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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Step-by-step explanation:

Let number of students be 'x'.

Also Let Amount each student will get be 'y'.

Total Amount will be number of students multiplied by Amount each student will get.

framing equation we get;

Total Amount = xyxy

Now Given:

each would get rs.2 less if 10 students were more

framing in equation for we get;

xy = (x+10)(y-2)xy=(x+10)(y−2)

Now by Using Multiplication property we get:

\begin{lgathered}xy = xy-2x+10y-20\\\end{lgathered}

xy=xy−2x+10y−20

Subtracting both side by xy and adding both side by 20 we get;

\begin{lgathered}xy-xy+20=xy-2x+10y-20+20-xy\\\\20 =-2x+10y\end{lgathered}

xy−xy+20=xy−2x+10y−20+20−xy

20=−2x+10y

Now Dividing both side by 2 we get;

\begin{lgathered}\frac{20}{2} = \frac{-2x}{2}+\frac{10y}{2}\\\\10 = -x+5y \ \ \ \ equation \ 1\end{lgathered}

2

20

=

2

−2x

+

2

10y

10=−x+5y equation 1

Also Given:

each would get rs.6 more of 15 student were less

xy = (x-15)(y+6)xy=(x−15)(y+6)

Now by Using Multiplication property we get:

\begin{lgathered}xy = xy+6x-15y-90\\\end{lgathered}

xy=xy+6x−15y−90

Subtracting both side by xy and adding both side by 90 we get;

\begin{lgathered}xy-xy+90=xy+6x-15y-90+90-xy\\\\90 =6x-15y\end{lgathered}

xy−xy+90=xy+6x−15y−90+90−xy

90=6x−15y

Now Dividing both side by 3 we get;

\begin{lgathered}\frac{90}{3} = \frac{6x}{3}-\frac{15y}{3}\\\\30 = 2x-5y \ \ \ \ equation \ 2\end{lgathered}

3

90

=

3

6x

−

3

15y

30=2x−5y equation 2

Now adding equation 1 and equation 2 we get;

\begin{lgathered}10+30 = (-x+5y)+ (2x-5y)\\\\40 = -x+5y+2x-5y\\\\40 = x\end{lgathered}

10+30=(−x+5y)+(2x−5y)

40=−x+5y+2x−5y

40=x

Now Substituting the value of 'x' in equation we get;

\begin{lgathered}-x+5y=10\\\\-40+5y=10\\\\5y =10+40\\\\5y =50\\\\y=\frac{50}{5} = 10\end{lgathered}

−x+5y=10

−40+5y=10

5y=10+40

5y=50

y=

5

50

=10

Total Amount = xy= 40 \times 10 = Rs. \ 400xy=40×10=Rs. 400

Hence we can say, There are 40 students and amount of money distributed among each is ₹10 and total Amount of Money is ₹400.