Question

The ratio ofpresent ages of Albert and salim is5:9.Five year hence ratio of their ages will be 3:5. Find their present ages

Answer 1

Given,

• The Ratio of Present ages of Albert and Salim is 5:9.
• Then, Five years after their ratio will be 3:5.

To Find,

• The Present Ages of Albert and Salim.

Solution :

$\implies$ Suppose the Present age of Albert and Salim be a

Therefore,

• The Present age of Albert = 5a
• Thee Present age of Salim = 9a

$\mapsto \underline{\sf{\pink{According \ to \ the \ Question :}}}$

$\implies \sf{\dfrac{5a + 5}{9a + 5} = \dfrac{3}{5}}$

$\implies \sf{5(5a + 5) = 3(9a + 5)}$

$\implies \sf{25a + 25 = 27a + 15}$

$\implies \sf{25 - 15 = 27a - 25a}$

$\implies \sf{10 = 2a}$

$\implies \sf{a = \dfrac{10}{2}}$

$\implies \boxed{\sf{a = 5}}$

Therefore,

$\boxed{\bold{\red{The \ Present \ age \ of \ Albert = 5a = 5(5) = 25 \ years}}}$

$\boxed{\bold{\red{The \ Present \ age \ of \ Salim = 9a = 9(5) = 45 \ years}}}$

$\rule{200}2$

Answer 2

Answer:

★ $\fbox\purple{\sf The\:present\:age\:of\:Albert\:is\:25\:years.}$

★ $\fbox\purple{\sf The\:present\:age\:of\:Salim\:is\:45\:years.}$

Step-by-step explanation:

$\large\underline\mathfrak\pink{Letting\:their\:age:-}$

• Let Albert's and Salim's age be x years.

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

• The ratio of present ages of Albert and Salim is $\fbox\purple{\sf \dfrac{5}{8}}$
• Five years hence, their ages will be $\fbox\purple{\sf \dfrac{3}{5}}$

So,

Albert's age = 5x and Salim's age = 11x

$\large\underline\mathfrak\pink{Five\:years\:hence:-}$

• Albert's age = (5x + 5)
• Salim's age = (9x + 5)

$\large\underline\mathfrak\purple{Equation:-}$

$\leadsto\sf{\dfrac{5x+5}{9x+5} = \dfrac{3}{5}}$

$\leadsto\textsf{5(5x+5) = 3(9x+5)}$

$\leadsto\textsf{25x+25 = 27x+15}$

$\leadsto\textsf{25x-27x = 15-25}$

$\leadsto\textsf{-2x = -10 => 2x = 10}$

$\leadsto\sf{x = \dfrac{10}{2}}$

$\leadsto\fbox\purple{\sf x = 5}$

$\large\underline\mathfrak\pink{Putting\:the\:value:-}$

• $\large\sf\purple{Albert's\:age = 5(5) = 25\:years}$
• $\large\sf\purple{Salim's\:age = 9(5) = 45\:years}$

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