Question 69

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.

Solution

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

According to ques,

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

=> $$6500-30x+\frac{15\times6500}{x}-450=6500$$

=> $$-30x^2+(15\times6500)-450x=0$$

=> $$x^2+15x-3250=0$$

=> $$(x+65)(x-50)=0$$

=> $$x=50,-65$$

$$\because x$$ cannot be negative, thus number of persons are 50

=> Ans - (A)


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