Question

Raj is 5 years younger than Ravi. 4 years later, Ravi will be twice as old as Raj. Find their present ages​

Answer 1

Answer:

Given :-

• Ravi is 5 years younger than Ravi.
• 4 years later, Ravi will be twice as old as Raj.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf Present\: Age_{(Ravi)} =\: a\: years$

$\mapsto \bf Present\: Age_{(Raj)} =\: (a - 5)\: years$

❒ 4 years later their ages will be :

✧ Age Of Ravi :

$\leadsto \sf\bold{\blue{Age_{(Ravi)} =\: (a + 4)\: years}}$

✧ Age Of Raj :

$\leadsto \sf Age_{(Raj)} =\: \{(a - 5) + 4\}\: years$

$\leadsto \sf Age_{(Raj)} =\: (a - 5 + 4)\: years$

$\leadsto \sf\bold{\blue{Age_{(Raj)} =\: (a - 1)\: years}}$

According to the question,

$\bigatar$ 4 years later, Ravi will be twice as old as Raj.

$\implies \bf \bigg\{Age_{(Ravi)}\bigg\} =\: 2\bigg\{Age_{(Raj)}\bigg\}$

$\implies \sf (a + 4) =\: 2(a - 1)$

$\implies \sf a + 4 =\: 2a - 2$

$\implies \sf a - 2a =\: - 2 - 4$

$\implies \sf {\cancel{-}} a =\: {\cancel{-}} 6$

$\implies \sf\bold{\purple{a =\: 6}}$

Hence, their required present ages are :

❒ Present Age Of Ravi :

$\longrightarrow \sf Present\: Age_{(Ravi)} =\: a\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Ravi)} =\: 6\: years}}$

❒ Present Age Of Raj :

$\longrightarrow \sf Present\: Age_{(Raj)} =\: (a - 5)\: years$

$\longrightarrow \sf Present\: Age_{(Raj)} =\: (6 - 5)\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Raj)} =\: 1\: years}}$

${\footnotesize{\bold{\underline{\therefore\: The\: present\: age\: of\: Ravi\: and\: Raj\: is\: 6\: years\: and\: 1\: years\: respectively\: .}}}}$

Answer 2

Given:-

$\hookrightarrow$ Raj is 5 years younger than Ravi

$\hookrightarrow$ 4 years later, Ravi will be twice as old as Raj

To find:-

$\hookrightarrow$ Their present ages

Answer:-

$\longmapsto$ Present age of Ravi = 6 years

$\longmapsto$ Present age of raj = 1 year

Explanation:-

Let,

Ravi age be 'x'

Raj age be 'y'

Given,

y = x - 5 --------( 1 )

Four years later Ravi will be twice as old as Raj

$\Longrightarrow$ x + 4 = 2 (y + 4)

Substitute equation ( 1 )

$\Longrightarrow$ x + 4 = 2 (x - 5) + 8

$\Longrightarrow$ x + 4 = 2x - 10 + 8

$\Longrightarrow\boxed{x = 6}$

∴Ravi age = 6 years

Raj's age = (x - 5) = 6 - 5 $\Longrightarrow$ 1 year

Therefore, Ravi's age is "6 years" and Raj's age is "1 year"