Question

some students planned picnic. The budget for food was INR 480. But 8 students failed to go and thus the cost of the food for each member increase by INR 10. How many students attended the picnic?

Answer 1

Let the number of students that turned up for the picnic be x. The budget for the food was 480. The amount per student was 480/x. If the eight students that did not turn up had also come the total number of students would be x + 8 and the amount payable by each student would have been 480/(x+8). The difference between 480/x and 480/(x +8) is 10.

480/x -480/(x +8) = 10

= 48/x - 48/(x + 8) = 1

= 48(x + 8) - 48x = x*(x + 8)

= 48x + 384 - 48x = x^2 + 8x

= x^2 + 8x - 384 = 0

= x^2 + 24x - 16x - 384 = 0

= x(x + 24) - 16(x + 24) = 0

= (x - 16)(x + 24) = 0

= x = 16 and x = -24

As the number of students cannot be negative, ignore x = -24.

The number of students that turned up for the picnic is 16

Answer 2

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