Question

20. A number is divided into two parts such that one part is 10 more than the
other. If the two parts are in the ratio 5:3, find the number and the two
parts.​

Answer 1

Explanation:

Since the two parts are in the ratio 5:3, then let the first number be 5x and second number be 3x. As second number is 10 more than the other, so it will be 3x+10.

Since the two parts are in the ratio 5:3, then let the first number be 5x and second number be 3x. As second number is 10 more than the other, so it will be 3x+10.5x=3x+10

Since the two parts are in the ratio 5:3, then let the first number be 5x and second number be 3x. As second number is 10 more than the other, so it will be 3x+10.5x=3x+102x=10

Since the two parts are in the ratio 5:3, then let the first number be 5x and second number be 3x. As second number is 10 more than the other, so it will be 3x+10.5x=3x+102x=10x=5

Since the two parts are in the ratio 5:3, then let the first number be 5x and second number be 3x. As second number is 10 more than the other, so it will be 3x+10.5x=3x+102x=10x=5The first number becomes 5(5)=25 and second number becomes 3(5)=15.

Since the two parts are in the ratio 5:3, then let the first number be 5x and second number be 3x. As second number is 10 more than the other, so it will be 3x+10.5x=3x+102x=10x=5The first number becomes 5(5)=25 and second number becomes 3(5)=15.The new number will be 25+15=40.

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Answer 2

$\huge\sf{\bold{\red{Given\::}}}$

• $\sf{One\:Part\:\leadsto\:10\:+\:x}$
• $\sf{Two\:Part\:in\:Ratio\:\leadsto\:5\::\:3}$

${ }$

$\huge\sf{\bold{\red{Find\::}}}$

• $\sf{Numbers\:and\:Two\:Parts}$

${ }$

$\huge\sf{\bold{\red{Solution\::}}}$

• $\sf{Let\:one\:part\:of\:number\:\leadsto\:x}$

• $\sf{Therefore,\:other\:part\:of\:number\:\leadsto\:x\:+\:10}$

${ }$

$\bigstar\underline{\boldsymbol{According \;to \;the\: given \;Question\; :}}$

${ }$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{\frac{x\:+\:10}{x}}\:=\:{\frac{5}{3}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{3\:(x\:+\:10)\:=\:5x}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{30\:=\:5x\:-\:3x}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{30\:=\:2x}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{x\:=\:{\frac{30}{2}}}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{x\:=\:15}$

${ }$

• $\sf{Therefore\:one\:part\:of\:number\:\mapsto\:15}$

$\:\:\:\:\:\:\:\::\:\Longrightarrow\sf\:{Other\:Part\:=\:15\:+\:10\:=\:25}$

${ }$

• $\sf{Hence\:Number\:=\:15\:+\:25\:\mapsto\:40}$

${ }$

$\:\:\:\:\:\:{\bold{\purple{\dag}}}\:{\underline{\sf{So,\:the\:number\:is\:{\mathfrak{\bold{\orange{40}}}}\:and\:the\:two\:parts\:is\:{\mathfrak{\bold{\orange{25}}}}}}}.$