Question

Present ages of Aahna and Vaibhav are in the ratio 3 : 5 . Nine years from now the ratio of their ages was be 4 : 5 . Find their present ages.

Answer 1

Answer :

• Aahna age = 5.4 years
• Vaibhav age = 9 years

Given :

• Present age of Aahna and Vaibhav are in the ratio 3:5
• Nine years from now the ratio of their ages was be 4:5

To find :

• Present age

Solution :

Given,the age of Aahna and Vaibhav are in the ratio 3:5 so,

• Let the age of Aahna and Vaibhav be 3x and 5x

Given,

Nine years from now the ratio of their ages was be 4:5 so,

• 3x + 9 / 5x + 9 = 4/5

》3x + 9 / 4x + 9 = 4/5

cross multiplying we get,

》5(3x + 9) = 4(5x + 9)

》15x + 45 = 20x + 36

》20x - 15x = 45 - 36

》5x = 9

》x = 5/9

Finding the present age :

• Aahna = 3x = 3(5/9) = 27/5 or 5.4 years
• Vaibhav = 5x = 5(5/9) = 45/5 = 9 years

Hence,

• Aahna age = 5.4 years
• Vaibhav age = 9 years

Answer 2

ɢɪᴠᴇɴ :

• Present ages of aahna and vaibhav are in ratio 3 : 5.

• Nine years from now their ratio of their ages was be 4 : 5.

$\:$

ᴛᴏ ғɪɴᴅ :

• Find their present ages.

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━$

Let their ages be 3x and 5x.

$\begin{gathered}\;\;\;\;\bf{\dag}\;{\underline{\sf{ \pmb{According \: to \: condition \ : }}}}\\\end{gathered}$

$\begin{gathered} \: \sf \leadsto \frac{3x + 9}{5x + 9} = \frac{4}{5} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto \: 5(3x + 9) = 4(5x + 9) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf( \: by \: cross \: multiplication \: ) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \leadsto \: 15x + 45 = 20x + 36 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \leadsto \: 45 \: - \: 36 = 20x \: - \: 15 x \\ \\ \sf \leadsto \: 9 = 5x \\ \\ \sf \leadsto \: x = \frac{9}{5} = 1.8 \\ \\ \\ \\\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━━━━━━━━━━━ \\ \\ \sf \: Aahna's \: age = 3x = 3 \times 1.8 = 5.4 \\ \\ \sf \: vaibhav's \: age = 5x = 5 \times 1.8 = 9 \\ \\ \\ \\ \sf \therefore \underline{Hence,Final \: answer \: is \: a \: Aahna's \: age = 5.4 \: years \: and \: vaibhav's \: age \: = 9 \: years} \end{gathered}$