Question

The age of Nandana and Harshit or in the radio 2 : 3 after 15 years the radio of their age will be 3 : 4 find their parents age...​

Answer 1

${\mathbf {\blue{S}{\underline{\underline{olution:-}}}}}$

$\mathfrak{\underline{AnswEr:-}}$

• The present age of Nandana = 30 years
• The present age of Harshita = 45 years

$\mathfrak{\underline{Given:-}}$

• The age of Nandana and Harshit or in the radio 2 : 3.
• After 15 years the radio of their age will be 3 : 4.

$\mathfrak{\underline{Need\:To\: Find:-}}$

• The present age of Nandana = ?
• The present age of Harshita = ?

${\mathbf {\blue{E}{\underline{\underline{xplanation:-}}}}}$

$\large\bold{\underline{\sf{Let:-}}}$

• The present age of Nandana be 2y.

$\large\bold{\underline{\sf{Then:-}}}$

• The present age of Harshita be 3y.

$\:\:\:\:\dag\bf{\underline \green{After\:15\: years:-}}$

• Nandana present age = 2y + 15
• Harshita present age = 3y + 15

$\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \: the \: Question :}}}}\mid}$

$\longrightarrow \sf {2y + \dfrac{15}{3y} + 15 = \dfrac{3}{4} }$

$\longrightarrow \sf {3 \times (3y + 15) = 4 \times (2y + 15)}$

$\longrightarrow \sf {9y + 45 = 8y + 60}$

$\longrightarrow \sf {9y- 8y = 60 - 45}$

$\longrightarrow\large\boxed{\sf{\purple{y\:=\;15}}}$

$\:\:\:\:\dag\bf{\underline{\underline \pink{Hence:-}}}$

$\longrightarrow \sf {The \:present \:age \:of\: Nandana = 2y}$

$\longrightarrow \sf {The\: present \:age \:of \:Nandana = 2 \times 15}$

$\longrightarrow \sf {The \:present \:age\: of\: Nandana = 30 \:years}$

$\:\:\:\:\dag\bf{\underline{\underline \blue{And:-}}}$

$\longrightarrow \sf {The\: present \:age \:of\: Harshita = 3y}$

$\longrightarrow \sf {The\: present \:age \:of\: Harshita = 3 \times 15}$

$\longrightarrow \sf {The \:present \:age \:of \:Harshita = 45 \:years}$

$\rule{200}{2}$

Answer 2

Answer:

Present age of Nandana is 30 years and the present age of Harshit is 45 years.

Step-by-step explanation:

Given :-

• The age of Nandana and Harshit are in the ratio 2:3.
• After 15 years, the ratio of their age will be 3:4.

To find :-

• Their present ages.

Solution :-

Consider,

• Present age of Nandana = 2x years
• Present age of Harshit = 3x years

After 15 years,

• Age of Nandana = (2x+15) years
• Age of Harshit = (3x +15) years

According to the question ,

• After 15 years, the ratio of their age will be 3:4.

$\to\sf{(2x+15):(3x+15)=3:4}$

$\to\sf{\dfrac{2x+15}{3x+15}=\dfrac{3}{4}}$

$\to\sf{9x+45=8x+60}$

$\to\sf{9x-8x=60-45}$

$\to\sf{x=15}$

★ Present age of Nandana = 2×15 = 30 years

★ Present age of Harshit = 3×15 = 45 years

_______________

VERIFICATION :-

• Nandana's present age = 30 years
• Harshit's present age = 45 years

15 years later,

★ Nandana's age = (30+15) = 45 years

★ Harshit's age = (45+15) = 60 years

A/Q,

Ratio of their ages = 3:4

→ 45:60 = 3:4

→ 3:4 = 3:4

Hence Verified !