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.
1. Answer :
From the given ratio, we have
length = 3x
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
2. Answer :
Share of the first person = 2x
Share of the second person = 3x
Share of the third person = 5x
Total Amount = $1000
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
3. Answer :
The inverse ratio of 12 : 13 is 13 : 12.
4. 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
5. 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
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.
7. 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.
8. 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.
9. Answer :
Duplicate ratio of 5 : 6 is
= 5^{2} : 6^{2}
= 25 : 36
So, the duplicate ratio of 5 : 6 is 25 : 36.
10. 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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