A certain amount is equally distributed among certain numbers of students each would get rs 2 less if 10 students were more and each would get rs 6 more if 15 students were less find the number of students and amount distributed
Answers
Answer:
Amount Distributed = Rs 400
40 Students
Step-by-step explanation:
Let say Amount was = Rs X
And Number of Students = S
Amount Received by each Student = X/S
Students increased by 10
so students = S + 10
Now Amount Received by each student = X/(S+10)
each would get rs 2 less if 10 students were more
X/(S + 10) = X/S - 2
Multiplying by S(S+10) both sides
=> XS = X(S+10) - 2S(S+10)
=> XS = XS + 10X - 2S² - 20S
=> 0 = 10X - 2S² - 20S
=> S² + 10S - 5 X = 0 Eq 1
Students Decreased by 15
so students = S - 15
Now Amount Received by each student = X/(S-15)
each would get rs 6 more if 15 students were less
X/(S - 15) = X/S + 6
Multiplying by S(S-15) both sides
=> XS = X(S-15) + 6S(S-15)
=> XS = XS - 15X + 6S² - 90S
=> 0 = - 15X + 6S² - 90S
=> 2S² - 30S - 5X = 0 - Eq2
Eq 2 - Eq 1
S² - 40S = 0
=> S(S-40) = 0
=> S = 40
40 Students
S² + 10S - 5 X = 0
=> 40² + 10×40 - 5X = 0
=> 1600 + 400 - 5x = 0
=> 5x = 2000
=> x = 400
Amount Distributed = Rs 400
number of students = 40
amount distributed = 400
