Question

Some glass flower vases were bought for Rs. 6000. Ten were damaged during transporting.
The remaining were sold for a total profit of 1200 by selling each for Rs. 60 more than what was paid. Find
the number of vases bought.
​

Answer 1

The number of vases bought=50

Step-by-step explanation:

Let x be the number of vases bought

C.P of vases=Rs 6000

C.P of 1 vase=$\frac{6000}{x}$

Number of vases were damaged=10

Remaining vases=x-10

S.P of 1 vase=$\frac{6000}{x}+60$

Total profit=RS 1200

S.P of (x-10) vases=$(x-10)(\frac{6000}{x}+60})=6000-\frac{60000}{x}+60x-600=60x+5400-\frac{60000}{x}$

S.P>C.P

Profit=S.P-C.P

1200=$60x+5400-\frac{60000}{x}-6000$

$1200+6000-5400=\frac{60x^2-60000}{x}$

$1800=\frac{60x^2-60000}{x}$

$1800x=60x^2-60000$

$60x^2-1800x-60000=0$

$x^2-30x-1000=0$

$x^2-50x+20x-1000=0$

$x(x-50)+20(x-50)=0$

$(x-50)(x+20)=0$

$x-5=0\implies x=50$

$x+20=0\implies x=-20$

It is not possible because number of vases is always a natural number.

Hence, the number of vases bought=50

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Answer 2

Step-by-step explanation:

The number of vases bought=50

Step-by-step explanation:

Let x be the number of vases bought

C.P of vases=Rs 6000

C.P of 1 vase=\frac{6000}{x}x6000

Number of vases were damaged=10

Remaining vases=x-10

S.P of 1 vase=\frac{6000}{x}+60x6000+60

Total profit=RS 1200

S.P of (x-10) vases=(x-10)(\frac{6000}{x}+60})=6000-\frac{60000}{x}+60x-600=60x+5400-\frac{60000}{x}

S.P>C.P

Profit=S.P-C.P

1200=60x+5400-\frac{60000}{x}-600060x+5400−x60000−6000

1200+6000-5400=\frac{60x^2-60000}{x}1200+6000−5400=x60x2−60000

1800=\frac{60x^2-60000}{x}1800=x60x2−60000

1800x=60x^2-600001800x=60x2−60000

60x^2-1800x-60000=060x2−1800x−60000=0

x^2-30x-1000=0x2−30x−1000=0

x^2-50x+20x-1000=0x2−50x+20x−1000=0

x(x-50)+20(x-50)=0x(x−50)+20(x−50)=0

(x-50)(x+20)=0(x−50)(x+20)=0

x-5=0\implies x=50x−5=0⟹x=50

x+20=0\implies x=-20x+20=0⟹x=−20

It is not possible because number of vases is always a natural number.

Hence, the number of vases bought=50