Question

2. If x is subtracted from each of the numbers
20, 37, 54 and 105, then the numbers so
obtained in this order are in proportion. What
is the mean proportional between [7x-5) and
{x+ 1)?
यदि संख्याओं 20,37,54 और 105 में से प्रत्येक से x
घटाया जाता है, तो इस तरह प्राप्त संख्याएँ समानुपात में होती
हैं। (7x-5) और (x +1) का मध्यानुपात ज्ञात कीजिए।
a) &
(b) 6
(c) 12
(d) 9​

Answer 1

Answer:

The mean proportion between (7 x - 5) and (x + 1) is  8

Step-by-step explanation:

Given as :

If x is subtracted from each of the numbers  20, 37, 54 and 105, then the numbers so  obtained in this order are in proportion.

The number thus formed = x - 20

                                            x - 37

                                            x - 54

                                            x - 105

A/Q The number are in proportion

i.e  (x - 20) : (x - 37) : : (x - 54) : (x - 105)

Or, $\dfrac{x-20}{x-37}$ = $\dfrac{x-54}{x-105}$

By cross multiply

(x - 20) × (x - 105) = (x - 37) × (x - 54)

Or, x² - 105 x - 20 x + 2100 = x² - 54 x - 37 x + 1998

Or,  x² -  x² - 125 x + 91 x + 2100 - 1998 = 0

Or, 0 - 34 x + 102 = 0

Or, 34 x = 102

∴    x = $\dfrac{102}{34}$

i.e  x = 3

So, The value of x = 3

Again

Two numbers area as -

(7 x - 5) = 7 × 3 - 5

            = 21 - 5 = 16

And

x + 1 = 3 + 1 = 4

Let The mean proportion between 16 , 4 = y

So, 16 : y : : y : 4

Or, y × y = 16 × 4

Or, y² = 64

∴   y = √64

i.e y = 8

So, The mean proportion = y = 8

Hence, The mean proportion between (7 x - 5) and (x + 1) is 8 . Answer