Selina Concise Class 6 Math Chapter 12 PROPORTION (including Word Problems) Exercise 12A Solution
EXERCISE 12A
(1) In each of the following, check whether or not the given ratios form a proportion:
(i) Product of extremes = 8 × 15 = 120
Product of means = 16 × 12 = 192
⇒ Product of extremes ≠ Product of means
The given two ratios do not form a proportion.
(ii) Product of extremes = 16 × 42 = 672
Product of means = 28 × 24 = 672
⇒ Product of extremes = Product of means
The given two ratios form a proportion.
(iii) 12 ÷ 3 = 4 and 8 ÷ 2 = 4
The given two ratios form a proportion.
(iv) Product of extremes = 15 × 32 = 800
Product of means = 40 × 20 = 800
⇒ Product of extremes = Product of means
The given two ratios form a proportion.
(v) 15/18 = 5/6 = 5 : 6 and 10/12 = 5/6
∴ 5 : 6 and 5 : 6
Product of extremes = 5 × 6 = 30
Product of means = 6 × 5 = 30
⇒ Product of extremes = Product of means
The given two ratios form a proportion.
(vi) 7/8 = 7 : 8 and 14 : 16 = 7 : 8
∴ 7 : 8 and 7 : 8
Product of extremes = 7 × 8 = 56
Product of means = 8 × 7 = 56
⇒ Product of extremes = Product of means
The given two ratios form a proportion.
(2) Find the value of x in each of the following proportion:
(3) Find the value of x so that the given four numbers are in proportion:
(i) x : 6 : : 10 : 15
We know, 15 × x = 6 × 10
⇒ x = 60/15 = 4
(ii) x : 4 : : 15 : 30
⇒ 30x = 4 × 15 = 60
⇒ x = 60/30 = 2
(iii) 2 : x : : 10 : 25
⇒ x × 10 = 25 × 2
⇒ x = 50/10 = 5
(iv) 4 : x : : 6 : 18
⇒ 6 × x = 18 × 4
⇒ x = 72/6 = 12
(v) 5 : 15 : : 4 : x
⇒ 5 × x = 15 × 4
⇒ x = 60/5 = 12
(vi) 4 : 10 : : 36 : x
⇒ 4 × x = 10 × 36
⇒ x = 360/4 = 90
(4) Let the third term be x.
The terms are = 6 : 18 : : x : 75
∴ 18 × x = 75 × 6
⇒ x = 450/18
⇒ x = 25
Hence, the third term is 25.
(5) Let the second term be x.
The term are = 9 : x : : 8 : 24
∴ 8 × x = 24 × 9
⇒ x = 216/8
⇒ x = 27
Hence, the second term is 27.
(6) Let the fourth term be x.
The terms are = 18 : 27 : : 32 : x
∴ 18 × x = 27 × 32
⇒ x = 864/18
⇒ x = 48
Hence, the fourth term is 48.
(7) Let the length and width be 5x m and 2x m.
The width (2x) = 40 m
∴ 2x = 40
⇒ x = 20
Therefore, the length is = 5 × 20 = 100 m
(8) Let the ratio of Sunday’s sale and whole week’s sale be 2x and 9x.
The sale of whole week (9x) = Rs 360
∴ 9x = 360
⇒ x = 40
Therefore, the Sunday’s egg sale is = Rs (2 × 40) = Rs 80.
(9) Let the weight of copper and zinc be 9x and 8x kg.
The weight of zinc (8x) = 9.6 kg
∴ 8x = 9.6
⇒ x = 9.6/8 = 1.2
Therefore the weight of the copper is = (9 × 1.2) kg = 10.8 kg
(10) Let the number of girls and boys be 2x and 5x.
The number of boys (5x) = 225
∴ 5x = 225
⇒ x = 225/5
⇒ x = 45
(i) The number of girls in the school = 2 × 45 = 90
(ii) The number of student in the school = (90 + 225) = 315.
(11) Total number of pass student = (1/5×225)= 45.
(12) The all possible proportion from the numbers 15, 18, 35 and 42.
(i) 15 : 18 : : 35 : 42
(ii) 42 : 18 : : 35 : 15
(iii) 42 : 35 : : 18 : 15
(iv) 15 : 18 : : 35 : 42