The Mid Point Theorem

To find the cost of production of a table given the manufacturer's gain, wholesale dealer's gain, and the retailer's gain, let's work backwards from the retail price of ₹1265. The calculations can be understood through the following steps:

Let the cost price of the table for the retailer be x. According to the problem, the retailer gains 25%. Therefore, the selling price (retail price) can be represented as:
$x%20%2B%20%5Cfrac%7B25%7D%7B100%7D%20%5Ccdot%20x%20%3D%201.25x$
Given that the retail price is ₹1265, it follows that:
$1.25x%20%3D%201265$
Solving for x:
$x%20%3D%20%5Cfrac%7B1265%7D%7B1.25%7D%20%3D%201012$
Thus, the cost price for the retailer is ₹1012.
Next, consider the cost to the wholesale dealer, y, with a gain of 15%. This means:
$y%20%2B%20%5Cfrac%7B15%7D%7B100%7D%20%5Ccdot%20y%20%3D%201.15y$
And since the cost to the retailer is ₹1012:
$1.15y%20%3D%201012$
Solving for y:
$y%20%3D%20%5Cfrac%7B1012%7D%7B1.15%7D%20%3D%20880$
Therefore, the cost price for the wholesale dealer is ₹880.
Finally, the cost of production, z, with the manufacturer gaining 10%, is expressed as:
$z%20%2B%20%5Cfrac%7B10%7D%7B100%7D%20%5Ccdot%20z%20%3D%201.10z$
Given the cost to the wholesale dealer is ₹880:
$1.10z%20%3D%20880$
Solving for z:
$z%20%3D%20%5Cfrac%7B880%7D%7B1.10%7D%20%3D%20800$
Thus, the cost of production of the table is ₹800.

Therefore, the correct answer is ₹800.

To find the co-ordinate of the midpoint of a line segment joining two points

P(2%2C-1)

and

Q(-3%2C4)

, we use the midpoint formula. The formula for the midpoint

M(x%2C%20y)

of a segment connecting points

(x_1%2C%20y_1)

and

(x_2%2C%20y_2)

is:

M%20%3D%20%5Cleft(%5Cfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%20%5Cfrac%7By_1%2By_2%7D%7B2%7D%5Cright)

Substitute the given coordinates into the formula:

M%20%3D%20%5Cleft(%5Cfrac%7B2%20%2B%20(-3)%7D%7B2%7D%2C%20%5Cfrac%7B-1%20%2B%204%7D%7B2%7D%5Cright)

Simplify each component:

M%20%3D%20%5Cleft(%5Cfrac%7B2%20-%203%7D%7B2%7D%2C%20%5Cfrac%7B3%7D%7B2%7D%5Cright)%20%3D%20%5Cleft(-%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B3%7D%7B2%7D%5Cright)

Thus, the coordinate of the midpoint is

(-%20%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B3%7D%7B2%7D)

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

The Mid Point Theorem

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs