Question

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

ratio 3:5. Find the numbers.ans for class 7​

Answer 1

Two numbers are in the ratio 2:3,if 4 be subtracted their ratio will be 3:5,find the numbers

Definition:

A relationship between two quantities, normally expressed as the quotient of one divided by the other.

Step-by-step explanation:

Let x and y be the numbers, therefore

[tex]\frac{x}{y} =\frac{2}{3} \\ 3x=2y\\ 3x-2y=0\\ [/tex]          (1)

As the ratio after subtraction by 4 is given by,

[tex]\frac{x-4}{y-4} =\frac{3}{5} \\ 5(x-4)=3(y-4)\\ 5x-20=3y-12\\ 5x-3y=-12+20\\ 5x-3y=8[/tex]            (2)

Multiply equation (1) by 5,

$15x-10y=0$

Multiply equation (2) by 3,

$15x-9y=24$

Subtract these equation,

[tex]15x-10y=0\\ 15x-9y=24[/tex]

(-)     (+)     (-)

__________

[tex]-y=-24\\ y=24\\[/tex]

Substitute the value of y in equation (1)

[tex]3x-2y=0\\ 3x-2[24] =0\\\\ 3x-48=0\\ x=\frac{48}{3} \\ x=16[/tex]

Therefore,the numbers are 16 and 24.