Question

two Numbers are in the ratio 5:6 . if 8 is subtracted from each , the ratio become 4:5 find the number ​

Answer fast

Answer 1

Step-by-step explanation:

Let us consider the two numbers are x and y

Given:

x/y = 5/6

x × 6 = y × 5

6x – 5y = 0………………..(1)

If 8 is subtracted from each of the numbers then the ratio is 4:5.

x−8y−8=45

⇒ 5x – 40 = 4y – 32

Then the equation is

5x – 4y = 8……………….(2)

From equation (1)

x = 5y/6

Substituting value of x in equation (2)

5(5y/6) – 4y = 8

y = 48

Substitute the value of y in equation (1) we get

6x – 5(48) = 0

6x = 240

x = 40

Therefore the numbers are 40 and 48..........

Hope this is helpful

Answer 2

Given :

➨ Two numbers are in the ratio = 5:6

If 8 is subtracted from each , the ratio become 4:5.

To Find :

➨ The required numbers.

Solution :

➨ Let the one number be 5x.

➨ According to question ,

$\tt{ \implies{\sf{\dfrac{One\:number -8}{Other\:number-8} = \dfrac{4}{5} }}}$

$\tt{\implies{\sf{\dfrac{5x - 8}{6x - 8} = \dfrac{4}{5} }}}$

$\tt{\implies{\sf{5(5x - 8) = 4(6x - 8 ) }}}$

$\tt{\implies{\sf{25x - 40 = 24x - 32 }}}$

$\tt{\implies{\sf{25x - 24x = - 32 + 40 }}}$

$\tt{\implies{ \boxed{ \tt{x = 8 }}}}$

$\therefore {\underline{\sf{\pink{One\:number\:is\:(5\times 8)=40.}}}}$

$\therefore {\underline{\sf{\pink{Other\:number\: is\:(6\times 8)=48.}}}}$

Verification :

➨ We have,

➨ One number = 40

➨ Other number =48

➨ Two numbers are in the ratio = 5 : 6

$\tt{\implies{ \sf{One\:number : Other\:number = 5:6 }}}$

$\tt{</p><p>\implies{ \sf{40 :48 = 5:6 }}</p><p>}$

$\tt{\implies{ \sf{\dfrac{\cancel{40}}{\cancel{48}} = 5 :6}}}$

$\tt{\implies{ \sf{ \dfrac{5}{6} = 5: 6 }}}$

$\tt{\implies{ \sf{5:6 = 5:6 }}}$

$\tt{\implies{ \boxed{ \tt{LHS = RHS }} }}$

$\bf{\therefore {\underline{\bf{ \: \: Verified.}}}}$