Question

Rupees 6500 were divided equally among a certain number of girls. .Had there been 15more girls each would get rupees 30 less find the original number of girls

Answer 1

Answer:

50

Step-by-step explanation:

Let the Original no. of girls = ×;

Case I:

Total amount that was divided = 6500;

No. of Girls = x;

So, The amount each girl got = 6500/x;

Case II:

Total amount that was divided = 6500;

No. of Girls = x+15;

So, The amount each girl got = 6500/(x+15);

Therefore,

  (6500/x) - (6500/x+15) = 30;

⇒(6500x + 97500 - 6500x)/{x*(x+15)} = 30;

⇒97500/($x^{2} +15x$) = 30;

⇒30*($x^{2} +15x$) = 97500;

⇒($x^{2} +15x$) = 3250;

⇒$x^{2} +15x$ - 3250 = 0;

⇒$x^{2} +65x-50x-3250 = 0$;

⇒$x(x+65)-50(x+65)=0;$

⇒$(x+65)(x-50)=0;$

∴either,

   $x+65=0$     or         $x-50=0$

⇒$x=-65$                  ⇒$x=50$

But,∵ x cannot be negative,

∴ the original no. of girls are 50.

HOPE THIS ANWER HELPS. ANY OTHER DOUBT, PLSS ASK.

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Answer 2

$\bigstar{\pmb{\huge{\underline{\mathfrak{\red{Answer}}}}}}$

Let the original number of persons be x.

Let the original number of persons be x. Then the amount received by each person = Rs. $\sf{\frac{6500}{x}}$

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

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