Ratios and Proportions Review Packet Exercises Answers Key
RATIO AND PROPORTION WORKSHEET WITH ANSWERS
Question : ane
The length and width of a rectangle is in the ratio iii : 5. If its perimeter is 48 cm, find its length and width.
Question : 2
If $1000 is divided amidst the three people in the ratio 2:3:v, find the share of each.
Question : 3
Detect the inverse ratio of 12 : 13.
Question : 4
If x : 2 and five : half dozen are inverse to each other, detect the value of "x"
Question : 5
Two numbers are in the ratio 2 : 3. If iv be subtracted from each, they are in the ratio 3 : 5. Observe the numbers.
Question : vi
Discover the compound ratio of two : 3, nine : 4 and 5 : 6.
Question : 7
Notice the ratio of 2 hours and 115 minutes.
Question : 8
Find the ratio of $2.viii and $1.4
Question : 9
Find the duplicate ratio of 5 : 6.
Question : x
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, nosotros have
length = 3x and width = 5x
Perimeter = 48
ii(l + due west) = 48
two(3x + 5x) = 48
8x = 24
x = 3
Therefore,
Length = three(iii) = 9 cm
Width = 5(3) = 15 cm
Question : ii
If $1000 is divided amid the three people in the ratio 2:three:five, observe the share of each.
Answer :
Share of the first person = 2x
Share of the 2nd person = 3x
Share of the tertiary person = 5x
Full Amount = $1000
That is, 2x + 3x + 5x = 1000
10x = 1000
ten = 100
Therefore,
Share of the showtime person = 2(100) = $200
Share of the 2nd person = 3(100) = $300
Share of the third person = 5(100) = $500
Question : iii
Find the changed ratio of 12 : thirteen.
Answer :
The inverse ratio of 12 : thirteen is 13 : 12
Question : 4
If ten : two and 5 : half-dozen are inverse to each other, find the value of "10"
Respond :
Considering the given two ratios are inverse to each other, the production of the 2 ratios is equal i.
(x : 2) ⋅ (5 : half-dozen) = 1
(x/ii) ⋅ (5/half dozen) = ane
5x / 12 = ane
ten = 12 / five
Question : 5
Two numbers are in the ratio ii : three. If 4 exist subtracted from each, they are in the ratio 3 : v. Discover the numbers.
Answer :
From the given ratio 2 : three, nosotros accept
first number = 2x
second number = 3x
From the data "If 4 be subtracted from each, they are in the ratio iii:5", we have
(2x-4) : (3x-four) = 3:5
Using cross product rule of proportion, we accept
5(2x-4) = three(3x-iv)
10x - twenty = 9x - 12
10 = eight
Therefore,
the showtime number = 2(8) = 16
the second number = 3(eight) = 24
Question : 6
Find the compound ratio of 2 : iii, ix : iv and 5 : 6.
Answer :
Compound ratio of two : 3, nine : 4 and 5 : 6 is
= (2 ⋅ nine ⋅ 5) : (3 ⋅ 4 ⋅ 6)
= 90 : 72
= 5 : 4
So, the compound ratio of 2 : 3, nine : 4 and v : 6 is v : four.
Question : 7
Find the ratio of 2 hours and 115 minutes.
Respond :
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.viii and $i.four
Answer :
$2.8 : $1.4 = (2.8 ⋅ 10) : (one.four ⋅ 10)
$2.8 : $ane.four = 28 : 14
$2.8 : $i.iv = two : ane
So, the ratio of $2.8 and $1.four is 2 : 1.
Question : 9
Observe the duplicate ratio of five : 6.
Respond :
Duplicate ratio of 5 : 6 is
= 5two : vi2
= 25 : 36
So, the duplicate ratio of 5 : vi is 25 : 36.
Question : 10
Find the triplicate ratio of 2 : three.
Answer :
Triplicate ratio of 2 : 3 is
= 23 : 3three
= eight : 27
So, the triplicate ratio of 2 : 3 is viii : 27.
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