Answer
Verified
439.8k+ views
Hint: It is given that there are two positive integers, so consider the two integers $a$ and $b$. After that, apply the condition given and examine which is the greater number.
Complete step-by-step answer:
We are given that there are two integers.
Now let us assume the two integers $a$ and $b$.
We are given that, the product of two positive integers is $936$, we get,
$\Rightarrow$ $ab=936$
Now write it in terms of any one term we get,
$\Rightarrow$ $a=\dfrac{936}{b}$ …………… (1)
Also, we are given that the integers are in the ratio $13:18$.
$\Rightarrow$ $\dfrac{a}{b}=\dfrac{13}{18}$ …………. (2)
Now substituting (1) in (2) we get,
$\Rightarrow$ $\dfrac{\dfrac{936}{b}}{b}=\dfrac{13}{18}$
Simplifying we get,
$\Rightarrow$ $\dfrac{936}{{{b}^{2}}}=\dfrac{13}{18}$
Now cross multiplying we get,
$\Rightarrow$ $13{{b}^{2}}=936\times 18$
Again, simplifying we get,
$\Rightarrow$ ${{b}^{2}}=\dfrac{936\times 18}{13}$
$\Rightarrow$ ${{b}^{2}}=1296$
Now taking square root on both sides we get,
$\Rightarrow$ $b=\pm \sqrt{1296}$
$\Rightarrow$ $b=\pm 36$
In the problem it is given that the integers are positive integers.
So, taking only positive integers,
$\Rightarrow$ $b=36$
Now substituting $b=36$ in (1) we get,
$\Rightarrow$ $a=\dfrac{936}{36}$
Now simplifying we get,
$\Rightarrow$ $a=26$
Now from assumption, we can say that $b$ is greater integer.
So, $36$ is the greater number.
Therefore, the correct answer is option (C).
Additional information:
The word integer originated from the Latin word “Integer” which means whole. It is a special set of whole numbers composed of zero, positive numbers and negative numbers and denoted by the letter Z. Positive numbers are those numbers which are having a plus sign ($+$). Most of the time, positive numbers are represented merely as a whole number without the plus sign ($+$). Every positive number is greater than zero, as well as negative numbers. On a number line, positive numbers are represented to the right of zero.
Note: Integers are the numbers which can be positive, negative or zero. These numbers are used to perform various arithmetic calculations, like addition, subtraction, multiplication and division. Every positive number is greater than zero, as well as negative numbers. In contrast to positive numbers, negative numbers are numbers symbolized with a minus sign ($-$). Negative numbers are represented to the left of zero on a number line.
Complete step-by-step answer:
We are given that there are two integers.
Now let us assume the two integers $a$ and $b$.
We are given that, the product of two positive integers is $936$, we get,
$\Rightarrow$ $ab=936$
Now write it in terms of any one term we get,
$\Rightarrow$ $a=\dfrac{936}{b}$ …………… (1)
Also, we are given that the integers are in the ratio $13:18$.
$\Rightarrow$ $\dfrac{a}{b}=\dfrac{13}{18}$ …………. (2)
Now substituting (1) in (2) we get,
$\Rightarrow$ $\dfrac{\dfrac{936}{b}}{b}=\dfrac{13}{18}$
Simplifying we get,
$\Rightarrow$ $\dfrac{936}{{{b}^{2}}}=\dfrac{13}{18}$
Now cross multiplying we get,
$\Rightarrow$ $13{{b}^{2}}=936\times 18$
Again, simplifying we get,
$\Rightarrow$ ${{b}^{2}}=\dfrac{936\times 18}{13}$
$\Rightarrow$ ${{b}^{2}}=1296$
Now taking square root on both sides we get,
$\Rightarrow$ $b=\pm \sqrt{1296}$
$\Rightarrow$ $b=\pm 36$
In the problem it is given that the integers are positive integers.
So, taking only positive integers,
$\Rightarrow$ $b=36$
Now substituting $b=36$ in (1) we get,
$\Rightarrow$ $a=\dfrac{936}{36}$
Now simplifying we get,
$\Rightarrow$ $a=26$
Now from assumption, we can say that $b$ is greater integer.
So, $36$ is the greater number.
Therefore, the correct answer is option (C).
Additional information:
The word integer originated from the Latin word “Integer” which means whole. It is a special set of whole numbers composed of zero, positive numbers and negative numbers and denoted by the letter Z. Positive numbers are those numbers which are having a plus sign ($+$). Most of the time, positive numbers are represented merely as a whole number without the plus sign ($+$). Every positive number is greater than zero, as well as negative numbers. On a number line, positive numbers are represented to the right of zero.
Note: Integers are the numbers which can be positive, negative or zero. These numbers are used to perform various arithmetic calculations, like addition, subtraction, multiplication and division. Every positive number is greater than zero, as well as negative numbers. In contrast to positive numbers, negative numbers are numbers symbolized with a minus sign ($-$). Negative numbers are represented to the left of zero on a number line.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE