Question

Some amount is distributed equally among a certain number of students. If there are 8 students less , every one will get Rs 10 more .if there are 16 students more , everyone will get Rs 10 less. What is the number of students and how much does each get

Answer 1

Little bit equations. But you will get

Ans. amount is ₹960. and Students are 32 in no.

Answer 2

Answer:

The number of students is 32 and each student will get Rs.960

Step-by-step explanation:

Let n be the no. of students initially and the total amount be x

Rs.x is distributed among n students equally

Each student gets amount = $\frac{x}{n}$

Now we are given that If there are 8 students less , every one will get Rs 10 more

$\Rightarrow \frac{x}{n-8}-\frac{x}{n}=10$

$8x= 10n^2 - 80n$ --- 1

Now we are given that if there are 16 students more , everyone will get Rs 10 less.

$\Rightarrow \frac{x}{n}-\frac{x}{n+16}=10$

$8x = 5n^2 + 80n$ --- 2

Solve equation 1 and equation 2

$10n^2 - 80n = 5n^2 + 80n$

$5n^2 =160n$

$n =32$

Substitute the value of n in 1

$8x= 10n^2 - 80n$

$8x= 10(32)^2 - 80(32)$

$8x= 7680$

$x= \frac{7680}{8}$

$x= 960$

Hence the number of students is 32 and each student will get Rs.960