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

$\huge\underline\frak{\fbox{AnSwEr :-}}$

Let the number of students be x and amount given to each student be ` y.

$\implies$ Total amount distributed is xy

From the first condition we get,

$\implies$ (x + 10) (y - 2) = xy

$\implies$ xy - 2x + 10y - 20 = xy

$\implies$ - 2x + 10y = 20

$\implies$ - x + 5y = 10 . . . (I)

From the 2nd condition we get,

$\implies$ (x - 15) (y + 6) = xy

$\implies$ xy + 6x - 15y - 90 = xy

$\implies$ 6x - 15y = 90

$\implies$ 2x - 5y = 30 . . . (II)

Adding equations (I) and (II)

$\implies$ - x + 5y = 10 + 2x - 5y = 30

$\implies$ x = 40

Substitute this value of x in equation (I)

$\implies$ - x + 5y = 10

$\implies$ - 40 + 5y = 10

$\implies$ 5y = 50

$\implies$ y = 10

Total amount distributed is = xy = 40 x 10 = rs 400.

$\implies$ rs` 400 distributed equally among 40 students.

Answer 2

Step-by-step explanation:

$\bf \underline{Question} \:$

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.

___________________________

$\bf \underline{To..Find} \:$

• The number of students and the amount distributed.

___________________________

$\bf \underline{Given \to} \:$

• A certain amount is equally distributed among certain number of students.
• Each would get rs 2 less if 10
• Students each would get rs 6 more if 15 students were less.

Supposed us assume ,there are:-

X students and each can be given Y rupees.

Now,

$\bf \underline{According..to..the..question..\to} \:$

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

=> (X+10) students would get each (Y-2)

$\tt Amount= (X+10)(Y-2)$

Each would get rs. 6 more if 15 students were less

=> (X-15) students would get each (Y+6)

$\tt \: Amount= (X-15)(Y+6) \\ </p><p></p><p> \tt \: (X+10)(Y-2)=(X-15)(Y+6) \\ </p><p></p><p> \tt \: XY-2X+10Y-20=XY+6X-15Y-90 \\ </p><p></p><p> \tt \: 8X-25Y=70. eq1$

$\bf \underline{ Similarity\to} \:$

$\tt \:XY=(X+10)(Y-2)</p><p></p><p> \tt \: XY=XY-2X+10Y-20 \\ </p><p></p><p> \tt \: 2X-10Y=-20. \\ </p><p></p><p> \tt \: 2X \times 4-10Y \times 4=-80 ....Eq2 \\ </p><p></p><p> \tt \: Using \: eq1 \: and \: eq2 \\ </p><p></p><p> \tt \red{X=40} \\ </p><p></p><p> \tt \red{Y=10}</p><p>$

$\tt \: xy=40\times10=400$

$\tt \: Answer \: INITIAL .. STUDENTS \: 40 \: \\ </h3><h3> \\ \tt \: TOTAL \: MONEY = 400 \\ </h3><p></p><h3> \tt \: EACH ..WOULD ..HAVE ..GOT.. 10</h3><p></p><p>$