The numbers 8, x, 9 and 36 are in proportion. Find x.
Ifx:15=8:12;findthevalueofx.
If 4, x, 32 and 40 are in proportion, find the value of x.
If x: y = 4: 5 and y: z = 6: 7; find x : y : z.
The length and breadth of a rectangle are in the ratio 5: 4. If its length is 80
cm, find the breadth.
Check whether the two ratios form a proportion or not:
(i) 6: 8 and 12: 16; (ii) 24: 28 and 36: 48
The first, third and fourth terms of a proportion are 12, 8 and 14
respectively. Find the second term.
If 4, x, 9 are in continued proportion, find the value x.
The ratio of the length of a school ground to its width is 5: 2. Find its length if
the width is 40 metres.
Express each of the following ratios in its simplest form:
(i) 60: 72
(ii) 324: 144
Find the ratio of the following in the simplest form:
(i) 75 paise to Rs 3
(ii) 35 minutes to 45 minutes
(iii) 8 kg to 400 gm
(iv) 48 minutes to 1 hour
Margarette works in a factory and earns Rs 955 per month. She saves Rs 185 per month from her earnings. Find the ratio of:
(i) her savings to her income
(ii) her income to her expenditure (iii) her savings to her expenditur
Answers
Answer:
8, x, 9 and 36 are in proportion
x = 32
x:15 = 8:12
x = 10
4, x, 32 and 40 are in proportion
x = 5
x:y = 4:5 and y:z = 6:7
x:y:z = 24:30:35
The length and breadth of a rectangle are in the ratio 5:4
breadth = 64 cm
(i) 6:8 and 12:16
Yes, they form a proportion.
(ii) 24:28 and 36:48
No, they do not form a proportion.
If the second term is x, then:
x = 21
4, x, 9 are in continued proportion
∴ x = 6
Of a school ground:
length : width = 5 : 2
length = 100 metres
Express each of the following ratios in its simplest form:
(i) 60:72 = 5:6
(ii) 324 : 144 = 9:4
Find the ratio of the following in the simplest form:
(i) 75 paise to Rs 3 = 1:4
(ii) 35 minutes to 45 minutes = 7:9
(iii) 8 kg to 400 gm = 20:1
(iv) 48 minutes to 1 hour = 4:5
Margarette earns Rs 955 per month
She saves Rs 185 per month
∴ Her expenditures per month = Rs 770
The ratio of:
(i) savings to income = 37:191
(ii) income to expenditures = 191:154
(iii) savings to expenditures = 37:154
Step-by-step explanation:
8, x, 9 and 36 are in proportion
∴ Products of means = Product of extremes
∴ 9x = 8 . 36
∴ x = 32
x:15 = 8:12
∴ Products of means = Product of extremes
∴ 12x = 15 . 8
∴ x = 10
4, x, 32 and 40 are in proportion
∴ Products of means = Product of extremes
∴ 32x = 4 . 40
∴ x = 5
x:y = 4:5
∴ 4y = 5x
∴ 28y = 35x
and y:z = 6:7
∴ 7y = 6z
∴ 28y = 24z
∴ 35x = 28y = 24z
∴ x/24 = y/30 = z/35
∴ x:y:z = 24:30:35
The length and breadth of a rectangle are in the ratio 5:4
length : breadth = 5 : 4
∴ Products of means = Product of extremes
∴ 5 x breadth = 4 x length = 4 x 80 cm
∴ breadth = 64 cm
Check whether the two ratios form a proportion or not:
(i) 6:8 and 12:16
Product of the means = 8 x 12 = 96
Product of the extremes = 6 x 16 = 96
Yes they form a proportion.
(ii) 24:28 and 36:48
Product of the means = 28 x 36 = 4 x 7 x 3 x 12
Product of the extremes = 24 x 48 = 4 x 3 x 2 x 12 x 4
No they do not form a proportion.
If the second term is x, then:
12:x::8:14
∴ 8x = 12 . 14
∴ x = 21
4, x, 9 are in continued proportion
∴ x^2 = 4 . 9
∴ x = 6
Of a school ground:
length : width = 5 : 2
∴ 2 x length = 5 x width = 5 x 40 metres
∴ length = 100 metres
Express each of the following ratios in its simplest form:
(i) 60:72 = 5:6 [cancelling common factor 12]
(ii) 324 : 144 = 12x27 : 12x12 = 9:4
Find the ratio of the following in the simplest form:
(i) 75 paise to Rs 3 = 75:300 = 3:12 = 1:4
(ii) 35 minutes to 45 minutes = 35:45 = 7:9
(iii) 8 kg to 400 gm = 8000:400 = 20:1
(iv) 48 minutes to 1 hour = 48:60 = 4:5
Margarette earns Rs 955 per month
She saves Rs 185 per month
∴ Her expenditures per month = Rs (955 - 185) = Rs 770
The ratio of:
(i) savings to income = 185:955 = 37:191
(ii) income to expenditures = 955:770 = 191:154
(iii) savings to expenditures = 185:770 = 37:154