New Learning Composite Mathematics Class 6 SK Gupta Anubhuti Gangal Ratio Proportion and Unitary Method Chapter 8E Solution
(2) (a) Product of extremes = 14 X 9 = 126
Product of means = 7 X 18 = 126
Since product of extremes = product of means
∴ given numbers are in proportion
(b) Product of extremes = 12 X 8 = 96
Product of means = 16X6 = 96
Since product of extremes = Product of means
∴ given numbers are in proportion
(c) Product of extremes = 4X17 = 68
Product of means = 7X9 = 63
Since product of extremes 7 product of means
∴ given numbers are in proportion
(d) Product of extremes = 180X200 = 36000
Product of means = 100 X 360 = 36000
Since product of extremes = Product of means
∴ given numbers are in proportion.
(e) Product of extremes = 20X9 = 180
Product of means = 8X30 = 240
Since product of extremes ≠ product of means
∴ given numbers are not in proportion
(f) Product of extremes = 34X102 = 3468
Product of means = 51X68 = 3468
Since product of extremes = Product of means
∴ given numbers are in proportion
(3) (a) 24/x = 18/15
Or , x = 24X15/18
∴ x = 20
(b) 3/8 = x/128
Or, x = 3X128/8
∴ x = 48
(c) 36/x = x/16
Or, x2 = 36X16
Or, x = √36X16
Or, x = 6X4
∴ x = 24
(d) 15/45 = 45/x
Or, x = 45X45/15
x = 135
(4) (a) 10/x = 5/18
Or, x = 10X18/5
∴ x = 36
(b) 24/20 = x/15
Or, x = 24X15/20
∴ x = 18
(c) 6.4/x = 20/8.5
Or, x = 6.4 X 8.5/20
∴ x = 2.72
(5) 9:105 = 150:1750
105:9 = 1750:150
9:150 = 150:1750
150:9 = 1750:105
(6) Let, the length of school ground be x
5:3 = x:45
Or, 5/3 = x/45
Or, x = 5X45/3
∴ x = 75
Ans – length of the ground is 75m
(7) Let the expenditure be be x
9:7 = 18000:x
Or, 9/7 = 18000/x
Or, x = 7X18000/9
∴ x = 14000
∴ Savings = RS (18000 – 14000)
= RS 4000