Question

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

Answer 1

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★ 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

Answer 2

Let numbers are 5x and 6x

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

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

=> 25x-40 = 24x-32

=> 25x-24x= 40-32

=> x= 8

Two numbers are 5x 8= 40 and 6x8 = 48