Problem Solving

1. The outline of a sign for an ice-cream store is made by placing 3/4 of the circumference of a circle with radius 2 feet on top of an isosceles triangle with height 5 feet, as shown below. What is the perimeter, in feet, of the sign?
(A) (3 Pi) + 3 (root3)
(B) (3 Pi) + 6 (root3)
(C) (3 Pi) + 2 (root33)
(D) (4 Pi) + 3 (root3)
(E) (4 Pi) + 6 (root3)
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2. A merchant purchased a jacket for $60 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant's gross profit on this sale?
(A) $0
(B) $3
(C) $4
(D) $12
(E) $15

sanju09 wrote:
The perimeter of the sign includes ¾ of the circumference of a circle with radius 2 feet (which is ¾*2*π*2 = 3 π feet), and the two legs of the isosceles triangle that shows the formation of cone. The chord associated with the left over quarter of the circle will form the diameter of the top of inverted cone, which got to be 2 √2 feet, (ask if any doubt), so the radius of top will be √2 feet. We can now consider the right triangle with base √2 feet and height 5 feet. Let's thank Pythagoras while finding each leg (the hypotenuse of the right triangle) = √ (2 + 25) feet = √27 feet = 3 √3 feet.

So, the required perimeter = 3 π feet + 2*3 √3 feet = (3 π + 6 √3) feet.

sanju09 wrote: Let the markup be $x such that it is 25 percent of $(60 + x)

Or x = (60 + x)/4

Or 4 x = 60 + x

Or x = 20.

So, the selling price is $80. A discount of 20 percent will bring the selling price down to $64, or a gross profit of [spoiler]$4[/spoiler] will be made on this sale.

trindadesn wrote:

sanju09 wrote:
The perimeter of the sign includes ¾ of the circumference of a circle with radius 2 feet (which is ¾*2*π*2 = 3 π feet), and the two legs of the isosceles triangle that shows the formation of cone. The chord associated with the left over quarter of the circle will form the diameter of the top of inverted cone, which got to be 2 √2 feet, (ask if any doubt), so the radius of top will be √2 feet. We can now consider the right triangle with base √2 feet and height 5 feet. Let's thank Pythagoras while finding each leg (the hypotenuse of the right triangle) = √ (2 + 25) feet = √27 feet = 3 √3 feet.

So, the required perimeter = 3 π feet + 2*3 √3 feet = (3 π + 6 √3) feet.

Thanks for this. I had got till 3Pi even earlier but I still dont get how you got the base of the triangle as 2(root2)

sanju09 wrote: Let the markup be $x such that it is 25 percent of $(60 + x)

Or x = (60 + x)/4

Or 4 x = 60 + x

Or x = 20.

So, the selling price is $80. A discount of 20 percent will bring the selling price down to $64, or a gross profit of [spoiler]$4[/spoiler] will be made on this sale.

I just don't get this one!

Apologise regd. the 2 qts in 1 post. I'm a little new here. What did you mean by Views to every single one will be gratified with one and the same consideration here. Why are views important?

sanju09 wrote:2. A merchant purchased a jacket for $60 and then determined a selling price that equaled the purchase price of the jacket plus a markup that was 25 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant's gross profit on this sale?
(A) $0
(B) $3
(C) $4
(D) $12
(E) $15

Let the markup be $x such that it is 25 percent of $(60 + x)

Or x = (60 + x)/4

Or 4 x = 60 + x

Or x = 20.

So, the selling price is $80. A discount of 20 percent will bring the selling price down to $64, or a gross profit of [spoiler]$4[/spoiler] will be made on this sale.

[spoiler]C[/spoiler]

sanju09 wrote:1. The outline of a sign for an ice-cream store is made by placing 3/4 of the circumference of a circle with radius 2 feet on top of an isosceles triangle with height 5 feet, as shown below. What is the perimeter, in feet, of the sign?
(A) (3 Pi) + 3 (root3)
(B) (3 Pi) + 6 (root3)
(C) (3 Pi) + 2 (root33)
(D) (4 Pi) + 3 (root3)
(E) (4 Pi) + 6 (root3)

The perimeter of the sign includes ¾ of the circumference of a circle with radius 2 feet (which is ¾*2*π*2 = 3 π feet), and the two legs of the isosceles triangle that shows the formation of cone. The chord associated with the left over quarter of the circle will form the diameter of the top of inverted cone, which got to be 2 √2 feet, (ask if any doubt), so the radius of top will be √2 feet. We can now consider the right triangle with base √2 feet and height 5 feet. Let's thank Pythagoras while finding each leg (the hypotenuse of the right triangle) = √ (2 + 25) feet = √27 feet = 3 √3 feet.

So, the required perimeter = 3 π feet + 2*3 √3 feet = (3 π + 6 √3) feet.

[spoiler]B[/spoiler]

Sanju,

i got 3pi, but i'm quite lost after that. how did you get 2√2?

sanju09 wrote:The chord associated with the left over quarter of the circle will form the diameter of the top of inverted cone, which got to be 2 √2 feet, (ask if any doubt), so the radius of top will be √2 feet. We can now consider the right triangle with base √2 feet and height 5 feet. Let's thank Pythagoras while finding each leg (the hypotenuse of the right triangle) = √ (2 + 25) feet = √27 feet = 3 √3 feet.

could you please elaborate on this?

ace_gre wrote:Circumference of the circle which forms the ice-cream is 3/4th of the circle==> an angle equivalent to 3/4 * 360 = 270.
The remainder of the circle forms an isosceles right triangle with the center.
Using pythagoras theorem, base = (4 + 4) ^1/2.

Hope the diagram in the attachment helps !

bhumika.k.shah wrote:i meant the Cost price and the mark up price sum...
another approach for that sum people????

rahul.s wrote:

bhumika.k.shah wrote:i meant the Cost price and the mark up price sum...
another approach for that sum people????