Some students planned a picnic. The budget for the food was Rs. 960. As eight of them failed to join the picnic, the cost of the food for each member increased by Rs 10. Find how many students went for the picnic.
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Step-by-step explanation:
Let the original number of students be x.
∴ Budget of each student = Rs 960 / x
When 8 boys failed to go to the picnic, then
Number of students who went to the picnic = x – 8
New budget of each student = Rs 960 / ( x - 8)
Given, New budget of each students – Budget of each student = Rs 6
960 / ( x – 8) - 960 / x = 6
960 [ x – x + 8 ] = 6x( x – 8)
160 [ 8 ] = x( x – 8)
x2 – 8x – 1280 = 0
x2 – 40x + 32x – 1280 = 0
x( x – 40) + 32 ( x – 40) = 0
x + 32 = 0 or x – 40 = 0
x = -32 or 40.
∴ x = 40 ( x cannot be negative)
Number of students who went to the picnic = x – 8 = 40 – 8 = 32.
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