Question

The present age of Chahat and Arshi are in the ratio 2:3. After 12 years, their age will be in the ratio 11:15. Find out the present age of Arshi.

Answer 1

Given :

• The present age of Chahat and Arshi are in the ratio 2:3. After 12 years, their age will be in the ratio 11:15.

To Find :

• The present age of Arshi = ?

Solution :

Let present age of Chahat be '2x' and present age of Arshi be '3x'.

⠀⠀━━━━━━━━━━━━━━━━━━━━━

★ According to the given Question now :

→ Chahat's age + 12 ÷ Arshi's age + 12 = 11 ÷ 15

→ 2x + 12 ÷ 3x + 12 = 11 ÷ 15

Cross multiplying both the sides :

→ 15(2x + 12) = 11(3x + 12)

→ 30x + 180 = 33x + 132

Combining like terms :

→ 180 - 132 = 33x - 30x

→ 48 = 3x

Dividing both the sides by 3 we get :

→ x = 16

⠀⠀━━━━━━━━━━━━━━━━━━━━

⚽ Finding present age of Arshi :

➻ Arshi's present age = 3x

➻ Arshi's present age = 3 × 16

➻ Arshi's present age = 48 years

• Hence,the present age of Arshi is 48 years.

═════════════════════════

❒ Points to Remember :

• If the present age is x, then y times the present age = yx.
• If the present age is x, then age y years later/hence = x + y.
• If the present age is x, then age y years ago = x – y.

═════════════════════════

Answer 2

$\huge{\boxed{\rm{\red{Question}}}}$

The present age of Chahat and Arshi are in the ratio 2:3. After 12 9years, their age will be in the ratio 11:15. Find out the present age of Arshi.

$\huge{\boxed{\rm{\red{Answer}}}}$

$\large{\boxed{\boxed{\sf{Given \: that}}}}$

• The present age of Chahat and Arshi are in the ratio 2:3

• After 12 years, their age will be in the ratio 11:15

$\large{\boxed{\boxed{\sf{To \: find}}}}$

• Present age of Arshi

$\large{\boxed{\boxed{\sf{Solution}}}}$

• Present age of Arshi = 48 years

$\large{\boxed{\boxed{\sf{What \: the \: question \: says \: ?}}}}$

$\large{\boxed{\boxed{\sf{Let's \: understand \: the \: concept \: 1^{st}}}}}$

• This question say that, there are two persons. Their names are Chahat and Arshi. The question is about their age. The present age of Chahat and Arshi are in a ratio of 2:3 Then the question say that after 12 years the ratio of their age will be 11:15. After that it asks to find the present age of Arshi.

$\large{\boxed{\boxed{\sf{How \: to \: do \: this \: question \: ?}}}}$

$\large{\boxed{\boxed{\sf{Let's \: see \: the \: procedure \: that \: is \: given \: below}}}}$

• Firstly we have to assume their present age. We assume Chatat age as 2x and Arshi's age as 3x. Now, we have to use a formula to find their age. After that a result is come. Then, we get the cake of x that is 16. As we assume her age as 3x . Now we have to multiply 3 by 16 . Then we get a result that is 48. And it's the present age of Arshi.

$\large{\boxed{\boxed{\sf{Let's \: solve \: it \: properly}}}}$

$\large{\boxed{\boxed{\sf{Assumptions}}}}$

• Let the present age of Chahat will be 2x.

• Let the present age of Arshi will be 3x.

$\large{\boxed{\boxed{\sf{Full \: solution}}}}$

$\large\purple{\texttt{As we know that}}$

☯ We let the present age of Chahat will be 2x and we let the present age of Arshi will be 3x.

$\large\purple{\texttt{Now according to the given question}}$

$\large\purple{\texttt{Let's carry on,}}$

$\leadsto$ Chahat age + 12 ÷ Arshi age + 12 = 11 ÷ 15

$\leadsto$ 2x + 12 ÷ 3x + 12 = 11 ÷ 15

$\leadsto$ 15(2x+12) = 11(3x+12)

$\large\mathfrak\blue{This \: result \: 15(2x+12) = 11(3x+12) \: is \: come}$

$\large\mathfrak\blue{When \: we \: Cross \: multiply \: the \: values}$

$\large\purple{\texttt{Continuing....}}$

$\leadsto$ 30x + 12 = 33x + 132

$\large\purple{\texttt{Now we have to combining like terms}}$

$\large\purple{\texttt{Let's carry on,}}$

$\leadsto$ 180 - 132 = 33x - 30x

$\leadsto$ 48 = 3x

$\leadsto$ x = 48/3

$\leadsto$ x = 16

◖ Arshi's present age is given below

$\leadsto$ Arshi's present age = 3x

$\leadsto$ Arshi's present age = 3 × 16

$\leadsto$ Arshi's present age = 48

$\bold{\pink{\fbox{\red{Hence, her present age is 48 years}}}}$

$\large{\boxed{\boxed{\boxed{\boxed{\boxed{\sf{48 \: is \: the \: answer}}}}}}}$

Hope it's helpful !!

Thank you all :)