Question

Two numbers are in the ratio 2 : 3. If 4 be subtracted from each, they are in the ratio 3 : 5. Find the number

Answer 1

$\huge\mathbb\red{Answer}$

Let the two no.s be x and y

$\mathcal\blue{the\: numbers \:are\: in\: the \:ratio \:3:4 }$

it means ; x/y = 3/4 ___ Equation 1

when 4 is subtracted from each of the numbers the ratio becomes 5:7

i.e; (x-4)/ (y-4) = 5/7___ Equation 2

Taking the equation 1 and crossed multiply we get 4x=3y

x= (3/4) y

now take the second equation and do the same thing and after simplification we get 7x-28 = 5y-20 ____ equation 3

substitute the value of x i.e; (3/4)y in equation 3

⏩7(3/4)y-28 = 5y-20

⏩(21y/4)-28 = 5y-20

⏩(21y/4)-5y = 28-20

(⏩21y-20y)/4 = 8 (take 4 as L.C.M)

y/4 = 8

y= 32

now substitute y=32 in the equation x=(3/4)y

we get x as 24.

therefore 24/32= (8*3)/(8*4)= 3/4

subtracting 4 from each we get 20/28= (4*5)/(4*7)= 5/7.

which satisfies the above conditions so the two numbers x and y are 24 and 32.