Answer
Verified
425.1k+ views
Hint: Factorise the given numbers carefully. Also keep in mind that the value of $y$ can be negative as well.
We have the given numbers as:
$210$ and $55$
Now, these can be factorized as
$210 = 2 \times 3 \times 5 \times 7$
$55 = 5 \times 11$
This shows that the HCF of $210$ and $55$ comes out to be $5$.
Since, it is given in the question that the HCF of $210$ and $55$ is of the form \[(210)(5) + 55y\]
That is,
\[5 = (210)(5) + 55y\]
On further evaluation, we get
\[ \Rightarrow 1050 + 55y = 5\]
\[ \Rightarrow 55y = - 1050 + 5\]
\[ \Rightarrow 55y = - 1045\]
\[ \Rightarrow y = \dfrac{{ - 1045}}{{55}}\]
$\therefore y = - 19$
So, the required solution is $(a){\text{ }} - 19$.
Note: To solve these types of questions, find out the HCF of the given numbers and substitute it in the given equation to obtain the required solution.
We have the given numbers as:
$210$ and $55$
Now, these can be factorized as
$210 = 2 \times 3 \times 5 \times 7$
$55 = 5 \times 11$
This shows that the HCF of $210$ and $55$ comes out to be $5$.
Since, it is given in the question that the HCF of $210$ and $55$ is of the form \[(210)(5) + 55y\]
That is,
\[5 = (210)(5) + 55y\]
On further evaluation, we get
\[ \Rightarrow 1050 + 55y = 5\]
\[ \Rightarrow 55y = - 1050 + 5\]
\[ \Rightarrow 55y = - 1045\]
\[ \Rightarrow y = \dfrac{{ - 1045}}{{55}}\]
$\therefore y = - 19$
So, the required solution is $(a){\text{ }} - 19$.
Note: To solve these types of questions, find out the HCF of the given numbers and substitute it in the given equation to obtain the required solution.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The cell wall of prokaryotes are made up of a Cellulose class 9 biology CBSE
What organs are located on the left side of your body class 11 biology CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
a Tabulate the differences in the characteristics of class 12 chemistry CBSE