Question

Rs 6500 is to be equally divided among a certain number of persons

Answer 1

let the certain number of personbe x

then , 6500÷x

Answer 2

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Let the original number of persons be x.

Then the amount received by each person = Rs. $\sf{\frac{6500}{x}}$

When 15 more persons are added, amount received by each person = Rs. $\sf{\frac{6500}{x+15}}$

A/C,

$\longrightarrow$$\sf{\frac{6500}{x} - \frac{6500}{x + 15} = 30}$

$\longrightarrow$$\sf{650( \frac{(x + 15) - x}{x(x + 15)} ) = 3}$

$\longrightarrow$$\sf{650 \times 15 = 3x(x + 15)}$

$\longrightarrow$$\sf{{x}^{2} + 15x - 3250 = 0}$

Here, a = 1, b = 15 and c = -3250

$\therefore$ $\sf{d = {b}^{2} - 4ac}$

$\longrightarrow$$\sf{ {(15)}^{2} - 4 \times 1 \times ( - 3250)}$

$\longrightarrow$$\sf{225 + 13000}$

$\longrightarrow$$\sf{13225 > 0}$

So, the real roots exist. Using the quadratic formula,

$\longrightarrow$$\sf{x = \frac{ - b ± \sqrt{d} }{2a}}$

$\longrightarrow$$\sf{\frac{ - 15 ± \sqrt{13225} }{2 \times 1}}$

$\longrightarrow$$\sf{ \frac{ - 15 ± 115}{2}}$

$\longrightarrow$$\sf{50 \: or \: - 65}$

As the number of persons cannot be negative, x ≠ -65, x = 50

Hence, the original number of persons = 50