Question

इस समय ए की आयु ब की आयु से दो गुनी है। 8 वर्ष बाद उनकी आयु 7:4 के अनुपात में हो जाएगी। इस समय प्रतेक की आयु कितनी है?​

Answer 1

◻$\large{\underline{\underline{\mathfrak{\green{\bf{Solution:-}}}}}}$.

$\large\underline{\:Find\:Here:-\:}$

• Age of A

• Age of B

◼$\large{\underline{\underline{\mathfrak{\bf{Explanation:-}}}}}$.

◼Let,

• Age Of A = x years

• Age of B = y years .

A/C to questions ,

• A age is twice the age of B

So,

$\large{\boxed{\:x= 2y}}$............(1)

Again, A/c to questions ,

• After 8 years ratio of there ages will be 7:4 !

So,

$\large{\boxed{\frac{x+8}{y+8}\:=\:7\::4}}}$

$\implies\:4(x+8)\:=\7(y+8)\:$

$\implies\:4x+32\:=\:7y+56$

$\implies\:4x-7y\:=\:56-32$

$\implies\:4x-7y\:=\:24$.........(2)

Solve Equations (1) and (2) .

• $\:x-2y\:=\:0$.........(3)

• $\:4x-7y\:=\:24$................(4)

Multiply by 4×(1) .

• $\:4x\:-\:8y\:=\:0$.........(5)

Now,

Subtract (5) - (4) ,

we get,

$\implies\:-y\:=-24$

$\boxed{\implies\:y\:=\:24}$

By equations (5), Keep value of y,

$\implies\:4x-8×24\:=\:0$

$\implies\:4x\:=\:8×24$

$\implies\:x\:=\frac{8×24}{4}$

$\boxed{\implies\:x\:=\:48}$

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$\large{\underline{\underline{\mathfrak{\bf{Answer:-}}}}}$.

• Age of A = 48 years .

• Age of B = 24 years .

______________________

$\large{\underline{\underline{\mathfrak{\vf{Answer\:Checking:-}}}}}$.

• A ages is twice the age of B

a/c to this ,

$\implies\:age\:of\:A\:=\:2×(age\:age\:of\:B)$

$\implies\:48\:=2×(24)$

$\implies\:48\:=\:48$

[Thats Proved ]

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