A certain amount is equally distributed among certain of students Each

1.	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.
Answer» ➸ GIVEN:- A certain amount is DISTRIBUTED equally to each and every student. If each would get Rs. 2 less if 10 student were more If each would get Rs. 6 more if 15 student were less. ➸ To Find:- Number of students and the amount distributed. ᬊ Required Response:- Let, Number of students be X & Amount distributed to each student y. Then, Total Amount distributed to all the students is 'xy'. According to given, each would get Rs. 2 less if 10 student were more... $(x + 10)(y - 2) = xy \\ x(y - 2) + 10(y - 2) = xy \\ xy - 2x + 10y - 20 = xy \\ - 2x + 10y - 20 = xy - xy \\ 2( - x + 5y - 10) = 0 \\ - x + 5y = 10$ -x+5y = 10 ➝① And according to each would get Rs. 6 more if 15 student were less. $(x - 15)(y + 6) = xy \\ x(y + 6) - 15(y + 6) = xy \\ xy + 6x - 15y - 90 = xy \\ 6x - 15y - 90 = xy - xy \\ 3(2x - 5y - 30) = 0 \\ 2x - 5y = 30$ 2x-5y = 30 ➝ ② By adding EQUATIONS ① & ② -x+5y = 10 2x-5y = 30 (+)________ x = 40 By Substituting Value of x[40] in any equation $2x - 5y = 30 \\ 2(40) - 5y = 30 \\ 80 - 5y = 30 \\ - 5y = 30 - 80 \\ y = \frac{ - 50}{ - 5} \\ y = 10$ y = 10 Total Amount Distributed is xy → 10×40 ☞ ₹400 Total Number of Students $\longmapsto\;{\red{\bold{40}}}$ Total Amount Distributed $\longmapsto\;{\purple{\bold{Rs.400}}}$ Amount Each Student Received $\longmapsto\;{\purple{\bold{Rs.10}}}$ $\boxed{\tt{@MrSovereign}}$ Hope This Helps!!

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.

Answer»

➸ GIVEN:-

A certain amount is DISTRIBUTED equally to each and every student.
If each would get Rs. 2 less if 10 student were more
If each would get Rs. 6 more if 15 student were less.

➸ To Find:-

Number of students and the amount distributed.

ᬊ Required Response:-

Let, Number of students be X & Amount distributed to each student y.

Then, Total Amount distributed to all the students is 'xy'.

According to given, each would get Rs. 2 less if 10 student were more...

$(x + 10)(y - 2) = xy \\ x(y - 2) + 10(y - 2) = xy \\ xy - 2x + 10y - 20 = xy \\ - 2x + 10y - 20 = xy - xy \\ 2( - x + 5y - 10) = 0 \\ - x + 5y = 10$

-x+5y = 10 ➝①

And according to each would get Rs. 6 more if 15 student were less.

$(x - 15)(y + 6) = xy \\ x(y + 6) - 15(y + 6) = xy \\ xy + 6x - 15y - 90 = xy \\ 6x - 15y - 90 = xy - xy \\ 3(2x - 5y - 30) = 0 \\ 2x - 5y = 30$

2x-5y = 30 ➝ ②

By adding EQUATIONS ① & ②

-x+5y = 10

2x-5y = 30

(+)________

x = 40

By Substituting Value of x[40] in any equation

$2x - 5y = 30 \\ 2(40) - 5y = 30 \\ 80 - 5y = 30 \\ - 5y = 30 - 80 \\ y = \frac{ - 50}{ - 5} \\ y = 10$

y = 10

Total Amount Distributed is xy → 10×40 ☞ ₹400

Total Number of Students

$\longmapsto\;{\red{\bold{40}}}$

Total Amount Distributed

$\longmapsto\;{\purple{\bold{Rs.400}}}$

Amount Each Student Received

$\longmapsto\;{\purple{\bold{Rs.10}}}$

$\boxed{\tt{@MrSovereign}}$

Hope This Helps!!