Find whether 12, 24, 18, 36 are in order that can be expressed as two ratios that are in proportion

Sum

Yes, 12 : 24 : : 18 : 36

Because product of extremes 12 × 36 = 432

Product of means = 24 × 18 = 432

12 : 24 : : 18 : 36.

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Chapter 3: Ratio and Proportion - Exercise 3.3 [Page 59]

Chapter 3 Ratio and Proportion
Exercise 3.3 | Q 4 | Page 59

If three quantities are in continued proportion; show that the ratio of the first to the third is the duplicate ratio of the first to the second.

Find the smallest number that must be subtracted from each of the numbers 20, 29, 84 and 129 so that they are in proportion.

If `a/b = c/d` Show that a + b : c + d = `sqrt(a^2 + b^2) : sqrt(c^2 + d^2)`.

If a : b = c : d, show that (a - c) b² : (b - d) cd = (a² - b² - ab) : (c² - d² - cd).

Verify the following:

60 : 105 : : 84 : 147

The cost of 4 dozen bananas is Rs 104. How many bananas can be purchased for Rs 6.50?

If a, b, c are in continued proportion, prove that: (a + b + c) (a – b + c) = a² + b² + c²

Bachhu Manjhi earns Rs. 24000 in 8 months. At this rate, in how many months does he earn Rs. 42000?

Are the following statements true?

45 km : 60 km = 12 hours : 15 hours

The mean proportion between `3 + 2sqrt(2)` and `3 - 2sqrt(2)` is ______.