Question

the ratio of two number is 3 : 4. if 5 is subtracted from each of the number the ratio becomes 5:7. find the number.

Answer 1

let the numbers be 3x and 4x .When. 5 is subtracted form them let the numbers be 5y and 7y respectively. 3x-5=5y and 4x-5=7y=> 3x-5y=5 and 4x-7y=5 . multiply first equation by 4 and second equation by 3 then we get 12x-20y=25 and 12x-21y=15 .Subtract 2nd equation from 1st equation , we get 12x-20y-(12x-21y)=25-15=10=> y=10 . So 3x-5(10)=5=>3x=55=> x=55/3 . So the numbers are 3(55/3) and 4(55/3) =>55 and 220/3 .

Answer 2

Answer:

Let one number be x and another number be y,

According to question x : y = 3 : 4

x = 3k, y = 4k …(i)

Again = $\frac{x -5}{y-5}$

⇒ 7x – 35 = 5y – 25

(by cross multiplication)

⇒ 7x – 5y – 10 ….(ii)

Substituting the value of x and y in equation (ii), we get

7 × 3k – 5 × 4k = 10

⇒ 21k – 20k = 10

⇒ k = 10

Hence, x = 3k = 3 × 10 = 30

and y = 4k = 4 × 10 = 40.