Question

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

numbers are
(a) (16, 24)
(b) (4, 6)
(c) (2, 3)
(d) none of these
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Answer 1

Answer:

Answer : I think opition (4 , 6).

Answer 2

Answer:

Given :

$\textsf{Ratio of two numbers = 2:3}$

$\textsf{After subtracting with 4 the ratio become 3:5}$

To find :

$\textsf{The numbers }$

Concept :

Let the numbers be 2x and 3x .

So , the number are subtracted by 4 and it became 3:5 . So , now the equation will be form like this -:

$\sf{\boxed{\dfrac{2x-4}{3x-4}=\dfrac{3}{5}}}$

After finding the value of x . Then , multiply the number with 2 and 3 .

Solution :

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

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

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

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

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

$\textsf{So , the value of x is 8}$

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Now , find the numbers -:

$\sf{\implies{▪︎First\:number=8×2}}$

$\sf{\implies{First\:number=16}}$

$\sf{\implies{▪︎Second\:number=8×3}}$

$\sf{\implies{Second \:number=24}}$

Answer :

So , the answer is option (a) .

Or the numbers are 16 and 24 respectively.