Question

The sum of two numbers which are in the ratio 2:5 is 21 the number are

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The sum of two numbers are in the ratio 2:5 is 21}$

$\underline{\textbf{To find:}}$

$\textsf{The two numbers}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the two numbers be x and y}$

$\mathsf{Then,}$

$\mathsf{x+y=21\;\;\;\&\;\;\;x:y=2:5}$

$\mathsf{x+y=21\;\;\;\&\;\;\;\dfrac{x}{y}=\dfrac{2}{5}}$

$\mathsf{y=21-x\;\;\;\&\;\;\;\dfrac{x}{y}=\dfrac{2}{5}}$

$\implies\mathsf{\dfrac{x}{21-x}=\dfrac{2}{5}}$

$\implies\mathsf{5x=42-2x}$

$\implies\mathsf{5x+2x=42}$

$\implies\mathsf{7x=42}$

$\implies\mathsf{x=\dfrac{42}{7}}$

$\implies\boxed{\mathsf{x=6}}$

$\mathsf{when\;x=6,\;y=21-6=15}$

$\therefore\textbf{The two numbers are 6 and 15}$

Answer 2

Answer:

x=6,y=15

Step-by-step explanation:

Given:- The sum of two numbers which are in the ratio 2:5 is 21.

To Find:- Two number i.e x , y.

Solution:

Let the two number be x & y.

$\frac{x}{y}$ = $\frac{2}{5}$  .......eq(1)

x+y=21 ......eq(2)

solve eq (1).

x=21-y .......eq(3)

Putting the value of eq(3) in eq(1)

$\frac{21-y}{y}$ = $\frac{2}{5}$

⇒5(21-y)=2y

⇒105-5y=2y

⇒7y=105

⇒y=$\frac{105}{7}$=15

now,putting the value of y in eq(3)

x=21-y=21-15=6

∴x=6,y=15

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