Question

Abhishek is 6 years older than jagdeesh.six years ago abhishek was twice as old as jagdeesh.write the situain in algebraic expression and find how old is each now ?

Answer 1

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{let:}}}}$

• $\sf{The\:age\:of\:Abhishek=x}$
• $\sf{The\:age\:of\:Jagdeesh=y}$

$\small{\underline{\green{\rm{Given:}}}}$

• $\sf{Abhishek\:is\:6\: years\: older\:than\:jugdeesh}$
• $\sf{6\: years\:ago\:Abhishek\:was\: twice\:of\: jugdeesh}$

$\small{\underline{\orange{\rm{To\: Find:}}}}$

• $\sf{The\:age\:of\:Abhishek\:and\: Jugdeesh}$

$\small{\underline{\green{\rm{According\: to\:1st\:case:}}}}$

$\rm{\implies x=y+6}$

$\rm{\implies x-y=6}$

$\rm\pink{\implies x-y=6-----(i)}$

$\small{\underline{\green{\rm{According\: to\:2nd\:case:}}}}$

$\rm{\implies x-6=2(y-6)}$

$\rm{\implies x-6=2y-12}$

$\rm{\implies x-2y=-12+6}$

$\rm\pink{\implies x-2y=-6------(ii)}$

• $\sf{in\:eq\:1st\: multiplying\:by\:2}$

$\rm{\implies 2x-2y=12}$

$\rm{\implies x-2y=-6}$

• $\sf{By\: solving\:equation\:we\:get}$

$\rm\red{\implies x=18}$

• $\rm{putting\: the\: value\: of\:x=18\:in\:eq\:1}$

$\rm{\implies x-y=6}$

$\rm{\implies 18-y=6}$

$\rm{\implies -y=6-18}$

$\rm\red{\implies y=12}$

Hence,

$\sf{\implies The\:age\:of\:Abhishek=x=18\: year's}$

$\sf{\implies The\:age\:of\: Jagdeesh=y=12\: year's}$

Answer 2

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$\huge\tt{GIVEN:}$

• Abhishek is 6 years older than jagdeesh
• Six years ago, Abhishek was twice as old as jagdeesh

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$\huge\tt{SOLUTION:}$

At present time,

Let us assume that the age of Jagdeesh is x , Then the age of Abhishek would be (x+6)

Six years ago,

↪Jagdeesh = (x-6)

↪Jagdeesh = (x-6)↪ Abhishek = (x+6-6)

We can say that,

↪(x-6) / (x+6-6) = 2x / x

↪x(x-6) = 2x(x+6-6)

↪2x - 6x = 3x + 12x - 12x

↪4x = 3x

↪x = 4 × 3

↪x = 12 years

↪x + 6 = 18 years

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Age of Jagdeesh = 12 years

Age of Abhishek = 18 years

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