\frac{12}{16}$
So, 12 : 16 is an equivalent ratios of 6 : 8.
Hence, 3 : 4 and 12 : 16 are equivalent ratios of 6 : 8.

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Question 352 Marks

Set up all proportions from the numbers 9, 150, 105, 1750.

Answer

All proportions are:9 : 150 = 3 : 50
9 : 105 = 3 : 35
9 : 1750
150 : 105 = 10 : 7
150 : 1750 = 3 : 35
105 : 1750 = 3 : 50
Thus, all proportions that can be formed are:
3 : 50, 3 : 35, 10 : 7, 9 : 1750, 1750 : 9, 7 : 10, 35 : 3 and 50 : 3

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Question 362 Marks

Find the ratio of the following in the simplest form:
3 weeks to 3 days.

Answer

3 weeks to 3 days = 3 weeks : 3 days
= 21 day : 3days
[1 week = 7 days]
= 3 × 7 = 3
= 7 : 1.

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Question 372 Marks

A car travels 165km in 3 hours.
How far will it travel in 7 hours?

Answer

A car travels 165km in 3 hours,
Speed of the car = Distance Time = 1653 = 55km/ h
Distance travel by the car in 7 hours = 55 × 7 = 385km.

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Question 382 Marks