(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

Formulate the following problems as a pair of equations, and hence find their solutions:
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Medium

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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.

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Formulate the following problems as a pair of equations, and hence find their solutions:Ritu can row downstream $20\, km$ in $2\, hours,$ and upstream $4\, km$ in $2\, hours.$ Find her speed of rowing in still water and the speed of the current.

Prashant purchases $2$ mobiles and $3$ memory cards for Rs. $6500$. The cost of one mobile and one memory card is Rs. $2950$. Represent this as a pair of linear equations in two variables.

If the following pair of equations has infinite solutions,then find the value of $k$:$5x + 2y = k$$10x + 4y = 3$

The sum of a two-digit number and the number obtained by reversing the digits is $66$. If the digits of the number differ by $2$,find the number. How many such numbers are there?

Solve the following pair of equations by the method of cross-multiplication:$2x + y = 35$$3x + 4y = 65$

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Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream $20\, km$ in $2\, hours,$ and upstream $4\, km$ in $2\, hours.$ Find her speed of rowing in still water and the speed of the current.

If the following pair of equations has infinite solutions,then find the value of $k$:
$5x + 2y = k$
$10x + 4y = 3$

Solve the following pair of equations by the method of cross-multiplication:
$2x + y = 35$
$3x + 4y = 65$