Question

harsh mother present age is six times harsh present age. harsh age five years from now will be one third of his mother present age. what are their present ages
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Answer 1

Answer:

The present ages of Harsh and his mother are 5 years and 30 years respectively.

Step-by-step-explanation:

Let the present age of Harsh be x years.

∴ The present age of Harsh's mother = 6x years

Now,

Five years after Harsh's age = ( x + 5 ) years

From the given condition,

$\displaystyle{\sf\:(\:x\:+\:5\:)\:=\:\dfrac{1}{\cancel{3}}\:\times\:\cancel{6}\:x}$

$\displaystyle{\implies\sf\:(\:x\:+\:5\:)\:=\:2x}$

$\displaystyle{\implies\sf\:x\:+\:5\:=\:2x}$

$\displaystyle{\implies\sf\:5\:=\:2x\:-\:x}$

$\displaystyle{\implies\sf\:x\:=\:5}$

$\displaystyle{\therefore\:\boxed{\pink{\sf\:Harsh's\:present\:age\:=\:5\:years\:}}}$

Now,

$\displaystyle{\sf\:Mother's\:present\:age\:=\:6x}$

$\displaystyle{\implies\sf\:Mother's\:present\:age\:=\:6\:\times\:5}$

$\displaystyle{\therefore\:\boxed{\red{\sf\:Mother's\:present\:age\:=\:30\:years\:}}}$

Answer 2

Answer:

$\qquad\qquad\underline{\textsf{\textbf{ \color{magenta}{Solution\:completed} }}}$

GIVEN :-

• Harsh's mother age is 6 times of Shobo.

• After 5yrs Harsh's age will be 1/3 of his mothers present age.

TO FIND :-

• Their present ages

SOLUTION :-

Let Harsh's Present age be x

Then Harsh's mother age will be 6x

Now,

According to the Question,

➙ x + 5 = 1/3 ( 6x )

We will solve this linear equation in two Variable to get the ages of Harsh and his mother.

➙ x + 5 = 1/3 (6x)

➙ x + 5 = 1/3 × 6x

➙ x + 5 = 2x

➙ x - 2x = -5

➙ -x = -5

➙ ${\large{\bold{\purple{\underline{x =\: 5}}}}}$

Hence Harsh's present age is 5yrs and present age of mother will be

Hence Harsh's present age is 5 yrs and present age of mother will be 5 × 6 = 30 yrs.

VERIFICATION :-

➠ x + 5 = 1/3 (6x)

➠ 5 + 5 = 1/3 × 6 × 5

➠ 10 = 2 × 5

➠ 10 = 10

➲ LHS = RHS

Our answer is Correct !