RATIO AND PROPORTION WORKSHEET WITH ANSWERS

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. 

Detailed Answer Key

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 

=  5² : 6²

=  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

=  2³ : 3³

=  8 : 27

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

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