Find the value of x in the following proportions : x : 50 :: 3 : 2

Sum

x : 50 : : 3 : 2
⇒ × x 2 = 50 x 3
x = `(50 xx 3)/(2)`
= 75.

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Chapter 6: Ratio and Proportion - Exercise 7.2

Chapter 6 Ratio and Proportion
Exercise 7.2 | Q 1.4

If y is the mean proportional between x and z, prove that: `(x^2 - y^2 + z^2)/(x^(-2) - y^(-2) + z^(-2)) = y^4`.

Find the third proportional to `x/y + y/x` and `sqrt(x^2 + y^2)`

If `x = (sqrt(a + 3b) + sqrt(a - 3b))/(sqrt(a + 3b) - sqrt(a - 3b))`, prove that: 3bx² – 2ax + 3b = 0.

Find two numbers whose mean proportional is 18 and the third proportional is 486.

Find the fourth proportional to:
2xy, x², y²

If the cost of a dozen soaps is Rs 285.60, what will be the cost of 15 such soaps?

If (a + 2 b + c), (a – c) and (a – 2 b + c) are in continued proportion, prove that b is the mean proportional between a and c.

Write True (T) or False (F) against the following statement:

12 : 18 : : 28 : 12

Are the following statements true?

7.5 litres : 15 litres = 5 kg : 10 kg

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