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Standard X

Mathematics

Solving Simultaneous Linear Equation Using Cramer's Rule

The greater o...

Question

The greater of two numbers is $8$ times the lesser and their sum is $180$ . Find the numbers.

140

and

30

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160

and

20

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110

and

40

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180

and

36

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Solution

The correct option is B $160$ and $20$
Let hte greater number be $x$ and smaller number be $y$
Given, $x = 8 y$ --- $(1)$
and $x + y = 180$ --- $(2)$
From equations $(1)$ and $(2),$ $8 y + y = 190 \Rightarrow 9 y = 180 \Rightarrow y = 20$

Substituting
$y = 20$ in the equation $(2)$ , we get $x = 160$

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The greater of two numbers is 8 times the lesser and their sum is 180. Find the numbers.

The correct option is B 160 and 20Let hte greater number be x and smaller number be yGiven, x=8y --- (1)and x+y=180 --- (2)From equations (1) and (2), 8y+y=190⇒9y=180⇒y=20Substitutingy=20 in the equation (2), we get x=160

The greater of two numbers is $8$ times the lesser and their sum is $180$ . Find the numbers.