Ratio and Proportion Test

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Ratio and Proportion Test - 15

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Question 1
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In an office, the working hours are $$10:30\text{ AM}$$ to $$5:30\text{ PM}$$ and in between $$30\text{ min.}$$ are spent on lunch. Find the ratio of office hours to the time spent for lunch.

A
$$7:30$$

B
$$1:14$$

C
$$14:1$$

D
$$30:7$$

Solution

Office hours are from $$10:30\text{ AM}$$ to $$5:30\text{ PM}$$ i.e. $$7\text{ hrs}$$ that is equal to $$420 \text{ min.}$$

And, the lunch time is equal to $$30\text{ min.}$$
So, the required ratio will be,
$$\Rightarrow 420:30$$
$$\Rightarrow 14:1$$
Question 2
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Arrange the following ratios in decreasing order.
$$2:3,\,3:4,\,5:6\ and $$ $$1:5$$

A
$$2:3>3:4>5:6>1:5$$

B
$$3:4>5:6>2:3>1:5$$

C
$$1:5>2:3>3:4>5:6$$

D
$$5:6>3:4>2:3>1:5$$

Solution

Given ratios are $$\dfrac{2}{3},\,\dfrac{3}{4},\,\dfrac{5}{6},\,\dfrac{1}{5}$$

The L.C.M of $$3,\,4,\,6,\,5$$ is $$2\times2\times3\times5=60$$

Now, $$\dfrac{2}{3}=\dfrac{2\times20}{3\times20}=\dfrac{40}{60}$$

$$\dfrac{3}{4}=\dfrac{3\times15}{4\times15}=\dfrac{45}{60}$$

$$\dfrac{5}{6}=\dfrac{5\times10}{6\times10}=\dfrac{50}{60}$$

$$\dfrac{1}{5}=\dfrac{1\times12}{5\times12}=\dfrac{12}{60}$$

Clearly, $$50/60 > 45/60 > 40/60 > 12/60$$

Therefore, $$\dfrac{5}{6} > \dfrac{3}{4} > \dfrac{2}{3} > \dfrac{1}{5}$$
So, $$5:6 > 3:4 > 2:3 > 1:5$$
Question 3
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If, $$13$$ is the antecedent and $$12$$ is the consequent, then the ratio is ........

A
$$13 : 12$$

B
$$12 : 13$$

C
$$1 : 3$$

D
$$3 : 2$$

Solution

In a ratio, the first term is called the antecedent and the second term is called the consequent. Therefore, the required ratio having $$13$$ as the antecedent and $$12$$ as the consequent is $$13 : 12$$.
Question 4
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In a ratio $$b : a$$, $$a$$ is called ______

A
Antecedent

B
Consequent

C
Constant

D
None of the above

Solution

In a ratio, the second term is called consequent. Thus, in $$b:a$$, $$a$$ is called the consequent.
$$b:a\longrightarrow \\ \downarrow $$ Consequent
Antecedent
Question 5
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The ratio of heights of two people A and B whose height are $$6 ft$$ and $$4 ft$$ is $$6 : 4$$. Here, $$6$$ is called ______

A
Constant

B
Consequent

C
Antecedent

D
None of these

Solution

In a ratio, the first term is called the antecedent. Therefore, in $$6 : 4$$, $$6$$ is called the antecedent.
Question 6
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In a ratio $$3:4$$, if the antecedent is $$12$$, then the consequent is

A
$$9$$

B
$$16$$

C
$$20$$

D
$$24$$

Solution

$$\dfrac{3}{4}=\dfrac{12}{x}\;$$
$$\Rightarrow\;3x=48$$
$$x=16$$
Question 7
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If $$7$$ is the consequent and $$15$$ is the antecedent of a ratio, then the ratio is ____

A
$$7 : 15$$

B
$$15 : 7$$

C
$$7 : 5$$

D
$$5 : 7$$

Solution

In a ratio, the first term is called the antecedent and the second term is called the consequent. Therefore, the given ratio is $$15 : 7$$.
Question 8
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In $$4 : 9$$, _________ is the antecedent

A
$$1$$

B
$$4$$

C
$$9$$

D
$$4$$ and $$9$$

Solution

$$\dfrac { a }{ b } =a:b\\ a\rightarrow Antecedent\\ b\rightarrow Consequent\\ 4:9\\ $$
$$4$$ is the Antecedent
Question 9
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Who ran at faster pace?
Misha ran $$9$$ laps in $$15$$ minutes and Myra ran $$12$$ laps in $$25$$ minutes.

A
Misha ran faster than Myra

B
Myra ran faster than Misha

C
Both ran at equal pace

D
Cannot be determined

Solution

Misha: $$ \dfrac {9}{15} \times \dfrac {5}{5} = \dfrac {45}{75}$$

Myra: $$ \dfrac {12}{25} \times \dfrac {3}{3} = \dfrac {36}{75}$$

$$\therefore$$ Misha ran faster as $$\dfrac {45}{74} > \dfrac {36}{75}$$.
Question 10
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The antecedent is _____, for a ratio of $$12\ m$$ and $$120\ cm$$

A
$$12$$

B
$$120$$

C
$$1,200$$

D
$$10$$

Solution

The ratio of two different quantities is not defined. Therefore, $$12\ m = 1200\ cm$$.
Thus, the required ratio is $$1200 : 120$$.
$$\Rightarrow 1200 : 120 = 10 : 1$$.
The antecedent of the given ratio is $$10$$.

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Ratio and Proportion Test - 15

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Ratio and Proportion Test - 15

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Question 1

$$7:30$$

$$1:14$$

$$14:1$$

$$30:7$$

Solution

Question 2

$$2:3>3:4>5:6>1:5$$

$$3:4>5:6>2:3>1:5$$

$$1:5>2:3>3:4>5:6$$

$$5:6>3:4>2:3>1:5$$

Solution

Question 3

$$13 : 12$$

$$12 : 13$$

$$1 : 3$$

$$3 : 2$$

Solution

Question 4

Antecedent

Consequent

Constant

None of the above

Solution

In a ratio, the second term is called consequent. Thus, in $$b:a$$, $$a$$ is called the consequent.

Question 5

Constant

Consequent

Antecedent

None of these

Solution

Question 6

$$9$$

$$16$$

$$20$$

$$24$$

Solution

Question 7

$$7 : 15$$

$$15 : 7$$

$$7 : 5$$

$$5 : 7$$

Solution

Question 8

$$1$$

$$4$$

$$9$$

$$4$$ and $$9$$

Solution

Question 9

Misha ran faster than Myra

Myra ran faster than Misha

Both ran at equal pace

Cannot be determined

Solution

Question 10

$$12$$

$$120$$

$$1,200$$

$$10$$

Solution

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