(A) Let the present ages of Rajan and Jay be $3x$ and $2x$ respectively.After five years,their ages will be $(3x + 5)$ and $(2x + 5)$.According to the

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Rajan: $15$ years,Jay: $10$ years

(A) Let the present ages of Rajan and Jay be $3x$ and $2x$ respectively.After five years,their ages will be $(3x + 5)$ and $(2x + 5)$.According to the problem,the ratio of their ages after five years is $4:3$,so:$\frac{3x + 5}{2x + 5} = \frac{4}{3}$Cross-multiplying gives: $3(3x + 5) = 4(2x + 5)$$9x + 15 = 8x + 20$$9x - 8x = 20 - 15$$x = 5$Therefore,the present age of Rajan is $3 \times 5 = 15$ years and the present age of Jay is $2 \times 5 = 10$ years.

Class 10 Mathematics Pair of Linear Equations in Two Variables Mix Examples - Pair of Linear Equations in Two Variables

Medium

The ratio of the present ages of Rajan and Jay is $3:2$. After five years,the ratio of their ages will be $4:3$. Find the present ages of both.

A
Rajan: $15$ years,Jay: $10$ years
B
Rajan: $12$ years,Jay: $8$ years
C
Rajan: $18$ years,Jay: $12$ years
D
Rajan: $21$ years,Jay: $14$ years

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Pair of Linear Equations in Two Variables

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Mix Examples - Pair of Linear Equations in Two Variables

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The ratio of the present ages of Rajan and Jay is $3:2$. After five years,the ratio of their ages will be $4:3$. Find the present ages of both.

Similar Questions

The sum of a two-digit number and the number obtained by interchanging the digits is always divisible by $\ldots \ldots \ldots \ldots$

$8$ men and $12$ women can finish a piece of work in $10$ days. While $6$ men and $8$ women can finish it in $14$ days. Find the time taken by one man alone and that by one woman alone to finish the work.

Solve the following pair of linear equations by the method of substitution: $8x + 5y = 9$ and $3x + 2y = 4$.

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