Some friends planned on a leisure trip where they had planned Rs.96 on eatables. 4 of them did not come. So the rest of them had to pay Rs. 4 each extra. The number of people who turned up on the trip was:
Show answer & explanation
Correct answer: A
Explanation
Given:
Total Expenses = ₹96
4 friends did not come
Each had to pay ₹4 extra
Formula:
Per capita Expenses = Total Expenses / Number of People
Let the initial number of people = x
Per capita Expenses = 96 / x
Four people did not come, so the remaining people = x − 4
New per capita Expenses = 96 / (x − 4)
Difference = ₹4
96/(x − 4) − 96/x = 4
LCM = x(x − 4)
96x − 96(x − 4) / x(x − 4) = 4
96x − 96x + 384 = 4x(x − 4)
384 = 4x² − 16x
96 = x² − 4x
x² − 4x − 96 = 0
(x − 12)(x + 8) = 0
x = 12
People on the trip = x − 4 = 8