**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**

**Solution:**

**(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) 3 ^{2} : 2^{2} 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**

**Solution:**

**(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.**

**Solution:**

**(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?**

**Solution:**

**(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.**

**Solution:**

**(15) Solve:**

**(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?**

**Solution:**

**(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?**

**Solution:**

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