**Question : 1 **

The length and width of a rectangle is in the ratio 3 : 5. If its perimeter is 48 cm, find its length and width.

**Question : 2 **

If $1000 is divided among the three people in the ratio 2:3:5, find the share of each.

**Question : 3 **

Find the inverse ratio of 12 : 13.

**Question : 4 **

If x : 2 and 5 : 6 are inverse to each other, find the value of "x"

**Question : 5 **

Two numbers are in the ratio 2 : 3. If 4 be subtracted from each, they are in the ratio 3 : 5. Find the numbers.

**Question : 6 **

Find the compound ratio of 2 : 3, 9 : 4 and 5 : 6.

**Question : 7 **

Find the ratio of 2 hours and 115 minutes.

**Question : 8 **

Find the ratio of $2.8 and $1.4

**Question : 9 **

Find the duplicate ratio of 5 : 6.

**Question : 10 **

Find the triplicate ratio of 2 : 3.

**Question : 1 **

The length and width of a rectangle is in the ratio 3 : 5. If its perimeter is 48 cm, find its length and width.

**Answer :**

From the given ratio, we have

length = 3x and width = 5x

Perimeter = 48

2(l + w) = 48

2(3x + 5x) = 48

8x = 24

x = 3

Therefore,

Length = 3(3) = 9 cm

Width = 5(3) = 15 cm

**Question : 2 **

If $1000 is divided among the three people in the ratio 2:3:5, find the share of each.

**Answer :**

Share of the first person = 2x

Share of the second person = 3x

Share of the third person = 5x

Total Amount = $1000

That is, 2x + 3x + 5x = 1000

10x = 1000

x = 100

Therefore,

Share of the first person = 2(100) = $200

Share of the second person = 3(100) = $300

Share of the third person = 5(100) = $500

**Question : 3 **

Find the inverse ratio of 12 : 13.

**Answer :**

The inverse ratio of 12 : 13 is 13 : 12

**Question : 4 **

If x : 2 and 5 : 6 are inverse to each other, find the value of "x"

**Answer :**

Because the given two ratios are inverse to each other, the product of the two ratios is equal 1.

(x : 2) ⋅ (5 : 6) = 1

(x/2) ⋅ (5/6) = 1

5x / 12 = 1

x = 12 / 5

**Question : 5 **

Two numbers are in the ratio 2 : 3. If 4 be subtracted from each, they are in the ratio 3 : 5. Find the numbers.

**Answer :**

From the given ratio 2 : 3, we have

first number = 2x

second number = 3x

From the information "If 4 be subtracted from each, they are in the ratio 3:5", we have

(2x-4) : (3x-4) = 3:5

Using cross product rule of proportion, we have

5(2x-4) = 3(3x-4)

10x - 20 = 9x - 12

x = 8

Therefore,

the first number = 2(8) = 16

the second number = 3(8) = 24

**Question : 6 **

Find the compound ratio of 2 : 3, 9 : 4 and 5 : 6.

**Answer :**

Compound ratio of 2 : 3, 9 : 4 and 5 : 6 is

= (2 ⋅ 9 ⋅ 5) : (3 ⋅ 4 ⋅ 6)

= 90 : 72

= 5 : 4

So, the compound ratio of 2 : 3, 9 : 4 and 5 : 6 is 5 : 4.

**Question : 7 **

Find the ratio of 2 hours and 115 minutes.

**Answer :**

2 hours = 2 ⋅ 60 = 120 minutes

2 hrs : 115 min = 120 min : 115 min

2 hrs : 115 min = 24 : 23

So, the ratio of 2 hours and 115 minutes is 24 : 23.

**Question : 8 **

Find the ratio of $2.8 and $1.4

**Answer :**

$2.8 : $1.4 = (2.8 ⋅ 10) : (1.4 ⋅ 10)

$2.8 : $1.4 = 28 : 14

$2.8 : $1.4 = 2 : 1

So, the ratio of $2.8 and $1.4 is 2 : 1.

**Question : 9 **

Find the duplicate ratio of 5 : 6.

**Answer :**

Duplicate ratio of 5 : 6 is

= 5^{2} : 6^{2}

= 25 : 36

So, the duplicate ratio of 5 : 6 is 25 : 36.

**Question : 10 **

Find the triplicate ratio of 2 : 3.

**Answer :**

Triplicate ratio of 2 : 3 is

= 2^{3} : 3^{3}

**=** 8 : 27

So, the triplicate ratio of 2 : 3 is 8 : 27.

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