Question

Slove the problem!! ​

Answer 1

$\huge \bf { \mid{ \overline{ \underline \red{answer - }}} \mid}$

The original number of persons is 50.

$\huge \underline{ \underline \mathfrak{explanation - }}$

Let the original number of persons be x.

Total amount to be divided =Rs 6500.

Share of each =Rs $\frac{6500}{x}$

New number of persons =(x+15).

Now, share of each =Rs $\frac{6500}{(x + 15)} . \\ \therefore \: \frac{6500}{x} - \frac{6500}{(x + 15)} = 30 \\ \implies \: \frac{1}{x} - \frac{1}{(x + 15)} = \frac{30}{6500} \\ \implies \: \frac{(x + 15) - x}{x(x + 15)} = \frac{3}{650} \\ \implies \: \frac{15}{( {x}^{2} + 15x) } = \frac{3}{650} \\ \implies \: 3( {x}^{2} + 15x) = 9750 \\ \implies \: {x}^{2} + 15x = 3250 \implies {x}^{2} + 15x - 3250 = 0$

$\implies {x}^{2} + 65x - 50x - 3250 = 0 \\ \implies \: x(x + 65) - 50(x + 65) = 0 \\ \implies \: (x + 65)( x- 50 = 0 \\ \implies \: x + 65 = 0 \: or x - 50 = 0 \\ \implies \: x = - 65 \: or \: = 50 \\ \implies \: x = 50 \: \: \: \:$.

Hence the original numbers of the persons is 50.

Answer 2

Answer:

Step-by-step explanation:

The original number of persons is 50.

\huge \underline{ \underline \mathfrak{explanation - }}

Let the original number of persons be x.

Total amount to be divided =Rs 6500.

Share of each =Rs \frac{6500}{x}

New number of persons =(x+15).

Now, share of each =Rs \frac{6500}{(x + 15)} . \\ \therefore \: \frac{6500}{x} - \frac{6500}{(x + 15)} = 30 \\ \implies \: \frac{1}{x} - \frac{1}{(x + 15)} = \frac{30}{6500} \\ \implies \: \frac{(x + 15) - x}{x(x + 15)} = \frac{3}{650} \\ \implies \: \frac{15}{( {x}^{2} + 15x) } = \frac{3}{650} \\ \implies \: 3( {x}^{2} + 15x) = 9750 \\ \implies \: {x}^{2} + 15x = 3250 \implies {x}^{2} + 15x - 3250 = 0