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)

About The Mid Point Theorem - CUET-UG

The Mid Point Theorem is a vital chapter for CUET-UG aspirants. Mastering the concepts covered in this chapter is essential for securing a top rank.

By rigorously practicing the previous year questions associated with this chapter, you can identify high-yield topics, understand the examiner's perspective, and boost your confidence during the actual exam.

Frequently Asked Questions

Why focus on The Mid Point Theorem PYQs?

Analyzing PYQs for this specific chapter reveals the most frequently tested concepts and the typical complexity of questions, allowing you to tailor your study plan efficiently.

How to best use this analysis?

Review the topic breakdown to see which sub-topics within The Mid Point Theorem carry the most weight. Then, tackle the questions iteratively to solidify your understanding.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

About The Mid Point Theorem - CUET-UG

Frequently Asked Questions

Why focus on The Mid Point Theorem PYQs?

How to best use this analysis?

The Mid Point Theorem

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

About The Mid Point Theorem - CUET-UG

Frequently Asked Questions

Why focus on The Mid Point Theorem PYQs?

How to best use this analysis?

Chapter Questions
2 MCQs