Question

Q.5) The age of Hari and Harry are in the ration 5:7. After two years the sum of their as will be 52 years. Find their present ages. full answer with whole equation​

Answer 1

Answer:

The present age of Hari = 20 years

The present age of Harry = 28 years

Step-by-step explanation:

Let,

• The present age of Hari = 5x
• The present age of Harry = 7x

After two years,

• The age of Hari = 5x + 2
• The age of Harry = 7x + 2

Also,

The sum of their as will be 52 years.

★ According to the Question :

$\longrightarrow$ (5x + 2) + (7x + 2) = 52

$\longrightarrow$ 5x + 7x + 4 = 52

$\longrightarrow$ 12x = 52 - 4

$\longrightarrow$ 12x = 48

$\longrightarrow$ x = 48/12

$\longrightarrow$ x = 4

__________________________

• The present age of Hari = 5x

$\longrightarrow$ 5 (4)

$\longrightarrow$ 20

The present age of Hari = 20 years

__________________________

• The present age of Harry = 7x

$\longrightarrow$ 7 (4)

$\longrightarrow$ 28

The present age of Harry = 28 years

Therefore,

The present age of Hari and Harry is 20 years and 28 years respectively.

Answer 2

G i v e n :

• The present age of Hari & Harry are in the ratio of 5 : 7. After two years, the sum of their (Hari and Harry) ages will be 52 years.

N e e d T o F i n d :

• The present age of Harry and Hari?

S o l u t i O n :

❍ Let's say, that the present age of Hari and Harry be 5x and 7x respectively.

⠀

⚘ After two years, their ages —

• Hari's age = (5x + 2) years
• Harry's age = (7x + 2) years

⠀

$\bigstar\:\underline{\textbf{According to the QuesTion Now :}}$

• After two years, the Sum of their (Hari and Harry) ages will be 52 years.

⠀

$:\implies\sf \Big\{5x + 2\Big\} + \Big\{7x + 2\Big\} = 52 \\\\\\:\implies\sf 5x + 2 + 7x + 2 = 52\\\\\\:\implies\sf 12x + 4 = 52\\\\\\:\implies\sf 12x = 52 - 4\\\\\\:\implies\sf 12x = 48\\\\\\:\implies\sf x = \cancel\dfrac{48}{12}\\\\\\:\implies{\underline{\boxed{\pink{\pmb{\frak{x = 4}}}}}}\;\bigstar$

⠀

Therefore,

• Present age of Hari, 5x = 5(4) = 20
• Present age of Harry, 7x = 7(4) = 28

⠀

$\therefore{\underline{\textsf{Hence, present age of Hari and Harry is \textbf{20 years} and \textbf{28 years} respectively.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

• V E R I F I C A T I O N :

⠀

• As we know that, sum of their ages will be 52 years after two years. So, let's Verify the answer by Substituting the value of 'x' —

⠀

$\dashrightarrow\sf 5x + 2+ 7x + 2= 52 \\\\\\\dashrightarrow\sf 5(4) + 2 + 7(4) + 2 = 52\\\\\\\dashrightarrow\sf 20 + 2 + 28 + 2 = 52\\\\\\\dashrightarrow\sf 48 + 4 = 52\\\\\\\dashrightarrow{\boxed{\boxed{\frak{\red{52 = 52}}}}}$

⠀$\qquad\qquad\therefore{\underline{\pmb{\blue{\mathcal{HENCE\; VERIFIED!}}}}}$