Question

two numbers are such that the ratio between them is 3 is to 5 if it is increased by 10 the ratio between the number so formed is 5:7 find the original number​

Answer 1

Answer:

Step-by-step explanation:

Question:-

Two numbers are such that the ratio between them is 3 is to 5 if it is increased by 10 the ratio between the number so formed is 5:7, then  find the original number​.

Answer:-

• Let the ratio constant be taken or assumed as x and y.
• So, the numbers we have are as
• x and y, both different constants

According to Question:-

The equation stands as:-

$\sf{\dfrac{x}{y} = \dfrac{3}{5}}$

$\sf{x = \dfrac{3y}{5}}$______________(1)

Now, second equation:-

$\dfrac{x+10}{y+10}= \dfrac{5}{7}$

$7(x+10) = 5(y+10)$

$7x+70 = 5y+50$

$7x-5y = -20$

Now, substituting value of x,

$7(\dfrac{3y}{5})-5y = -20$

$\dfrac{21y-25y}{5} = -20$

$21y-25y = -100$

4y = 100

y = 25

Now, finding the value of x.

$x = \dfrac{3y}{5}$

$=\dfrac{3 \times 25}{5}$

x = 15

Note that:-

• Cross multiplication was used.
• Placement or substitution method was used.

Answer 2

Step-by-step explanation:

Given : -

• two numbers are such that the ratio between them is 3 is to 5

• if it is increased by 10 the ratio between .

• the number so formed is 5:7

To Find : -

• find the original number

Let x and y be the two numbers .

Now,

According to the question :

∵ x = 3y / 5 ........( 1 ).

∵ ( x + 10 ) : ( y + 10 ) = 5 : 7 .

⇒ 7( x + 10 ) = ( y + 10 ) 5 .

⇒ 7x + 70 = 5y + 50 .

⇒ 7x + 20 = 5y. ........( 2 ).

Put value of 'x' from equation ( 1 ) in ( 2 ) .

⇒ 7× 3y/5 + 20 = 5y .

⇒ ( 21y + 100 ) / 5 = 5y .

⇒ 100 = 4y .

∴ y = 25 .

Put y = 25 in equation ( 1 ), we get

⇒ x = 3 × 25 / 5

∴ x = 15

Hence Original numbers are x and y = 15 and 25 .

More information : -

A term is either a single number or variable, or the product of several numbers or variables.

• In elementary mathematics, a term is either a single number or variable, or the product of several numbers or variables.

For Example, : -

3x + 2x² + 5x + 1 = 2x² + (3+5)x + 1 = 2x² + 8x + 1, with like terms collected.

• A series is often represented as the sum of a sequence of terms.