5 : □ : : 10 : 8 : : 15 : □

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

Fill in the Blanks

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

What least number must be added to each of the numbers 6, 15, 20 and 43 to make them proportional?

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

If (a² + b²)(x² + y²) = (ax + by)²; prove that: `a/x = b/y`.

Write (T) for true and (F) for false in case of the following:

30 bags : 18 bags : : Rs 450 : Rs 270

Show that the following numbers are in continued proportion:

36, 90, 225

If ax = by = cz; prove that `x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2`

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

If a, b, c are in continued proportion, prove that: abc(a + b + c)³ = (ab + bc + ca)³

If a, b, c, d are in continued proportion, prove that: `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d`

The first, third, and fourth terms of a proportion are 9, 24, and 32. Find the second term.