Question

Q : 2

Ratna has ₹ 200 more than three times the amount Rafik has. If ₹ 300 from the amount with Ratna are given to Rafik, the amount with Ratna will be 7/4 times the amount with Rafik. Find the initial amount with Rafik.

Answer 1

$\textbf{SOLUTION :}$



The amount with Ratna is ₹ 200 more than three times the amount with Rafik.



Let the initial amount with Rafik be ₹ x


» Ratna has ₹ 3x + 200


₹ 300 from Ratna are given to Rafik.


» amount remaining with Ratna is

₹ ( 3x + 200 - 300 )

= ₹ ( 3x - 100 )


» now Rafik has ₹ ( x + 300 ).



The amount with Ratna is $\frac{7}{4}$ times the amount with Rafik.

$> \: \frac{amount \: with \: ratna}{amount \: with \: rafik} \: = \: \frac{7}{4} \\ \\ > \: \frac{3x - 100}{x + 300} \: = \: \frac{7}{4} \\ \\ > \: 4 \: = > \: \: 3x - 100 = 7 \: = > x + 300 \\ \\ > \: 12x - 400 = 7x + 2100 \\ \\ > \: 12x - 7x = 2500 \\ \\ > \: 5x = \textbf{2500} \\ \\ > \: x = \textbf{500}$



$\textbf{Ans :}$ Initial amount with Rafik is ₹ $\textbf{500}$.

Answer 2

$\textbf{SOLUTION :}$

The amount with Ratna is ₹ 200 more than three times the amount with Rafik.

Let the initial amount with Rafik be ₹ x

» Ratna has ₹ 3x + 200

₹ 300 from Ratna are given to Rafik.

» amount remaining with Ratna is

₹ ( 3x + 200 - 300 )

= ₹ ( 3x - 100 )

» now Rafik has ₹ ( x + 300 ).

The amount with Ratna is \frac{7}{4}

4

7

times the amount with Rafik.

$\begin{lgathered}> \: \frac{amount \: with \: ratna}{amount \: with \: rafik}$ \: = \: \frac{7}{4} \\ \\ > \: \frac{3x - 100}{x + 300} \: = \: \frac{7}{4} \\ \\ > \: 4 \: = > \: \: 3x - 100 = 7 \: = > x + 300 \\ \\ > \: 12x - 400 = 7x + 2100 \\ \\ > \: 12x - 7x = 2500 \\ \\ > \: 5x = \textbf{2500} \\ \\ > \: x = \textbf{500}\end{lgathered}

>

amountwithrafik

amountwithratna

=

4

7

>

x+300

3x−100

=

4

7

>4=>3x−100=7=>x+300

>12x−400=7x+2100

>12x−7x=2500

>5x=2500

>x=500

$\textbf{Ans :}Ans : Initial amount with Rafik is ₹ \textbf{500}$