Question

Two numbers are in the ratio 2:3. If 5 is added to each number, then the new numbers are in the ratio 3:4 find the numbers​

Answer 1

Answer:

Given :-

• Two numbers are in the ratio of 2 : 3.
• 5 is added to each number, then the new numbers are in the ratio of 3 : 4.

To Find :-

• What is the numbers.

Solution :-

Let,

$\mapsto \bf{First\: number =\: 2y}$

$\mapsto \bf{Second\: number =\: 3y}$

$\pink{\bigstar}\: \: \bf{According\: to\: the\: question\: :-}$

$\leadsto$ 5 is added to each number, then the new numbers are in the ratio of 3 : 4.

$\implies \sf \dfrac{First\: number + 5}{Second\: number + 5} =\: New\: number$

$\implies \sf \dfrac{2y + 5}{3y + 5} =\: \dfrac{3}{4}$

$\pink{\bigstar}\: \: \bf{By\: doing\: cross\: multiplication\: we\: get\: :-}$

$\implies \sf 3(3y + 5) =\: 4(2y + 5)$

$\implies \sf 9y + 15 =\: 8y + 20$

$\implies \sf 9y - 8y =\: 20 - 15$

$\implies \sf\bold{\purple{y =\: 5}}$

Hence, the required numbers are :

➲ First number :

$\longrightarrow \sf First\: number =\: 2y$

$\longrightarrow \sf First\: number =\: 2(5)$

$\longrightarrow \sf\bold{\red{First\: number =\: 10}}$

➲ Second number :

$\longrightarrow \sf Second\: number =\: 3y$

$\longrightarrow \sf Second\: number =\: 3(5)$

$\longrightarrow \sf\bold{\red{Second\: number =\: 15}}$

${\small{\bold{\purple{\underline{\therefore\: The\: numbers\: are\: 10\: and\: 15\:. </p><p>\:}}}}}$

Answer 2

▪ Given :-

• The ratio of two numbers is 2:3

• After adding 5 to each number three ratio of new numbers is 3:4

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▪ To Find :-

• Both of the Numbers

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▪ Solution :-

Let,

The First Number be = 2x

According to the Given Condition ,

Second Number Must be = 3x

《After Adding 5 to each number》

• First Number = 2x + 5

• Second Number = 3x + 5

According to the Given Condition ,

$\sf{ \dfrac{2x + 5}{3x + 5} } = \frac{3}{4} \\ \\ \sf : \longmapsto \: 4(2x + 5) = 3(3x + 5) \\ \\ : \longmapsto \: \sf8x + 20 = 9x + 15 \\ \\ : \longmapsto \: \sf9x - 8x = 20 - 15 \\ \\ \Large \purple{ :\longmapsto \underline {\boxed{{\bf x = 5} }}}$

$\huge \underline \mathcal{Hence,}$

• First Number = 2 × 5 = 10

• Second Number = 3 × 5 = 15

$\pink{\underline \mathcal{{So,\:The \:\:Two\: \:Numbers \: \:are\: \: 10 \:\: And\:\: 15}}}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is\:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer}}$

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