Question

the present age of Ram and Rahim are in the ratio 4:3 .Four years later their ages will be in the ratio 5:6 what are their present ages

Answer 1

4x. 3x
+5 +5
5. 6
x*9= 5*1
x=5/9

Answer 2

Correct Question:-

The present age of Ram and Rahim are in the ratio $4:3$ .Four years later their ages will be in the ratio $6:5.$ What are their present ages.

Solution:-

It is given that the ratio of the present ages of Ram and Rahim is $4:3,$

Let us take the present age of Ram be $(4x)$

And Rahim's be$(3x)$

After four years:

Ram's age=$(4x+4)yrs.$

Rahim's age=$(3x+4)yrs.$

According to Question,

$(4x+4) : (3x+4)= 6:5$

$⟾\dfrac{4x+4}{3x+4}=$$\frac{6}{5}$

$⟾\sf{5}(4x+4)=6(3x+4)$

$⟾\sf{20x+20=18x+24}$

$⟾\sf{20x-18x=24-20}$

$⟾\sf{2x=4}$

⟾$\sf{x}=\dfrac{4}{2}$

⟾$\sf{x=2}$

Therefore,we got the value of x,i.e.$2$

≈Present age of Ram=

$(4×2)=8$

≈Present age of Rahim=

$(3×2)=6$

$\sf\green{Let's\: verify\:the\:ans:-}$

$\sf\dfrac{Present\:age\:of\Ram}{Present\:age\:of\Rahim}$

⟾$\sf\dfrac{8}{6}$

⟾$\sf\dfrac{4}{3}$(Table of 2)

⟾$\sf\red{4 : 3 }$

Hence,L.H.S.=R.H.S.

Therefore,the solution is correct.