Question

Just now
14
Ten years ago Reena's age was half of
Sona's age.If the ratio of their present
ages is 3:4 ,what will be the sum of
their present ages? *
(3 Points)​

Answer 1

GivEn:-

• Ten years ago Reena's age was half of Sona's age.

• ratio of their present ages is 3:4

To find:-

• sum of their present ages?

SoluTion:-

✩ Let's assume present age of Reena be 3x years

✩ And present age of Sona be 4x years

$\;\;\;\sf \star\;{\underline{\red{As\;Per\;GivEn\; Question\;:}}}$

✇ Ten years ago Reena's age was half of Sona's age.

⠀⠀

★ So, Their ages before 10 years -

• Age of Reena after 10 years = (3x - 10) years

• Age of Sona after 10 years = (4x - 10) years

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━━━━━━━

✇ According to givEn condition -

$\dashrightarrow$ Age of Reena = $\sf \dfrac{1}{2}$ × Age of Sona

$\sf \dag\;{\underline{\pink{Put\;the\;value\;of\;their\;ages\;:}}}$

$\dashrightarrow\sf (3x - 10) = \dfrac{1}{2} \times (4x - 10)$

$\dashrightarrow\sf 2(3x - 10) = (4x - 10)$

$\dashrightarrow\sf 6x - 20 = 4x - 10$

$\dashrightarrow\sf 6x - 4x = -10 + 20$

$\dashrightarrow\sf 2x = 10$

$\dashrightarrow\sf x = \cancel{ \dfrac{10}{2}}$

$\dashrightarrow{\underline{\boxed{\sf{\purple{x = 5}}}}}$ ★

━━━━━━━━━━━━━━━

✇ Now, Put the value of x in their assumed ages -

• Present age of Reena = 3x = 3 × 5 = 15 years

• Present age of Reena = 4x = 4 × 5 = 20 years

⠀⠀ ━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\sf \dag\;{\underline{\blue{Therefore,\;the\;sum\; their\; present\;age\;:}}}$

$\dashrightarrow\sf 15 + 20$

$\dashrightarrow{\underline{\boxed{\sf{\purple{35\;years}}}}}$ ★

$\therefore\sf \underline{The\;sum\;of\;their\; present\;age\;is\;35\;years.}$

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Answer 2

Given :

• 10 years ago , Reena's age was half of Sona's age .
• The ratio of their present ages is 3:4.

To find :

• Sum of their present ages.

Solution :

Consider,

• Present age of Reena = 3x years
• Present age of Sona = 4x years

According to the question :-

• 10 years ago, Reena's age was half of Sona's age.

10 years ago ,

• Age of Reena = (3x-10) years
• Age of Sona = (4x-10) years

$\to\sf{3x-10=\dfrac{1}{2}\times(4x-10)}$

$\to\sf{6x-20=4x-10}$

$\to\sf{6x-4x=-10+20}$

$\to\sf{2x=10}$

$\to\sf{x=5}$

★Present age of Reena = (3×5) = 15 years

★ Present age of Sona = (4×5) = 20 years

The sum of their present ages,

= (15+20) years= 35 years

Therefore, the sum of their present ages is 35 years.