Question

Present ages of Shivaji and Ashok are in the ratio 5 : 4. Five years from now the ratio of their ages will be 6:5.

Find their ages.​

Answer 1

Answer:

Shivaji's present age is 25 and Ashok's present age is 20.

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Step-by-step explanation:

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ATQ, the present ages of Shivaji and Ashok are in the ratio 5 : 4, since the fraction has been reduced to its lowest form, their present ages will be the number multiplied by a constant term, in this case, let it be 'x'.

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Their present ages are:

• Shivaji = 5x

• Ashok = 4x

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Five years from now, their ages will be:

• Shivaji = Present age + 5 years = 5x + 5

• Ashok = Present age + 5 years = 4x + 5

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According to the question;

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$\sf \dashrightarrow \dfrac{Shivaji's \ age \ 5 \ years \ from \ now}{Ashok's \ age \ 5 \ years \ from \ now} = \dfrac{6}{5}$

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We know that Shivaji's and Ashok's age in five years will be (5x + 5) and (4x + 5) respectively. On substituting the two values in the fraction we get:

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$\sf \dashrightarrow \ \dfrac{5x + 5}{4x + 5} = \dfrac{6}{5}$

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On cross-multiplying we get:

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$\sf \dashrightarrow \ 5(5x + 5) = 6(4x + 5)$

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$\sf \dashrightarrow \ 25x + 25 = 24x + 30$

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On transposing the terms from the RHS to the LHS we get:

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$\sf \dashrightarrow \ 25x + 25 - 24x - 30 = 0$

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$\sf \dashrightarrow \ 25x - 24x - 30 + 25 = 0$

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$\sf \dashrightarrow \ x - 5 = 0$

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$\sf \dashrightarrow \ \textsf{\textbf{x = 5}}$

∴ The value of 'x' is 5. Now we'll substitute this value in the expressions given for their present ages to find their age.

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Shivaji's present age:

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$\sf \dashrightarrow Shivaji's \ Present \ Age = 5x$

$\sf \dashrightarrow Shivaji's \ Present \ Age = 5(5)$

$\sf \dashrightarrow Shivaji's \ Present \ Age = 25$

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Ashok's present age:

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$\sf \dashrightarrow Ashok's \ Present \ Age = 4x$

$\sf \dashrightarrow Ashok's \ Present \ Age = 4(5)$

$\sf \dashrightarrow Ashok's \ Present \ Age = 20$

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∴ Shivaji's present age is 25, and Ashok's present age is 20.

Answer 2

✫ The ages of shivaji and ashok are 25 years and 20 years ✫

Step-by-step explanation:

Given: Present ages of shivaji and ashok are in the ratio 5:4.Five years from now the ratio of their ages will be 6:5.

To find: Ages of shivaji and ashok

Solution:

Let the ages of shivaji and ashok be 5x years and 4x years respectively.

After 5 years,

• Age of shivaji = 5x + 5 years
• Age of ashok = 4x + 5 years

Then,

$\\ :\implies\sf{ \frac{5x + 5}{4x + 5} = \frac{6}{5} }$

Cross multiplying the values,

$\\ :\implies\sf{5(5x + 5) =6(4x + 5) }\\ \\ :\implies\sf{25x + 25 = 24x + 30}\\ \\ :\implies\sf{25x - 24x = 30 - 25}\\ \\ :\implies \underbrace{\boxed{\mathfrak{x = 5}}} \: \pink{ \bigstar}$

Therefore,

• Age of shivaji = 5x + 5 = 5(5) + 5 = 25 + 5 = 30 years
• Age of ashok = 4x + 5 = 4(5) + 5 = 20 + 5 = 25 years

Hence,

• The ages of shivaji and ashok are 25 years and 20 years.