Question

Two numbers are in the ratio of 5:6. If 8 is subtracted from each of the numbers, the ratio becomes 4:5. find the numbers

Answer 1

let the two no be x and y
therefore x / y = 5 / 6
6 * x = 5 * y
6 * x - 5 * y = 0             * 5
    30 * x -     25 * y = 0 ..................(i)
also (x - 8)/(y - 8) = 4 / 5
5 * x - 40 = 4 * y - 32
5 * x - 4 * y - 8 = 0                 *6
30 * x - 24 * y - 48 = 0 .....................(ii)
subtracting  (i) from (ii)
y - 48 = 0
y = 48
putting y = 48 in x/y = 5/6
x/48 = 5/6
x = 5 * 48 / 6
x = 5 * 8
x = 40
therefore the two numbers are 40 and 48
follow me......

Answer 2

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Let the first number be $5x$ and second number be $6x.$

If $8$ is subtracted,

Then the numbers are,

$(5x - 8)$ and $(6x - 8)$

And their ratio is $\frac{4}{5}$

ATQ

$\frac{5x - 8}{6x - 8} = \frac{4}{5}$

$5(5x - 8) = 4(6x - 8)$

$25x - 40 = 24x - 32$

$25x - 24x = - 32 + 40$

$x = 8$

Then the numbers are:-

$5x = 5(8 )= 40$

$6x = 6(8) = 48$

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