Question

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Rs. 6500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs. 30 less. Find the original number of persons.




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Answer 1

Answer:

Let number of persons be n.

Share of each person = 6500/n ------------ (i)

There been 15 persons = 6500/n+15 ---------- (ii)

Solving (i) and(ii) we get

= 6500/n - 6500/n+15 = 30

= 6500*15/n^2 + 15n = 30

= 6500*15/30 = n * n +15n

= 3250=n * n +15n

= n^2 + 15n-3250 = 0

= (n+65)(n-50) = 0

n=-65, n=50

Since n cannot be negative. n = 50

Hope it helps you

Answer 2

$\star\:\:\:\sf\large\underline\blue{Question:-}$

• Rs. 6500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs. 30 less. Find the original number of persons.

$\star\:\:\:\sf\large\underline\blue{Solution:-}$

• Let the total number of people be x.

Therefore,according to the given conditions,

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

$\sf \implies \frac{6500(x + 15) - 6500x}{x(x + 15)} = 30$

$\sf \implies97500 = 30 {x}^{2} + 450x$

$\sf \implies30 {x}^{2} + 450x - 97500 = 0$

On solving the given quadratic equation, we get,

x=50 and x=-65

But number of people can't be negative,

So,

Total number of people is 50.