Question

A certain amount is equally distributed among certain number 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 the amount distributed.​

Answer 1

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Answer 2

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

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

Decreased by 15

so = 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