New Learning Composite Mathematics SK Gupta Anubhuti Gangal Class 7 Ratio and Proportion and Unitary Method Self Practice 7A Solution
(1) Express each of the following ratios in its simplest form.
(a) A length of 6 cm to a length of 8 cm.
(b) An area of 20 cm square to an area of 45 cm square.
(c) A volume of 26 litres to a volume of 65 litres.
(d) A population of 50 thousand to a populatino of 1.5 lakh.
(e) 1/4 : 2
(f) 1/2 : 1/8
(g) 0.75 : 1
(h) 14 cm to 1 m
(i) 25 cm to 50 mm
(j) 15 m to 1 km
(2) Ravi earns Rs. 84,000 a year and spends Rs. 63,000 a year. Find the simplest form the ratio of
(a) Ravi’s income to his savings
(b) Money that Ravi saves to the money he spends.
(3) There are 12,000 students in a university, out of which 5,600 are girls. Find the simplest form, the ratio of
(a) number of girls to the number of students
(b) number of boys to the number of girls
(c) number of boys to the number of students
(4) Which is a greater ratio of the following pairs?
(a) 3:2 or 4:3
(b) 7:10 or 8:11
(c) 32 : 22 or 3 : 2
(d) 3 : 5 or 0.66 : 1
(e) 1/5 : 1/7 or ¼ : 1/9
(5) Write the ratios – 4:9, 5:8 and 3:7 in order, from the least to the greatest.
(6) If 1:b = 4:7 and b:c = 5:3, then find a:b:c
(7) If a:b = 5:6 and b:c = 9:4, then find a:c
(8) The sides of a triangle are in the ratios, 1:1.5:2 and its perimeter is 18 cm. Find the length of each side.
(9) In an examination, 100 marks are distributed among 3 questions so that they are very proportional to 8,5,7. Find the marks of each question.
(10) The length of three ribbons are in the ratio 7:5:9. If the sum of the lengths of the three ribbons is 42 cm, find the length of the smallest ribbon.
(11) Shyam lost his weight in the ratio 9:5. His original weight was 90 kg. What is his new weight?
(12) A, B and C contributed Rs. 25,000, Rs, 50,000, Rs. 75,000 respectively in a business and their share of his profits are proportional to the capital they contributed. If the profits are Rs. 48,000, what is the share of each of them?
(13) a legacy of Rs. 1,08,000 is to be divided among 3 sons in the ratio 3/2 : 9/4 : 3, How much does each of them receive?
(14) A map drawn to a scale of 1 cm to 1 km, measures 24 cm by 18 cm. If the areas of land and water represented are in the ratio of 7:2, find in square km, the land area represented.
(a) Increase 180 in the ratio 6:9.
(b) Decrease Rs. 900 in the ratio 5:3
(c) Find the multiplying factor which decreases 120 kg to 84 kg.
(d) Two distances are in the ratio 15:8, the larger is 60 km, what is the smaller?
(e) A boy worked 8 hours a day. In what ratio , did his earnings change when, the pay was raised from Rs. 50 per hours Rs. 500 a day.
(16) A photo measuring 7.5 cm by 5 cm is enlarged, so that the larger side becomes 18 cm. What does the shorter side become? In what ratio is the area increased?
(17) At the beginning of a war, the numbers of war planes possessed by two powers of 1.6 :1. the weaker power having 400. In a general engagement, each power loses the same number of planes but, the ratio is changed to 2:1. How many planes does each lose?