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Thủ Thuật Hướng dẫn What number must be added to each of the numbers 711 and 19 so that the resulting numbers may be in continued proportion? 2022

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ML Aggarwal Solutions Class 10 Mathematics Solutions for Ratio and Proportion Exercise 7.2 in Chapter 7 – Ratio and Proportion

Question 6 Ratio and Proportion Exercise 7.2

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    ML Aggarwal Solutions Class 10 Mathematics Solutions for Ratio and Proportion Exercise 7.2 in Chapter 7 – Ratio and Proportion ML Aggarwal Solutions Class 10 Mathematics Solutions for Ratio and Proportion Exercise 7.2 in Chapter 7 – Ratio and Proportion 1. What must be added to each of the numbers 7, 11 and 19, so that the resulting numbers may be in continued proportion?Answer & SolutionWhat number must be added to each of the numbers 7, 4 and 2 so that the resulting numbers may be in a continued proportion?Answer
    (Detailed Solution Below)What must be added to each of the number 711 and 19 so that the resulting numbers may be in the continued proportion?What number must be added to each of the number 5 9 7 12 to get the numbers which are in proportion?What number must be added to each of the numbers 7 4 and 2 so that the resulting number may be in a continued proportion?What must be added to each of the numbers 7/10 19 25 so that the resultant numbers are in proportion?

What number must be added to each of the numbers 5, 11, 19, and 37 so that they are in proportion?

Answer:

Consider x to be added to 5, 11, 19 and 37 to make them in proportion

5 + x: 11 + x :: 19 + x: 37 + x

It can be written as

(5 + x)
(37 + x) = (11 + x) (19 + x)

By further calculation

beginarrayl 185+5 x+37 x+x^2=209+11 x+19 x+x^2 \ 185+42 x+x^2=209+30 x+x^2 endarray

So we get

42 x-30 x+x^2-x^2=209-185

12x = 24

x = 2

Hence, the least number to be added is 2.

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ML Aggarwal Solutions Class 10 Mathematics Solutions for Ratio and Proportion Exercise 7.2 in Chapter 7 – Ratio and Proportion

Question 10 Ratio and Proportion Exercise 7.2

What number must be added to each of the numbers 16, 26, and 40 so that the resulting numbers may be in continued proportion?

Answer:

Consider x be added to each number

16 + x , 26 + x and 40 + x are in continued proportion

It can be written
as

(16 + x)/ (26 + x) = (26 + x)/ (40 + x)

By cross multiplication

(16 + x) (40 + x) = (26 + x) (26 + x)

On further calculation

beginarrayl 640+16 x+40 x+x^2=676+26 x+26 x+x^2 \ 640+56 x+x^2=676+52 x+x^2 \ 56 x+x^2-52 x-x^2=676-640 endarray

So we get

4x = 36

x = 36/4 = 9

Hence, 9 is the number to be added to each of the numbers.

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1. What must be added to each of the numbers 7, 11 and 19, so that the resulting numbers may be in continued proportion?

1.

2.

3.

4.

Answer & Solution

Answer & Solution

Answer: Option 4

Solution:

Let X be the required number, then
(7 + X) : (11 + X) :: (11 +X) : (19 + X)
(7 + X) (19 + X) = (11 + X)2
X2 + 26X + 133 = X2 + 22X + 121
4X = – 12 or X = – 3

What number must be added to each of the numbers 7, 4 and 2 so that the resulting numbers may be in a continued proportion?

This question was previously asked in

SSC MTS 2022 (Held On : 11 Oct 2022 Shift 3 ) Official Paper 15

View all SSC MTS Papers >

2435

Answer
(Detailed Solution Below)

Option 1 : 2

Free

CT : GK (Ancient History)

10 Questions 10 Marks 6 Mins

Given

7,4 and 2 should be in a continued proportion

Concept

Continued proportion means the ratio between the first and the second is equal to the ratio between the second and the third

Calculation

let x is added in each number

(7 + x)/(4 + x) = (4 +
x)/(2 + x)

⇒ (7 + x) (2 + x) = (4 + x) (4 + x)

⇒ 14 + 7x + 2x + x2 = 16 + 8x + x2

⇒ 14 + 9x + x2 = 16 + 8x + x2

⇒ 14 + 9x = 16 + 8x

⇒ 9x – 8x = 16 – 14

⇒ x = 2

∴ 2 must be added to each of the numbers 7, 4 and 2 so that the resulting numbers may be in a continued proportion.

Last
updated on Sep 28, 2022

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Let’s discuss the concepts related to Ratio and Proportion and Direct or Indirect Proportion. Explore more from Quantitative Aptitude here. Learn now!

What must be added to each of the number 711 and 19 so that the resulting numbers may be in the continued proportion?

Hence, the least number to be added is 2.

What number must be added to each of the number 5 9 7 12 to get the numbers which are in proportion?

Hence, 3 must be added to each of the numbers: 5, 9, 7 and 12, to get the numbers which are in proportion.

What number must be added to each of the numbers 7 4 and 2 so that the resulting number may be in a continued proportion?

∴ 2 must be added to each of the numbers 7, 4 and 2 so that the resulting numbers may be in a continued proportion.

What must be added to each of the numbers 7/10 19 25 so that the resultant numbers are in proportion?

Answer: 2 is to be added to each no.
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