Question

the ratio of two numbers is 3:5. if each number is increased by 10 the ratio between the numbers formed is 5:7. find the number

iska answer 118/39​

Answer 1

Solution :

$\bf{\green{\underline{\bf{Given\::}}}}$

The ratio of two numbers is 3:5. If each number is increased by 10 the ratio between the numbers formed is 5:7.

$\bf{\green{\underline{\bf{To\:find\::}}}}$

The number.

$\bf{\green{\underline{\bf{Explanation\::}}}}$

Let the two number be r & m.

$\leadsto\sf{r:m=3:5}\\\\\leadsto\sf{\dfrac{r}{m} =\dfrac{3}{5}} \\\\\leadsto\sf{5r=3m}\\\\\leadsto\bf{r=\dfrac{3m}{5} ..................(1)}$

A/q

$\longrightarrow\sf{\dfrac{r+10}{m+10} =\dfrac{5}{7} }\\\\\\\longrightarrow\sf{7(r+10)=5(m+10)}\\\\\\\longrightarrow\sf{7r+70=5m+50}\\\\\\\longrightarrow\sf{7\bigg(\dfrac{3m}{5} \bigg)+70=5m+50}\\\\\\\longrightarrow\sf{\dfrac{21m}{5} +70=5m+50}\\\\\\\longrightarrow\sf{\dfrac{21m+350}{5} =5m+50}\\\\\\\longrightarrow\sf{21m+350=25m+250}\\\\\\\longrightarrow\sf{21m-25m=250-350}\\\\\\\longrightarrow\sf{-4m=-100}\\\\\\\longrightarrow\sf{m=\cancel{\dfrac{-100}{-4} }}$

$\longrightarrow\sf{\red{m=25}}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=\dfrac{3(25)}{5} }\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{75}{5} }}\\\\\\\longrightarrow\sf{\red{r=15}}$

Thus;

The number is r = 15 & m = 25 .

Answer 2

$\tt{\green{\huge{Solution_{MV} \::- }}}$

QUESTION :

The ratio of two numbers is 3:5.

If each number is increased by 10 the ratio between the numbers formed is 5:7.

Find the numbers.

SOLUTION :

The two numbers are in the ratio 3 : 5

Let them be 3x and 5x respectively .

Now :

3X + 10 / 5x + 10 = 5 / 7

=> 7 ( 3X + 10 ) = 5 ( 5X + 10 )

=> 21 X + 70 = 25 X + 50

=> 4X = 20

=> X = 5

=> 3X = 15

=> 5X = 25

Hence the required numbers are 15 and 25 respectively.

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.........THE GIVEN ANSWER IS WRONG......