Question

The present ages of Veeru and Neeru are in the ratio 3:4. Five years from now, the ratio of their ages will be 4:5. Find their present ages.
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Answer 1

Answer:

Given :-

• The present ages of Veeru and Neeru are in the ratio of 3 : 4.
• Five years from now, the ratio of their ages will be 4 : 5.

To Find :-

• What is their present ages.

Solution :-

Let,

$\mapsto\: \rm{\bold{Present\: age\: of\: Veeru =\: 3x\: years}}$

$\mapsto\: \rm{\bold{Present\: age\: of\: Neeru =\: 4x\: years}}$

Five years later :

$\leadsto\: \sf Age\: of\: Veeru =\: (3x + 5)\: years$

$\leadsto \: \sf Age\: of\: Neeru =\: (4x + 5)\: years$

According to the question,

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

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

By doing cross multiplication we get,

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

$\implies \sf 16x + 20 =\: 15x + 25$

$\implies \sf 16x - 15x =\: 25 - 20$

$\implies \sf \bold{\purple{x =\: 5}}$

Hence, the present age of Veeru and Neeru are :

$\bigstar\: \sf\bold{Age\: of\: Veeru\: :-}$

$\longrightarrow \sf 3x\: years$

$\longrightarrow \sf 3(5)\: years$

$\longrightarrow \sf \bold{\red{15\: years}}$

$\bigstar\: \sf \bold{Age\: of\: Neeru\: :-}$

$\longrightarrow \sf 4x\: years$

$\longrightarrow \sf 4(5)\: years$

$\longrightarrow \sf\bold{\red{20\: years}}$

$\therefore$ The present age of Veeru and Neeru is 15 years and 20 years respectively.

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VERIFICATION :-

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

By putting x = 5 we get,

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

$\implies \sf \dfrac{15 + 5}{20 + 5} =\: \dfrac{4}{5}$

$\implies \sf \dfrac{\cancel{20}}{\cancel{25}} =\: \dfrac{4}{5}$

$\implies \sf\bold{\pink{\dfrac{4}{5} =\: \dfrac{4}{5}}}$

Hence, Verified.

Answer 2

                                                                                   

Given :-

The present ages of Veeru and Neeru are in the ratio 3:4. Five years from now, the ratio of their ages will be 4:5.

To Find :-

Present ages

Solution :-

Let the ratio of present ages of Veeru and Neeru be 3a and 4a

Given, After 5 years ratio becomes 4:5

3a + 5/4a + 5 = 4:5

3a + 5/4a + 5 = 4/5

5(3a + 5) = 4(4a + 5)

(5 × 3a) + (5 × 5) = (4 × 4a) + (4 × 5)

15a + 25 = 16a + 20

15a - 16a = 20 - 25

-a = -5

a = 5

Hence

Age of Veeru = 3a = 15 years

Age of Neeru = 4a = 20 years