Page 179 - classs 6 a_Neat

PROPORTION
COMPARISON OF TWO RATIOS PROPORTION if two ratios are equal, we say that they are in proportion and use the symbol
‘: : ‘ or • =’ to equate the two ratios.
1. Two ratios can be compared by making the consequents (the denominators) the same. EXAMPLE:1 It is given that the weights of 150 litres and 100 litres of kerosene oil are 135 kg and
2. To make the consequents the same, find the LCM of the denominators. 90 kg respectively.
3. Then, the ratio with the greater antecedent (the numerator) is greater. Then, the ratio of volumes= 150 litres: 100 litres
Just try:3 Compare ratios 5:12 and 3:20 = 150:100 = 150 = 3 = 3: 2.
100 2
EXERCISE 13-A And, the ratio of weights = 135 kg: 90 kg
135 3
1. Express the following ratios as fractions and reduce them to the lowest form. = 135:90 = 90 = 2 = 3: 2.
a. 12:36 b. 27:81 C. 44:77 d. 15:95 e. 14:91 Thus. (150 litres): (100 litres)= (135 kg): (90 kg)
2. Write the given ratios in the simplest form. ⇒ 150 : 100 = 135 : 90
a. 15 cm to 35 cm b.₹10 to 228 c. 40 kg to 1 60 kg ⇒ 150: 100: : 135 : 90.
d. 80 seconds to 16 seconds 30 chocolates to 50 chocolates FOUR NUMBERS IN PROPORTION
3. Write the following ratios in the simplest form. Four numbers a, b, c, dare said to be in proportion if a: b = c: d and we write, a: b :: c: d.
a.1 hr 15 min : 45 min We read it as ‘a is to bas c is to d’.
b. ₹2.50 : ₹4.50 Here a, b, c, d are respectively known as first, second, third and fourth term of the given proportion.
c. 150 p: ₹2 The 1st and 4th terms are called the extreme terms or extremes.
d. 3 months : 1 year 3 months The 2nd and 3rd terms are called the middle terms or means.
e. dozen : 1 score In a proportion a: b:: c: d. we always have (ax d) =(bx c),
4. Identify the larger ratio in the following pairs. i.e., product of extremes = product of means.
a. 4:7, 15:28 b. 6:22, 9: 11 c. 3:10, 2:15 EXAMPLE:2 In 45 : 90 : : 3 : 6, we have:
d. 7:9, 5:81 e. 5:32, 7:144 product of extremes = ( 45 x 6) = 270,
5. Write the following ratios in descending order. product of means= (90 x 3) = 270.
a. 1 :2, 2:3, 3:4 b. 7:9, 9:11, 2:3 c. 5:7, 6:13, 3:14 product of extremes = product of means.
d. 3:10, 7:20, 11 :30 e. 3:8, 5:24, 7:48
6. The ratio of the number of girls to boys in a class is 6: 11 . If the total number of students in the class is 51, SOLVED EXAMPLES
find the number of girls in the class.
7. A box contains some lollypops and chocolates. They are in the ratio of 7:9. If the EXAMPLE:3 Are the ratios 45 g : 60 g and 36 kg: 48 kg in proportion?
total number of items in the box is 480, find the number of each variety. SOLUTION We have:
8. Given that a teacher earns ₹45,000 a month and that her monthly expenditure is <30,000, answer the 45 3
following questions. 45 g· 60 g = 45 : 60 = 60 = 4 = 3: 4.
a.What is the ratio of her expenditure to her income?
b.What is the ratio of her savings to her income? 36kg : 48kg = 36: 48 = 36 = 3 = 3: 4.
c.What is the ratio of her savings to her expenditure? 48 4
9. A survey was done to find the number of families who read two popular newspa pers-The Times of ∴ the ratios 45 g : 60 g and 36 kg : 48 kg are in proportion.
India (TOI) and Hindustan Times (HT)-in a residential colony. Six hundred families were surveyed. EXAMPLE:4 Are 30, 40, 45. 60 in proportion?
The survey revealed that 350 families read TOI while 250 families read HT. Find the ratio of:
SOLUTION We have: 30: 40 = 30 = 3 ⋅ and,45:60 = 45 = 3 ⋅
a. a. The readers of HT to the readers of TOI. 40 4 60 4
b. The readers of HT to the total number of families surveyed. ∴ 30 : 40 = 45 : 60.
c. The readers of TOI to the total number of families surveyed. Hence, 30, 40, 45, 60 are in proportion.
d. Which is the larger ratio-the ratio answer b, or the ration in answer c? Alternative method Product of extremes= (30 x 60) = 1800.
e. Divide ₹720 among A, Band C in the ratio 5:4:9. Product of means = ( 40 x 45) = 1800.
∴ product of extremes = product of means. Hence, 30: 40:: 45: 60.