Question

two numbers are in the ratio 5:6 if 8 is subtracted from each of the number the ratio becomes 4:5 find the numbers

Answer 1

let the ratio be 5x and 6x.
According to question,
5x-8÷6x-8=4÷5
or,(5x-8)5=4*6x-8
or,25x-40=24x-32
or,-40+32=24x-25x
or,-8=-x
x=8 answer

Answer 2

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

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