Question

Ravi is ten years older then Rehan. Five years ago, one seventh of Rehan age was equal to the one fifth of Rehan age. Find their present ages.

Answer 1

Gɪᴠᴇɴ :

Ravi is 10 years older than Rehan.

Five years ago, one seventh of Ravi's age was equal to one fifth of Rehan's age.

Tᴏ ꜰɪɴᴅ :

Present ages of Ravi & Rehan

Sᴏʟᴜᴛɪᴏɴ :

Let present ages of Ravi be a years & present age of Rehan be b years.

A/q to 1st case :

➪ a = b + 10 ...(i)

A/q to 2nd case :

➪ 1/7(a - 5) = 1/5(b - 5)

➪ (a - 5)/7 = (b - 5)/5

➪ 7(b - 5) = 5(a - 5)

➪ 7b - 35 = 5a - 25

➪ 7b = 5a - 25 + 35

➪ 7b = 5a + 10

➪ 7b = 5(b + 10) + 10

➪ 7b = 5b + 50 + 10

➪ 7b - 5b = 60

➪ 2b = 60

➪ b = 60/2

➪ b = 30

Hence, present age of Rehan = 30 Years.

Now putting value in (i)

➪ a = 30 + 10

➪ a = 40

Hence, present age of Ravi = 40 Years.

Tʜᴇʀᴇꜰᴏʀᴇ,

Present ages of Ravi & Rehan are 40 years & 30 years respectively.

Answer 2

Answer:

Let the Present Age of Rehan be n and Present Age of Ravi be (10 + n) i.e. 10 years older than Rehan.

$\underline{\bigstar\:\textsf{5 Years Ago, Acc ^\text n to Question :}}$

$:\implies\sf \dfrac{1}{7} \times Ravi=\dfrac{1}{5} \times Rehan\\\\\\:\implies\sf \dfrac{1}{7}\bigg\lgroup (n + 10)- 5\bigg\rgroup=\dfrac{1}{5}\bigg\lgroup n-5\bigg\rgroup\\\\\\:\implies\sf \dfrac{1}{7}\bigg\lgroup n + 5\bigg\rgroup=\dfrac{1}{5}\bigg\lgroup n - 5\bigg\rgroup\\\\\\:\implies\sf (n + 5)5 = 7(n - 5)\\\\\\:\implies\sf 5n + 25 = 7n - 35\\\\\\:\implies\sf 35 + 25 = 7n - 5n\\\\\\:\implies\sf 60 = 2n\\\\\\:\implies\sf \dfrac{60}{2} = n\\\\\\:\implies\underline{\boxed{\sf n = 30}}$

$\rule{150}{1}$

$\underline{\bf{\dag}\:\textsf{Present Age :}}$

$\bullet\:\:\textsf{Rehan = n = \textbf{30 years}}\\\bullet\:\:\textsf{Ravi = (n + 10) = \textbf{40 years}}$