Question

10 year ago mohan was thrice the old ram was bur 10 year hence he will be twice old as ram find the mohan present age

Answer 1

10 years ago,

Let the age of Ram was x years

And the age of Mohan was 3x years [ 3 times of ram's age ]

∴ Present age of Ram = age before 10 years + 10 years

      ⇒ x years + 10 years

      ⇒ ( x + 10 ) years

Present age of Ram = ( x + 10 ) years

∴ Present age of Mohan = age before 10 years + 10 years

     ⇒ 3x years + 10 years

    ⇒ ( 3x + 10 ) years

According to the question,

10 year hence, Mohan will be twice old as Ram.

Age of Mohan 10 years hence = present age + 10 years

Age of Mohan 10 years hence = 3x + 10 years + 10 years

Age of Mohan 10 years hence = ( 3x + 20 ) years

Age of Ram 10 years hence = present age + 10 years

Age of Ram 10 years hence = ( x + 10 ) years + 10 years

Age of Ram 10 years hence = ( x + 20 ) years

∴ 3x + 20 years = 2( x + 20 ) years

⇒ 3x + 20 = 2x + 40

⇒ 3x - 2x = 40 - 20

⇒ x = 20

Thus,

Present age of Mohan = 3x + 10 years = 3( 20 ) + 10 years = 60 + 10 years

Present age of mohan is 70 years.

Answer 2

Let Mohan age = x
Ram age = y

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A.T.Q.
x-10=3(y-10)
x-10=3y-30
x-3y=-30+10
x-3y=-20----1

Second
x+10=2(y+10)
x+10=2y+20
x-2y=20-10
x-2y=10----2

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Solving both the equations

x-3y=-20
x-2y=10
In equation second multiply by (-) sine

x-3y=-20
-x+2y=-10
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-y=-30
y=30

Putting y in equation 1

x-3y=-20
x-3(30)=-20
x-90=-20
x=-20+90
x=70

Mohan present age =70