Question

35. Two numbers are in the ratio of 2:3. If 2 is added to both, the ratio becomes 3/4. ​

Answer 1

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Answer 2

$\Large{\underline{\underline{\bf{\:Question}}}}$

Two numbers are in the ratio of 2:3. If 2 is added to both, the ratio becomes 3/4.

$\Large{\underline{\underline{\bf{\:Solution}}}}$

$\Large{\underline{\bf{\:Given}}}$

➥$\textsf{Ratio Of Two Number = 2:3}$

➥$\textsf{If 2 is added to both, the ratio becomes 3/4}$

$\Large{\underline{\underline{\bf{\:Explanation}}}}$

Let,Two Number are x and y .

$\:\:\:\:\:\:\small\textsf{\green{( According to Question )}}$

$\:\:\:\:\:\:\small\textsf{\green{ (Ratio Of Two Number = 2:3 )}}$

➥$\sf{\:x:y\:=\:2:3}$

➥$\sf{\:\dfrac{x}{y}\:=\:\dfrac{2}{3}}$

➥$\sf{\pink{\:3x-2y\:=\:0}}$......[equ(1)]

$\:\:\:\small\textsf{\green{ (If 2 is added to both, the ratio becomes 3/4)}}$

➥$\sf{\:(x+2):(y+2)\:=\:3:4}$

➥$\sf{\:(4x+8-3y-6)\:=\:0}$

➥$\pink{\sf{\:(4x-3y)\:=\:-2}}$.....[equ(2)]

$\:\:\:\:\:\:\small\textsf{\green{( Multiply by 4 in equ(1) and 3 in equ(2) )}}$

• $\sf{\:(12x-8y)\:=\:0}$
• $\sf{\:(12x-9y)\:=\:-6}$

$\:\:\:\:\:\:\small\textsf{\green{( Subtract above equation )}}$

➥$\sf{\boxed{\boxed{\orange{\:y\:=\:6}}}}$

$\:\:\:\:\:\:\small\textsf{\green{( Keep Value of y in equ(1) )}}$

➥$\sf{\:(3x-2\times6)\:=\:0}$

➥$\sf{\:(3x)\:=\:12}$

➥$\sf{\:x\:=\:\dfrac{\cancel{12}}{\cancel{3}}}$

➥$\sf{\boxed{\boxed{\orange{\:x\:=\:4}}}}$

$\Large{\underline{\underline{\bf{\:Thus}}}}$

➩$\pink{\textsf{First Number is x = 4}}$

➩$\pink{\sf{\:Second\:Number\:is\:y\:=\:6}}$

_________________

$\Large{\underline{\underline{\bf{\:Answer\:Verification}}}}$

Case(1):-

$\:\:\:\:\:\:\small\textsf{\green{ (Ratio Of Two Number = 2:3 )}}$

➩$\sf{\:(x:y)\:=\:(2:3)}$

➩$\sf{\:(\cancel{4}):(\cancel{6})\:=\:(2:3)}$

➩$\sf{\:(2:3)\:=\:(2:3)}$

L.H.S.=R.H.S.

Case(1) Proved !

__________________

Case(2):-

$\:\:\:\small\textsf{\green{ (If 2 is added to both, the ratio becomes 3/4)}}$

➩$\sf{\:(x+2):(y+2)\:=\:(3:4)}$

➩$\sf{\:(4+2):(6+2)\:=\:(3:4)}$

➩$\sf{\:(\cancel{6}):(\cancel{8})\:=\:(3:4)}$

➩$\sf{\:(3:4)\:=\:(3:4)}$

Both Case are proved .

Hence, we can say that the value of first and second number is correct.

__________________