Answer:
[tex]Ratio = 11:13[/tex]
Step-by-step explanation:
Represent Amar age with x
Represent Kabir age with y
So, we have:
Presently
[tex]x : y = 3 : 4[/tex]
After 4 years
[tex]x + 4 : y + 4 = 7 : 9[/tex]
Simplify both ratios:
[tex]x : y = 3 : 4[/tex]
[tex]\frac{x}{y} = \frac{3}{4}[/tex]
Cross Multiply
[tex]4x = 3y[/tex]
Make x the subject
[tex]x = \frac{3}{4}y[/tex]
[tex]x + 4 : y + 4 = 7 : 9[/tex]
[tex]\frac{x + 4}{y + 4} = \frac{7}{9}[/tex]
Cross Multiply
[tex]7(y+4) = 9(x+4)[/tex]
Open Brackets
[tex]7y + 28 = 9x + 36[/tex]
Collect Like Terms
[tex]9x = 7y + 28 - 36[/tex]
[tex]9x = 7y -8[/tex]
Substitute [tex]\frac{3}{4}y[/tex] for x in [tex]9x = 7y -8[/tex]
[tex]9(\frac{3}{4}y) = 7y - 8[/tex]
[tex]\frac{27}{4}y = 7y - 8[/tex]
[tex]6.75y = 7y - 8[/tex]
[tex]6.75y - 7y = - 8[/tex]
[tex]-0.25y = - 8[/tex]
[tex]y = -8/-0.25[/tex]
[tex]y = 32[/tex]
Substitute 32 for y in [tex]x = \frac{3}{4}y[/tex]
[tex]x = \frac{3}{4} * 32[/tex]
[tex]x = \frac{3* 32}{4}[/tex]
[tex]x = \frac{96}{4}[/tex]
[tex]x = 24[/tex]
So, in 20 years time, the ratio of the ages would be:
[tex]x + 20 : y + 20[/tex]
This gives
[tex]24 + 20 : 32 + 20[/tex]
[tex]44 : 52[/tex]
Divide by 4
[tex]44/4:52/4[/tex]
[tex]11:13[/tex]
Hence, the Ratio is
[tex]Ratio = 11:13[/tex]
