Find the value of x in the following proportions : 3 : x = 24 : 2

Sum

3 : x = 24 : 2
⇒ × x 24 = 3 x 2
∴ x = `(3 xx 2)/(24)`
= `(1)/(4)`.

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Chapter 6: Ratio and Proportion - Exercise 7.2

Chapter 6 Ratio and Proportion
Exercise 7.2 | Q 1.2

Given four quantities a, b, c and d are in proportion. Show that: (a – c)b² : (b – d)cd = (a² – b² – ab) : (c² – d² – cd)

Find the mean proportion of: (a – b) and (a³ – a²b), a> b

What number should be subtracted from each of the numbers 23, 30, 57 and 78 so that the remainders are in proportion ?

Find two numbers such that the mean proportional between them is 28 and the third proportional to them is 224.

Find the value of x in each of the following proportion:

27 : x : : 63 : 84

Show that the following numbers are in continued proportion:

48, 60, 75

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: (a⁴ + c⁴) : (b⁴ + d⁴) = a² c² : b² d².

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

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