Question

Present ages of Tanzin and Tashi are in the ratio 3:2. Five years from now the ratio of their ages will be 4:3. Find their present ages.​

Answer 1

⇝ Given :-

• Present ages of Tanzin and Tashi are in the ratio 3 : 2

• Five years from now the ratio of their ages will be 4 : 3

⇝ To Find :-

• Their Present Ages.

⇝ Solution :-

As the ages of Tanzin and Tashi are in the ratio 3 : 2.

Therefore Let,

• Present Age of Tanzin = $\rm3x$ years

• Present Age of Tashi = $\rm2x$ years

❒ Five Years From Now :

• Age of Tanzin = $\rm(3x+5)$ years

• Age of Tashi = $\rm(2x+5)$ years

⏩ According To Question :

▪ Five years from now the ratio of their ages will be 4 : 3 which means :

$\rm\large \pink\bigstar \: \: \red{ \frac{3x + 5}{2x + 5} = \frac{4}{3} }$

$:\longmapsto \rm 3(3x + 5) = 4(2x + 5)$

$:\longmapsto \rm 9x + 15 = 8x + 20$

$:\longmapsto \rm 9x - 8x = 20 - 15$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 5} }}}$

Hence,

Present Age of Tanzin = $\rm3x$ = 15 years

Present Age of Tashi = $\rm2x$ = 10 years

Therefore,

$\pink{\begin{cases} \bf Tanzin's\:Present\:Age = 15 \:years \\  \\  \bf Tashi's\:Present\:Age = 10 \: years\end{cases}}$

Answer 2

Given :-

Present ages of Tanzin and Tashi are in the ratio 3:2. Five years from now the ratio of their ages will be 4:3.

To Find :-

Their present ages

Solution :-

Let their present ages be 3t and 2t

3t + 5/2t + 5 = 4/3

3(3t + 5) = 4(2t + 5)

9t + 15 = 8t + 20

9t - 8t = 20 - 15

t = 5

Therefore

Present age of Tanzin = 3t = 3(5) = 15 years

Present age of Tashi = 2t = 2(5) = 10 years