How much % above the cost price should a shopkeeper mark his good so that after allowing a discount of 10%, he should gain 26%?
The diameter of a circle is 10cm. If the distance of a chord from the centre of the circle be 4cm then , find the length of the chord.
Pls hlp!
If there is a markup of m, then we have
(1+m) * .90 = 1.26
m = 0.4, or 40%
Draw the chord, and a radius which bisects it, and the radii to the two ends. Then you will note that you have two 3-4-5 right triangles. So, the chord length is 6.
Rahim's first sum............... Cost price=100%. Gain=26%, meaning that selling price is 126% after 10% discount. So marked price before discount was 126%+10%. Therefore marked price should be at 136%
Rahim's second sum............... Diameter=10cm.. Radius=10/2=5cm. So we have formed a right angled triangle with hypotenuse 5cm,height 4cm and base as half of chord. So we are to use pythagorous theorem. 5 square=4square +half chord square.. So 5^2=4^2+(1/2 chord)^2. 25-16=(1/2chord)^2. 9=(1/2 chord)^2. Root 9=1/2 chord. 3=1/2 chord. So full chord is 3*2 which is equal to 6cm ........................... Rahim second sum....................... Cost price=100%. Gain=26%, meaning that selling price is 126% after 10% discount. So marked price before discount was 126%+10%. Therefore marked price should be at 136%
Better check your math. The markup is not 36%, since the 10% discount also applies to part of the markup.
Try some actual numbers.
Sure, I can help you with both questions.
Question 1: How much % above the cost price should a shopkeeper mark his goods so that after allowing a discount of 10%, he should gain 26%?
To solve this, let's assume the cost price (CP) of the goods is X.
Step 1: Calculate the selling price (SP) after a discount of 10%.
The selling price after a discount of 10% is given by:
SP = X - 0.1X = 0.9X
Step 2: Calculate the marked price (MP) which allows a gain of 26%.
The marked price is given by:
MP = X + 0.26X = 1.26X
Step 3: Calculate the % markup above the cost price.
We know that the selling price with a discount is 0.9X, so we need to find the percentage of markup from the cost price (X) to 0.9X.
Using the formula:
% Markup = ((MP - CP) / CP) * 100
Plugging in the values:
((1.26X - X) / X) * 100 = 26
Simplifying:
0.26X / X = 0.26
0.26 = 0.26
So, the shopkeeper should mark his goods at a markup of 26%.
Question 2: The diameter of a circle is 10cm. If the distance of a chord from the center of the circle is 4cm, then find the length of the chord.
To find the length of the chord, we can use the theorem that states that if a perpendicular is drawn from the center of a circle to a chord, it bisects the chord. This means that the distance of the chord from the center of the circle is equal to half the length of the chord.
Given that the distance of the chord from the center is 4cm, we can conclude that the length of the chord is 2 times the distance, or 2 * 4 = 8cm.
Therefore, the length of the chord is 8cm.
I hope this helps! Let me know if you have any more questions.