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Question

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A.27

B.31

C.36

D.41

Answer

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Given data: The product of two positive integers is 936.

The ratio of those integers is \[13:18.\]

Now, let us assume that the two integers are a and b, where ${\text{b > a}}$

From the given data, we can say that

$

ab = 936...........(i) \\

\dfrac{a}{b} = \dfrac{{13}}{{18}}..............(ii) \\

a = \dfrac{{13}}{{18}}b.............(iii) \\

$

On substituting the value of ‘a’ in equation (i), we will get

\[

(\dfrac{{13}}{{18}}b)b = 936 \\

\Rightarrow {b^2} = 936\left( {\dfrac{{18}}{{13}}} \right) \\

On{\text{ }}simplifying{\text{ }}we{\text{ }}get, \\

\Rightarrow {b^2} = 72(18) \\

\Rightarrow {b^2} = 1296 \\

On{\text{ }}taking{\text{ }}square{\text{ }}root{\text{ }}we{\text{ }}get,{\text{ }} \\

\Rightarrow b = \pm 36 \\

\]

But it is given that ‘a’ and ‘b’ are positive integers, giving us the value of ‘b’ i.e.

$b = 36$

Now, putting the value of ‘b’ in equation (iii)

$

a = \dfrac{{13}}{{18}}(36) \\

\Rightarrow a = 13(2) \\

\Rightarrow a = 26 \\

$

From the assumption we made it is clear the ‘b’ is the greater integer and ${\text{b = 36}}{\text{.}}$

Hence,

$

ab = 936, \\

\Rightarrow \dfrac{a}{b} = \dfrac{{13}}{{18}} \\

\Rightarrow a = \dfrac{{13}}{{18}}b \\

\Rightarrow b = \dfrac{{18}}{{13}}a..........(iv) \\

$

On substituting the value of ‘b’ in equation (i), we will get

\[

{\text{a(}}\dfrac{{{\text{18}}}}{{{\text{13}}}}{\text{a) = 936}} \\

\Rightarrow {{\text{a}}^{\text{2}}}{\text{ = 936}}\left( {\dfrac{{{\text{13}}}}{{{\text{18}}}}} \right) \\

{\text{On simplification we get,}} \\

\Rightarrow {{\text{a}}^{\text{2}}}{\text{ = 52(13)}} \\

\Rightarrow {{\text{a}}^{\text{2}}}{\text{ = 676}} \\

{\text{On taking square root, we get,}} \\ \]

$\Rightarrow$ $a$ =$\pm$ $26$

But it is given that ‘a’ and ‘b’ are positive integers, giving us the value of ‘a’ i.e.

${\text{a = 26}}$

Now, putting the value of ‘a’ in equation (iv)

$

{\text{b = }}\dfrac{{{\text{18}}}}{{{\text{13}}}}{\text{(26)}} \\

\Rightarrow {\text{b = 18(2)}} \\

\Rightarrow {\text{b = 36}} \\

$