Question

The ages of Raju and Ravi are in the ratio 3:4 .Four years from now the ratio of their ages will be 4:5 . Find their present ages

Answer 1

Answer:

12 year and 16 year

Step-by-step explanation:

Let the present age of Raju and Ravi be 3x and 4x respectively.

After 4 year:

Age of Raju = present age + 4 = 3x + 4

Age of Ravi = pres. age + 4 = 4x + 4

Given, ratio of their age will be 4:5.

⇒ (3x + 4)/(4x + 4) = 4/5

⇒ 5(3x + 4) = 4(4x + 4)

⇒ 15x + 20 = 16x + 16

⇒ 20 - 16 = 16x - 15x

⇒ 4 = x

Hence,

present age of Raju = 3x = 3(4) = 12 year

present age of Ravi = 4x = 4(4) = 16 yr

Answer 2

Answer:

Given :-

• The ages of Raju and Ravi are in the ratio of 3 : 4.
• Four years from now the ratio of their ages will be 4 : 5.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto \bf{Present\: age\: of\: Raju =\: 3x\: years}$

$\mapsto \bf{Present\: age\: of\: Ravi =\: 4x\: years}$

❒ After four years :

$\leadsto \sf Age\: of\: Raju =\: (3x + 4)\: years$

$\leadsto \sf Age\: of\: Ravi =\: (4x + 4)\: years$

According to the question :

$\implies \sf (3x + 4) : (4x + 4) =\: 4 : 5$

$\implies \sf \dfrac{3x + 4}{4x + 4} =\: \dfrac{4}{5}$

By doing cross multiplication we get,

$\implies \sf 4(4x + 4) =\: 5(3x + 4)$

$\implies \sf 16x + 16 =\: 15x + 20$

$\implies \sf 16x - 15x =\: 20 - 16$

$\implies \sf \bold{\purple{x =\: 4}}$

Hence, the required ages of Raju and Ravi are :

➲ Present age of Raju :

$\longrightarrow \sf Present\: Age_{(Raju)} =\: 3x\: years$

$\longrightarrow \sf Present\: Age_{(Raju)} =\: 3 \times 4\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Raju)} =\: 12\: years}}$

➲ Present age of Ravi :

$\longrightarrow \sf Present\: Age_{(Ravi)} =\: 4x\: years$

$\longrightarrow \sf Present\: Age_{(Ravi)} =\: 4 \times 4\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Ravi)} =\: 16\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Raju\: and\: Ravi\: is\: 12\: years\: and\: 16\: years\: respectively\: .}}}}$