Question

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A certain amount is equally distributed among certain of students Each would get Rs. 2 less if 10 student were more and each would get Rs. 6 more if 15 student were less. Find the number of student and the amount distributed.

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Answer 1

₹400 were distributed among 40 students.

Step-by-step explanation:

✯Let us assume that distributed amount = x rs.

Among no.of students = y

✯Let after distributing x rs. Among y students each student will get = x/y = z rs.

Therefore x/y = z

=> x = yz consider it as equation -- 1

✯It is given that if 10 students were more each student would get 2 rs. Less

=> x/(y+10) = z -2

=> x = (z-2)(y+10)

=> x = yz-2y+10z-20

✯From equation 1 yz = x

=> x = x-2y+10z-20

Both sides x will get cancelled

✯Therefore 10z -2y = 20 equation--2

Given if 15 students were less each student would get 6 rs. More

=> x/(y-15) = (z + 6)

=> x = (z+6)(y-15)

X = zy + 6y -15z -90

From equation--1

X = x + 6y -15z -90

6y -15z = 90 equation--3

On solving 2 and 3 equations we get

z = 10 and y = 40

X = yz = 10*40 = 400

✯Therefore among 40 students 400 rs. Were distributed.☺︎︎