Kinh Nghiệm về What number must be subtracted from each of the numbers 11 13 20 and 25 so that the resulting numbers make a proportion? 2022
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What number should be added to each of these numbers 12, 22, 42 and 72 so that the resulting numbers may be in proportion?
Which number should be subtracted from each of the numbers 13 25 55 so that resulting numbers would be in continued proportion?What number must be subtracted from each of the numbers 21 13 19 27 so that the resulting numbers are in proportion?What number must be subtracted from each of numbers 10 12 19 and 24 to get the numbers which are in proportion?How do you make a number into a proportion?
Let x be subtracted from each term, then
23 – x, 30 – x, 57 – x and 78 – x are proportional
23 – x : 30 – x : : 57 – x : 78 – x
⇒ `(23 – x)/(30 – x) = (57 – x)/(78 – x)`
⇒ (23 – x) (78 – x) = (30 – x) (57 – x)
⇒ 1794 – 23x – 78x + x2 = 1710 – 30x – 57x + x2
⇒ x2 – 101x + 1794 = x2 –
87x + 1710
⇒ x2 – 101x + 1794 – x2 + 87x – 1710 = 0
⇒ –14x + 84 = 0
⇒ 14x = 84
∴ x = `(84)/(14)` = 6
Hence 6 is to be subtracted.
Given:
The numbers 104, 34, 110 and 36
Concept used:
If a, b, c and d are four numbers and they are in continued proportion
Then a ∶ b ∶∶ c ∶ d
⇒ ad = cb
⇒ a/b = c/d
Calculation
Let the number x added
Now, according to question,
(104 + x) ∶ (34 + x) ∶∶ (110 + x) ∶ (36 + x)
⇒ (104 + x) × (36 + x) = (110 + x) × (34 + x)
⇒ 3744 + 36x + 104x + x2 = 3740 + 34x + 110x + x2
⇒ 3744 + 140x = 3740 + 144x
⇒ 4x = 4
Then x = 1
∴ The required number is 1.
Alternate Method
Calculations:
Let the number x added
Now, according to question,
(104 + x) ∶ (34 + x) ∶∶ (110 + x) ∶ (36 + x)
⇒ (104 + x)/(34 + x) = (110 + x)/(36 + x)
Let’s check options one by one,
For 1 option,
After adding 9 to each number, numbers will be 113, 43, 119 and 45
For them to be in continued proportion this ratio must be equal
⇒ 113/43 ≠ 119/45
Hence option 1 is not correct
For 2 option,
After adding 3 to each number, numbers will be 107, 37, 113 and 39
For them to be in continued proportion this ratio must be equal
⇒ 107/37 ≠ 113/39
Hence option 2 is not correct
For 3 option,
After adding 1 to each number, numbers will be 105, 35, 111 and 37
For them to be in continued proportion this ratio must be equal
⇒ 105/35 = 111/37 = 3
Hence option 3 is correct
For 4 option,
After adding 4 to each number, numbers will be 108, 38, 114 and 40
For them to be in continued proportion this ratio must be equal
⇒ 108/38 ≠ 114/40
Hence option 4 is not correct
∴ The correct answer is option 3.
Let's discuss the concepts related to Ratio and Proportion and Mean Proportional. Explore more from Quantitative Aptitude here. Learn now!
What number should be added to each of these numbers 12, 22, 42 and 72 so that the resulting numbers may be in proportion?
Answer
Verified
Hint: Product of extremes is equal to the product of mean. Proportional numbers are represented as [a:b::c:d] , where [a,d] are the extremes and [b,c] are known as the mean. In this question four proportional numbers are given so first we will add a common unknown number to them and then we will use means and extremes property to find the unknown number.
Complete step-by-step answer:
Given the four proportional numbers [12:22::42:72]
Let [x] be the
number added to each of these numbers, so the new numbers become
First number [ = 12 + x]
Second number [ = 22 + x]
Third number [ = 42 + x]
Fourth number [ = 72 + x]
Now after adding an unknown numbers, since the resulting numbers need to be in proportion so we can write these numbers as
[12 + x:22 + x::42 + x:72 + x]
Now we know the means and extremes property of proportionality where the product of extremes is equal to the product of mean, hence we
can write
[left( 12 + x right) times left( 72 + x right) = left( 22 + x right) times left( 42 + x right)]
Now by solving this
[
Rightarrow 12 times 72 + 12x + 72x + x^2 = 22 times 42 + 22x + 42x + x^2 \
Rightarrow 864 + 84x = 924 + 64x \
Rightarrow 84x - 64x = 924 - 864 \
Rightarrow 20x = 60 \
Rightarrow x = 3 ;
]
Therefore we get the value of [x = 3]
Hence we can say if we add 3 to the numbers 12,
22, 42 and 72 the resulting numbers will be in proportion.
The resulting numbers are [15:25::45:75]
So, the correct answer is “3”.
Note: The numbers are proportional when the ratio of the LHS of the proportions is equal to the RHS of the proportion. To check if the numbers are in proportion we just find their ratio of both the sides.
The given numbers [12:22::42:72] are not in proportion since their ratios are not equal
[dfrac1222 =
dfrac4272]
Now if we add 3 to each numbers then they become proportional
[
dfrac1525 = dfrac4575 \
dfrac35 = dfrac35 \
]
Which number should be subtracted from each of the numbers 13 25 55 so that resulting numbers would be in continued proportion?
Hence, 5 needs to be subtracted from 13,25,55 such that they are in continued proportion.What number must be subtracted from each of the numbers 21 13 19 27 so that the resulting numbers are in proportion?
Answer: When we subtract 3 from each of the numbers 21, 30, 19 and 27 resulting numbers are : 18, 27, 16, 24. They are in same proportion.What number must be subtracted from each of numbers 10 12 19 and 24 to get the numbers which are in proportion?
Hence, 4 must be subtracted from each of the numbers: 10, 12, 19 and 24, to get the numbers which are in proportion.How do you make a number into a proportion?
Proportion says that two ratios or fractions are equal Suppose, we have two pairs of numbers, say a, b and c, d, then we can say that ( a, b ) and ( c, d ) are in proportion if ab=cd. For example, 12=36, as on solving 36, we get 12. Now, the number we have is 15, 18, 35, and 42. Tải thêm tài liệu liên quan đến nội dung bài viết What number must be subtracted from each of the numbers 11 13 20 and 25 so that the resulting numbers make a proportion?