Question

8. Shalinis was three times as old as her son two
years ago Two years hence twice of her age will
be equal to five times that of her son's age. Find
their present ages.​

Answer 1

Answer:

REFER IN ATTACHMENT

MARK AS BRAINLIST ANSWER

Answer 2

$\huge\mathfrak{Answer:}$

$\large\underline{\sf{\blue{Given:}}}$

• We have been given that Two years ago, Shalini was 3 times as old as her son
• Two years hence twice of her age will be equal to five times that of her son's age

$\large\underline{\sf{\blue{To \: Find:}}}$

• We have to find the present ages of Shalini and her son

$\large\underline{\sf{\blue{Solution:}}}$

Let Present age of Shalini = x

Present age of Shalini's son = y

$\large\underline{\mathfrak{\red{According \: to \: first \: Condition:}}}$

Two years ago, we know that

Shalini age = x - 2

Shalini son age = y - 2

Shalini age was 3 times as the age of his son

$\boxed{\sf{( \: Shalini \: age \: ) = 3 \times ( \: Son \: age \: ) }}$

$\implies \sf{ x - 2 = 3 \: ( y-2 ) }$

$\implies \sf{ x - 2 = 3y - 6}$

$\implies \sf{ 3y - x = 4 \qquad }$ ----------(1)

$\sf{}$

$\large\underline{\mathfrak{\red{According \: to \: second \: Condition:}}}$

Two years hence from present

Age of Shalini = x + 2

Age of Shalini son = y + 2

$\sf{}$

Twice the age of Shalini will be equal to five times the age of her son

$\boxed{\sf{2 \: ( \: Shalini \: age \: ) = 5 \: ( \: Son \: age \: ) }}$

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

$\implies \sf{2x + 4 = 5y + 10 }$

$\implies \sf{2x - 5y = 6 \qquad }$----------(2)

$\sf{}$

Multiplying by 2 in equation 1 and adding it with 2 we get

$\hookrightarrow \sf{6y - 2x + 2x - 5y = 8 + 6}$

$\hookrightarrow \sf{6y - 5y = 8 + 6}$

$\hookrightarrow \boxed{\sf{y = 14}}$

Putting y = 14 in equation 1

$\hookrightarrow \sf{3 \times 14 - x = 4}$

$\hookrightarrow \sf{x = 42 - 4}$

$\hookrightarrow \boxed{\sf{x = 38}}$

$\sf{}$

Present age of Shalini = 38 years

Present age of Shalini son = 14 years

__________________________________

$\LARGE\underline{\green{\mathtt{Verification:}}}$

Two years ago

• Age of Shalini = 38 - 2 = 36
• Age of Shalini son = 14 - 2
• From above information it is clear that Two years ago Age of Shalini was twice the age of her son

Two year hence

• Age of Shalini = 38 + 2 = 40
• Age of Shalini son = 14 + 2 = 16
• 2 x Age of Shalini = 80
• 5 x Age of Shalini son = 80

Hence Verified !!

_________________________________

$\large\purple{\underline{\underline{\mathtt{Extra \: Information:}}}}$

• Tips for solving ages Question
• If the current age is x, then n times the age will be nx.
• If the current age is x, then age n years later will be x + n.
• If the current age is x, then age n years ago was x - n.
• The ages are in a ratio a : b then ages will be ax and bx.
• If the current age is x, then 1/n of the age will be x/n

_________________________________