Question

the present ages of anmol and supriya are in the ratio 2:3. 10 years from now their qges will be in the ration 3:4. What is the present age of anmol​

Answer 1

$\bold{\underline{\underline{Assume\::}}}$

Let their -

• Ages be "M" years.

$\bold{\underline{\underline{Solution\::}}}$

According to question,

Present ages of anmol and supriya are in the ratio 2:3.

So,

• Present age of Anmol = (2M) years
• Present age of Supriya = (3M) years

$\bold{\underline{10\:years\:from\:now}}$

• Age of Anmol = (2M + 10) years
• Age of Supriya = (3M + 10) years

10 years from now their ges will be in the ration 3:4.

$\implies\:\dfrac{2M\:+\:10}{3M\:+\:10}\:=\:\dfrac{3}{4}$ __ (eq 1)

Cross-multiply them

$\implies\:4(2M\:+\:10)\:=\:3(3M\:+\:10)$

$\implies\:8M\:+\:40\:=\:9M\:+\:30$

$\implies\:9M\:-\:8M\:=\:40\:-\:30$

$\implies\:M\:=\:10$

So,

Age of Anmol = 2M

$\Rightarrow\:2(10)$

$\Rightarrow\:20\:years$

Age of Supriya = 3M

$\Rightarrow\:3(10)$

$\Rightarrow\:30\:years$

∴ Age of Anmol is 20 years.

Verification

From above calculations we have M = 10

Put value of M in (eq 1)

$\implies\:\dfrac{2(10)\:+\:10}{3(10)\:+\:10}\:=\:\dfrac{3}{4}$

$\implies\:\dfrac{20\:+\:10}{30\:+\:10}\:=\:\dfrac{3}{4}$

$\implies\:\dfrac{30}{40}\:=\:\dfrac{3}{4}$

$\implies\:\dfrac{3}{4}\:=\:\dfrac{3}{4}$

Answer 2

Answer:

The present ages are -

• Anmol = 20 years
• Supriya = 30 years

Step-by-step explanation:

Given :

Present ages ratio = 2 : 3

Ratio of ages after 10 years = 3 : 4

To find :

Their present age of Anmol

Solution :

$\textbf{\small{\underline{Let the-}}}$

• Anmol as 2x
• Supriya as 3x

$\textbf{\small{\underline{After 10 years - }}}$

• Anmol = (2x + 10)
• Supriya = (3x + 10)

★ $\boxed{\sf{\frac{(2x + 10)}{(3x + 10)} = \frac{3}{4}}}$

$\sf{\implies} \: \frac{(2x + 10)}{(3x + 10)} = \frac{3}{4} \\ \sf{\implies} \: cross \: multiply \\ \sf{\implies} \: 4(2x + 10) = 3(3x + 10) \\ \sf{\implies} \: 8x + 40 = 9x + 30 \\\sf{\implies} \: 8x - 9x = 30 - 40 \\ \sf{\implies} \: \cancel - x = \cancel - 10 \\ \implies\small{\green{\boxed{\green{\boxed{\red{\textsf{x = 10}}}}}}}$

$\rule{300}{1.5}$

★ Value of 2x

$\sf{\implies} \:2(10) \\ \sf{\implies} \:20$

Anmol is 20 years old.

$\rule{300}{1.5}$

★ Value of 3x

$\sf{\implies} \:3(10) \\ \sf{\implies} \:30$

Supriya is 30 years old.

$\therefore$ The present ages are -

• Anmol = 20 years
• Supriya = 30 years