Question

the ages of ruby and ranju are in ratio 5:3. ten years hence the ratio of their ages will be 7:5 find their present age.

Answer 1

Answer:

present ages of ruby = 5x = 5*5 = 25

present age of ranju = 3x = 3*5 = 15

Step-by-step explanation:

5x+10 / 3x + 10 = 7/5

25x+50 = 21x + 70

25x - 21x = 70 - 50

4x = 20

x = 5

Answer 2

Find the present ages of Ruby and Ranju ,if their age ratio is 5:3 and after ten years their ratio will be 7:5

Definition:

A ratio is an ordered pair of numbers while a proportion is an equation in which two ratios are set equal to each other.

Step-by-step explanation:

Let x be the present age of Ruby and y be the present age of Ranju,so it is expressed as follows,

[tex]\frac{x}{y} =\frac{5}{3}\\ 3x=5y\\ 3x-5y=0[/tex]          (1)

After ten years their ages will be in the ratio 7:5,so

[tex]\frac{x+10}{y+10}=\frac{7}{5}\\ 5(x+10)=7(y+10)\\ 5x+50=7y+70\\ 5x-7y=70-50\\ 5x-7y=20[/tex](2)

Multiply Equation (1) by 5 ,and equation (2) by 3,so we get

[tex]15x-25y=0\\ 15x-21y=60[/tex]

Subtract these two equations,

[tex]15x-25y=0\\ 15x-21y=60[/tex]

(-)    (+)       (-)

____________

[tex]-4y=-60\\ y=15[/tex]

Substitute $y=15$ in equation (1)

[tex]3x-5y=0\\ 3x-5(15)=0\\ 3x-75=0\\ 3x=75\\ x=25[/tex]

Therefore,the present age of Ruby is 25 and Ranju is 15.