Question

Two number are in the ratio 2:3. If 4 be subtracted from each, they are in the ratio 3:5. The number are​

Answer 1

Answer:

The Numbers are 16 and 24.

Step-by-step explanation:

Gívєn -

Two numbers are in Ratio = 2 : 3

If 4 is subtracted from each, they are in the ratio = 3:5

Tσ fínd -

The Numbers

Sσlutíσn -

Let the numbers be as -

• One as 2x
• Second as 3x

$\rule{300}{1.5}$

When 4 is subtracted -

• First Number --> (2x - 4) --> 3
• Second Number --> (3x - 4) --> 5

$\rule{300}{1.5}$

★ $\boxed{\sf{\frac{(2x - 4)}{(3x - 4)} = \frac{3}{5}}}$

$\sf{\implies} \: \dfrac{(2x - 4)}{(3x - 4)} = \dfrac{3}{5}$

$\sf{\implies} \:Cross \: Multiply$

$\sf{\implies} \:5(2x - 4) = 3(3x - 4)$

$\sf{\implies} \:10x - 20 = 9x - 12$

$\sf{\implies} \:10x - 9x = 20 - 12$

$\sf{\implies} \:x = 8$

$\rule{300}{1.5}$

First Number -

$\sf{\implies} \:2x$

$\sf{\implies} \:2(8)$

$\sf{\implies} \:16$

First Number = 16

$\rule{300}{1.5}$

Second Number -

$\sf{\implies} \:3x$

$\sf{\implies} \:3(8)$

$\sf{\implies} \:24$

Second Number = 24

$\therefore$ The Numbers are 16 and 24.

Answer 2

Answer:

$\huge{\pink{\green{\sf{first\:number=16}}}}$

$\huge{\pink{\green{\sf{second\:number=24}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In question we have to find two unknown numbers by the given information.

▪So according to given question:

$\: \: \: \: \: \: \: \: \: \: { \orange{ \underline{given}}} \\ {\green{ratio = 2 : 3}} \\ {\green{let \: first \: number= 2x}} \\ {\green{let \: second \: number= 3x}} \\ \: \: \: \: \: \: \: \: \: \: { \red{ \underline{again,}}} \\ {\green{ratio = 3 : 5 \: \: (when \: 4 \: is \: subtracted \: from \: each \: number}} \\ {\green{let \: first \: number= 3x}} \\ {\green{let \: second \: number= 5x}}$

▪So from this information we get two eqn in which only one variable to be find that is X.

$\to \frac{2x - 4}{3x - 4} = \frac{3x}{5x} \\ \to 10 {x}^{2} - 20x = 9 {x}^{2} - 12x \\ \to 10 {x}^{2} - {9x}^{2} = - 12x + 20x \\ \to {x}^{2} = 8x \\ \to x \times x = 8x \\ \to x = \frac{8x}{x} \\ \to x = 8$

▪We get the value of x that is x=8.

$\to first \: number = 2x \\ { \green{\therefore first \: number = 2 \times 8 = 16}} \\ \\ \to second \: number = 3x \\ { \green{\therefore second \: number = 3 \times 8 = 24}}$

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