Question

Raman bought certain number of glass vessels ₹600 2 of them broke then he sold the remaining for ₹10 more than he had given for it, thereby gaining ₹50 on the whole, how many glass vessel did he buy and also.Find the cost of each glass be x

Answer 1

$\sf\large\underline{Let:}$

$\tt{\implies The\:number\:of\:buying\:glass=x}$

$\tt{\implies The\:number\:of\:selling\:glass=y}$

$\sf\large\underline{To\: Find:}$

$\rm{\implies Total\:number\:of\:glass=?}$

$\sf\large\underline{Solution:}$

$\sf\large\underline{Given,\:that:}$

Raman bought certain number of glass vessels ₹600. 2 of them broke then he sold the remaining for ₹10 more than he had given for it, thereby gaining ₹50 on the whole.

$\sf\large\underline{According\:to\: question:}$

$\tt{\implies (buying\: glass)(selling\:glass)=Rs.600}$

$\tt{\implies xy=600}$

$\tt{\implies y=\frac{600}{x}}$

• profit on remaining selling glass for Rs.10 and profit on whole for Rs.50]

$\tt{\implies (x-2)(y+10)=600+50}$

• Putting the value of y here]

$\tt{\implies (x-2)(\frac{600}{x}+10)=650}$

$\tt{\implies \frac{600x}{x}+10x-\frac{1200}{x}-20=650}$

$\tt{\implies \frac{600x+10x^2}{x}-\frac{1200}{x}=670}$

$\tt{\implies \frac{600x+10x^2-1200}{x}=670}$

$\tt{\implies 10x^2+600x-670x-1200=0}$

$\tt{\implies 10x^2-70x-1200=0}$

• Dividing by 10 on both sides , here]

$\tt{\implies x^2-7x-120=0}$

• Here, splitting the middle term here]

$\tt{\implies x^2-15x+8x-120=0}$

$\tt{\implies x(x-15)+8(x-15)=0}$

$\tt{\implies \therefore\:x=15\:and\:-8}$

• Here negative value can't be the number of glass so we have to take x=15

Therefore, Raman bought 15 glass for Rs.600

Answer 2

$\bf\large{\underline{Question:-}}$

Raman bought certain number of glass vessels ₹600 2 of them broke then he sold the remaining for ₹10 more than he had given for it, thereby gaining ₹50 on the whole, how many glass vessel did he buy and also.Find the cost of each glass be x

$\bf\large{\underline{Given:-}}$

• Raman bought certain glass vessel at ₹ 600
• 2 of them broke.
• he sold remaining for 10 ₹ more than he had given for it
• therefore he gaining 50₹ on the whole.

$\bf\large{\underline{To\:find:-}}$

• how many glass vessel did he buy and also.Find the cost of each glass be x

$\bf\large{\underline{solution:-}}$

Let,

• The number of buying glass = x and selling glass =y

$\bf\large{\underline{According\:to\:Question:-}}$

$\tt →xy=600 \\\tt→y=\frac{600}{x}$

• he gain 10₹ profit on remaining glass and whole 50₹

$\tt→(x-2)(y+10)=600+50$

putting vue of y here.

$\tt→ (x-2)(\frac{600}{x}+10)=650\\\tt→\frac{600}{x}+10x-\frac{1200}{x}-20=650\\\tt→ \frac{600x+10x^2+1200}{x}=670\\\tt→ 10x^2-600x-670x-1200=0\\\tt→ 10x^2-70x-1200=0(Divided\:by\:10\:both\:side)$

we get,

$\tt→ x^2-7x-120=0 \\\tt→ x^2-15x+8x-120=0\\\tt→ x(x-15)+8(x-15)=0\\\tt→(x-15)(x+8)=0\\\tt→ x-15=0,x+8=0\\\tt→ x=15, x=-8$

here,

we take x=15

because x= -8 is a negative value . so we neglect it.

Hence,

Raman purchase 15 glass of ₹600