Ratio and Proportion Test

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Ratio and Proportion Test - 19

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Weekly Quiz Competition

Question 1
1 / -0

Sides of two similar triangles are in the ratio $$4:9$$.Area of these triangles are in the ratio

A
$$2:3$$

B
$$4:9$$

C
$$81:16$$

D
$$16:81$$

Solution

Given:Ratio of sides of similar triangles$$=\dfrac{4}{9}$$

We know that if two triangles are similar,

ratio of areas is equal to the ratio of squares of corresponding sides.

So, $$\dfrac{area \,\, of\,\, triangle\,\, 1}{area \,\, of\,\, triangle\,\, 2}=\dfrac{{\left(side\,\, of\,\, triangle\,\, 1\right)}^{2}}{{\left(side\,\, of\,\, triangle\,\, 2\right)}^{2}}$$

$$\dfrac{area \,\, of\,\, triangle\,\, 1}{area \,\, of\,\, triangle\,\, 2}={\left(\dfrac{4}{9}\right)}^{2}=\dfrac{16}{81}$$

$$\dfrac{area \,\, of\,\, triangle\,\, 1}{area \,\, of\,\, triangle\,\, 2}=\dfrac{16}{81}$$
Question 2
1 / -0

The food stocks in a hostel are sufficient for 1200 students for 20 days . If 400 more students joined the hostel , the stocks just for ... days .

A
12

B
15

C
18

D
21

Solution

Let food stock is sufficient for $$x$$ days.
Given,
$$M_{1}=1200$$
$$D_{1}=20$$
$$M_{2}=1200+400=1600$$
$$D_{2}=x$$
Then, using $$M_{1}D_{1}=M_{2}D_{2}$$
$$1200\times 20 = 1600\times x$$
$$x=\dfrac{1200\times 20}{1600}$$
$$x=15$$
Therefore, now the food stock is sufficient for $$15$$ days.
Question 3
1 / -0

The ratio of 8 books to 12 books is ?

A
$$2:3$$

B
$$5:2$$

C
$$4:5$$

D
$$5: 4$$

Solution

The ratio of 8 book to 12 book is=$$\dfrac{8}{12}=\dfrac{2}{3}=2:3$$
Question 4
1 / -0

If A, B, C divide Rs. 1200 in the ratio 2 : 3 : 5, then B's share is

A
Rs. 240

B
Rs. 600

C
Rs. 380

D
Rs. 360

Solution

Given that,
Total money =$$ Rs. 1200$$
$$A: B: C = 2:3:5$$
B's share = $$\cfrac{3}{(2 + 3 + 5)} \times 1200 = 360$$
Question 5
1 / -0

Mark the correct alternative of the following.
A ratio equivalent to $$2:3$$ is

A
$$4 : 3$$

B
$$2 : 6$$

C
$$6 : 9$$

D
$$10 : 9$$

Solution

Given the ratio is $$2:3$$.
Now,
$$\dfrac{6}{9}$$
$$=\dfrac{2\times 3}{3\times 3}$$
$$=\dfrac{2}{3}$$.
So the equivalent ratio is $$6:9$$.
Question 6
1 / -0

The ratio $$384 : 480$$ in its simplest form is

A
$$3 : 5$$

B
$$5 : 4$$

C
$$4 : 5$$

D
$$2 : 5$$

Solution

Given the ratio is
$$384:480$$
$$=96\times 4: 96\times 5$$
$$=4:5$$.
Question 7
1 / -0

If Rs. $$840$$ is divided between $$P$$ and $$Q$$ in the ratio $$3:4$$, then P's share is

A
Rs. $$340$$

B
Rs. $$480$$

C
Rs. $$360$$

D
Rs. $$400$$

Solution

Given $$P:Q=3:4$$
Sum of ratio terms $$=3+4=7$$
$$\therefore P's$$ share $$=\dfrac{3}{7}\times 840$$
$$=360$$
Hence, option (C) is the correct answer
Question 8
1 / -0

A ratio equivalent to $$2:5$$ is

A
$$6:15$$

B
$$4:5$$

C
$$5:2$$

D
$$5:4$$

Solution

The simplest form of ratio $$6 : 15 =2\times 3:5\times 3= 2 : 5$$

So, $$2 : 5$$ is equivalent to $$6 : 15$$
Question 9
1 / -0

Mark the correct answer in the following:
Choose the correct statement:

A
$$(5:8) > (3:4)$$

B
$$(5:8) < (3:4)$$

C
two ratios cannot be compared

D
None of the above

Solution

We know that
$$5:8=5/8$$ and
$$3:4=3/4$$

To compare the ratios, we make their denominator same.
$$\therefore 5:8=\dfrac 58$$
And, $$3:4=\dfrac34=\dfrac68 $$ [Multiplying both numerator and denominator by $$2$$]

Since, $$5<6$$
$$\Rightarrow \dfrac58<\dfrac68$$
$$\therefore (5:8) < (3:4)$$

Hence, Option (B) is the correct answer.
Question 10
1 / -0

The ratio of $$20$$ minutes to $$1$$ hour is

A
$$20:1$$

B
$$1:3$$

C
$$1:4$$

D
$$2:5$$

Solution

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Re-Attempt Weekly Quiz Competition

Ratio and Proportion Test - 19

Result

Ratio and Proportion Test - 19

Score

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Rank

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SHARING IS CARING

Question 1

$$2:3$$

$$4:9$$

$$81:16$$

$$16:81$$

Solution

Question 2

12

15

18

21

Solution

Question 3

$$2:3$$

$$5:2$$

$$4:5$$

$$5: 4$$

Solution

Question 4

Rs. 240

Rs. 600

Rs. 380

Rs. 360

Solution

Question 5

$$4 : 3$$

$$2 : 6$$

$$6 : 9$$

$$10 : 9$$

Solution

Question 6

$$3 : 5$$

$$5 : 4$$

$$4 : 5$$

$$2 : 5$$

Solution

Question 7

Rs. $$340$$

Rs. $$480$$

Rs. $$360$$

Rs. $$400$$

Solution

Question 8

$$6:15$$

$$4:5$$

$$5:2$$

$$5:4$$

Solution

Question 9

$$(5:8) > (3:4)$$

$$(5:8) < (3:4)$$

two ratios cannot be compared

None of the above

Solution

Question 10

$$20:1$$

$$1:3$$

$$1:4$$

$$2:5$$

Solution

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