Question

The ratio between two numbers is 4:7. If 8 is added to each number, the ratio becomes 3:5. Find the numbers.

Answer 1

Let the 2 numbers be x and y respectively.

Given

The ratio between two numbers is 4:7.

$\implies \dfrac{x}{y} = \dfrac{4}{7}$

$\implies 7x=4y$

$\implies 7x-4y=0--(1)$

If 8 is added to each number, the ratio becomes 3:5.

$\implies \dfrac{x+8}{y+8}=\dfrac{3}{5}$

$\implies 5x+40=3y+24$

$\implies 5x-3y=24-40$

$\implies 5x-3y= -16--(2)$

(1) * 3

(2) * 4

$21x-12y=0\\\underline{20x-12y=-64}\\\underline{\underline{x=64}}$

Now, Substituting the value of x in the second equation. we get,

$320-3y=-16\\\implies -3y =-16-320\\\implies -3y = -336\\\implies y = 112$

$\boxed{\boxed{\bold{Therefore, \ the \ numbers \ are \ 64 \ and \ 112}}}}}}$

                                                           

Answer 2

$\blue{\underline{\underline{\sf{Given-}}}}$

The ratio between two numbers is 4:7.

$\blue{\underline{\underline{\sf{So,}}}}$

Let one number be 4x

And another number be 7x

$\blue{\underline{\underline{\sf{Now,}}}}$

According to the question,

If 8 is added to each number then the ratio becomes 3:5

$\blue{\underline{\underline{\sf{Here:}}}}$

$\implies\bf \frac{4x+8 }{7x+8}= \frac{3}{5}$

$\implies \bf 5 \times (4x+8) = 3\times (7x+8)$

∵ Cross Multiplication

$\implies \bf 20x+40 = 21x+24$

$\implies \bf 40-24 = 21x-20x$

∵ Taking (24) to LHS and (20x) to RHS

$\implies \bf 16=1x$

$\red{\underline{\sf{REQUIRED\:\: NUMBERS\:\: ARE-}}}$

4x = 4 × 16 = 64

7x = 7 × 16 = 112

Hence,

The numbers are 64 and 112