Question

The ages of Ramu and Lakshman are in ratio of 6:7 five years later the sum of their ages will be 36 what are their present ages. ​

Answer 1

$\bf{\underline{\underline \blue{Solution:-}}}$

$\sf\underline{\red{\:\:\: AnswEr:-\:\:\:}}$

• The present age of Ramu = 12 Years
• The present age of Laxman = 14 Years

$\sf\underline{\red{\:\:\: Given:-\:\:\:}}$

• The ages of Ramu and Lakshman are in ratio of 6:7 five years later the sum of their ages will be 36.

$\sf\underline{\red{\:\:\: Need\:To\: Find:-\:\:\:}}$

• The present age of Ramu = ?
• The present age of Laxman = ?

$\bf{\underline{\underline \blue{Explanation:-}}}$

Let the present age of ramu is 6y

And, the present age of laxman is 7y.

$\sf\underline{\red{\:\:\: After\:5\: years:-\:\:\:}}$

• Ramu's Age = (6y + 5)
• Laxman's Age = (7y + 5)

$\sf\underline{\red{\:\:\: A.T.Q:-\:\:\:}}$

$\dashrightarrow\sf {6y + 5 + 7y + 5 = 36}$

$\dashrightarrow\sf {13y + 10 = 36}$

$\dashrightarrow\sf {13y = 36 - 10}$

$\dashrightarrow\sf {13y = 26}$

$\dashrightarrow\sf {y = \dfrac{\cancel{26}}{\cancel{13}}\:}$

$\dashrightarrow\sf {y = 2}$

$\sf\underline{\green{\:\:\: ThereFore:-\:\:\:}}$

$\dashrightarrow\sf {The\:present\:age\:of\:Ramu = 6y}$

$\dashrightarrow\sf {The \:present\:age\:of\:Ramu = 6 \times 2}$

$\dashrightarrow\sf {The\:present\:age\:of\:Ramu = 12 \: years}$

$\sf\underline{\red{\:\:\: And:-\:\:\:}}$

$\dashrightarrow\sf {The\:present\:age\:of\:Laxman = 7y}$

$\dashrightarrow\sf {The\:present\:age\:of\:Laxman = 7 \times 2}$

$\dashrightarrow\sf {The\:present\:age\:of\:Laxman = 14 \: years}$

$\rule{200}{2}$

Answer 2

$\sf\large\purple{\underbrace{ Question : }}$

The ages of Ramu and Lakshman are in ratio of 6:7 five years later the sum of their ages will be 36 what are their present ages...?

$\sf\large\purple{\underbrace{ Answer : }}$

★ Given that,

☯ The ratio of ages of Ramu & Lakshaman = 6:7

☯ After 5 years the sum of their ages = 36.

★ To find,

☯ Present ages of Ramu & Lakshaman.

★ Let,

↪ Present age of Ramu = 6x

↪ Present age of Lakshman = 7x

★ 5 years later,

↪ Ramu's age = 6x + 5

↪ Lakshman's age = 7x + 5

★ According to question,

$\bf\:\implies 6x + 5 + 7x + 5 = 36$

$\bf\:\implies 13x + 10 = 36$

$\bf\:\implies 13x = 36 - 10$

$\bf\:\implies 13x = 26$

$\bf\:\implies x = \frac{26}{13}$

$\bf\:\implies x = 2$

• Now substitute the value of x in their ages

$\bf\:\implies Ramu's \: \: age : 6(2) = 12$

$\bf\:\implies Lakshman's \: \: age : 7(2) = 14$

$\underline{\boxed{\bf{\red{ \therefore Ramu's \: age = 12 \: years.Lakshman's \: age = 14 \: years. }}}}\:\orange{\bigstar}$