5 : □ : : 10 : 8 : : 15 : □ - Mathematics

5 : `square` : : 10 : 8 : : 15 : `square`

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5 : 4 : : 10 : 8 : : 15 : 12

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Chapter 3: Ratio and Proportion - Exercise 3.3 [Page 58]

Chapter 3 Ratio and Proportion
Exercise 3.3 | Q 1. (iii) | Page 58

If b is the mean proportion between a and c, show that: `(a^4 + a^2b^2 + b^4)/(b^4 + b^2c^2 + c^4) = a^2/c^2`.

If `a/b = c/d` prove that each of the given ratios is equal to

`(5a + 4c)/(5b + 4d)`

Find the mean proportion of the following :

`28/3` and `175/27`

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

If `a = (b + c)/(2), c = (a + b)/(2)` and b is mean proportional between a and c, prove that `(1)/a + (1)/c = (1)/b`.

If 24 workers can build a wall in 15 days, how many days will 8 workers take to build a similar wall?

If a, b, c and d are in proportion, prove that: `(a^2 + ab)/(c^2 + cd) = (b^2 - 2ab)/(d^2 - 2cd)`

If x, y, z are in continued proportion, prove that: `(x + y)^2/(y + z)^2 = x/z`.

Choose the correct answer from the given options :

The third proportional to `6(1)/(4)` and 5 is

10 books is to 15 books as 3 books is to 15 books