Solve the following question and mark the best possible option.Q. AB, CD and EF are three parallel lines, in that order. Let d1 end d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1:d2 = 2:1, P is a point on AB, Q and S are points on CD and R is a point on F-F, If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?a)slightly less than 10 unitsb)10 unitsc)slightly greater than 10 unitsd)slightly less than 20 unitse)slightly greater than 20 unitsCorrect answer is option 'E'. Can you explain this answer?

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Solve the following question and mark the best possible option.

Q. AB, CD and EF are three parallel lines, in that order. Let d₁ end d₂ be the distances from CD to AB and EF respectively. d₁and d₂ are integers, where d₁:d₂= 2:1, P is a point on AB, Q and S are points on CD and R is a point on F-F, If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?

a)
slightly less than 10 units
b)
10 units
c)
slightly greater than 10 units
d)
slightly less than 20 units
e)
slightly greater than 20 units

Correct answer is option 'E'. Can you explain this answer?

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Solve the following question and mark the best possible option.Q. AB, ...

d₁ : d₂ QR =?
SR is least If SR is least, it means SR =1. Let’s take QS =x. Also PQ =2. Hence

This value is slightly greater than 20 units.

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Solve the following question and mark the best possible option.Q. AB, ...

Solution:

To solve this question, we need to find the value of QR when the value of SR is the least. Let's break down the problem step by step.

Step 1: Understanding the given information
- AB, CD, and EF are three parallel lines in that order.
- d1 and d2 are the distances from CD to AB and EF, respectively.
- The ratio of d1 to d2 is 2:1.
- P is a point on AB.
- Q and S are points on CD.
- R is a point on EF.

Step 2: Understanding the quadrilateral PQRS
- PQRS is a quadrilateral formed by the points P, Q, R, and S.
- The area of PQRS is given as 30 square units.

Step 3: Finding the value of SR
- As the value of SR is the least, we need to minimize the distance between R and S.
- Since the lines EF and CD are parallel, the distance between any point on EF and CD will remain constant.
- Therefore, the value of SR will be constant regardless of the position of R on EF.

Step 4: Finding the value of QR
- To find the value of QR, we need to consider the given ratio of d1 to d2.
- Since d1 and d2 are the distances from CD to AB and EF, respectively, the ratio of d1 to d2 can be written as d1/d2 = 2/1.
- From the given information, we can conclude that d1 is twice the value of d2.
- Let's assume the value of d2 as x. Therefore, the value of d1 will be 2x.
- As the distance between AB and CD is parallel, we can consider the triangles formed by APQ and CRQ to be similar.
- By using the similarity of triangles, we can equate the ratios of corresponding sides:
- QR/QP = CR/CQ
- QR/(QR + d1) = d2/(d2 + x)
- QR/(QR + 2x) = x/(x + x)
- QR/(QR + 2x) = x/2x
- QR/(QR + 2x) = 1/2
- 2QR = QR + 2x
- QR = 2x

Step 5: Finding the value of QR when SR is the least
- Since the value of SR is constant and does not affect the value of QR, we can ignore it while finding the value of QR.
- From the above step, we have found that QR = 2x, where x is the value of d2.
- As x is an integer, we need to find the integer value of QR that satisfies the given condition.
- Considering the options provided, the value of QR that satisfies the condition is slightly greater than 20 units (option E).

Therefore, the correct answer is option E - slightly greater than 20 units.

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Solve the following question and mark the best possible option.Q. AB, CD and EF are three parallel lines, in that order. Let d1 end d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1:d2 = 2:1, P is a point on AB, Q and S are points on CD and R is a point on F-F, If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?a)slightly less than 10 unitsb)10 unitsc)slightly greater than 10 unitsd)slightly less than 20 unitse)slightly greater than 20 unitsCorrect answer is option 'E'. Can you explain this answer?

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Solve the following question and mark the best possible option.Q. AB, CD and EF are three parallel lines, in that order. Let d1 end d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1:d2 = 2:1, P is a point on AB, Q and S are points on CD and R is a point on F-F, If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?a)slightly less than 10 unitsb)10 unitsc)slightly greater than 10 unitsd)slightly less than 20 unitse)slightly greater than 20 unitsCorrect answer is option 'E'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Solve the following question and mark the best possible option.Q. AB, CD and EF are three parallel lines, in that order. Let d1 end d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1:d2 = 2:1, P is a point on AB, Q and S are points on CD and R is a point on F-F, If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?a)slightly less than 10 unitsb)10 unitsc)slightly greater than 10 unitsd)slightly less than 20 unitse)slightly greater than 20 unitsCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Solve the following question and mark the best possible option.Q. AB, CD and EF are three parallel lines, in that order. Let d1 end d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1:d2 = 2:1, P is a point on AB, Q and S are points on CD and R is a point on F-F, If the area of the quadrilateral PQRS is 30 square units, what is the value of QR when value of SR is the least?a)slightly less than 10 unitsb)10 unitsc)slightly greater than 10 unitsd)slightly less than 20 unitse)slightly greater than 20 unitsCorrect answer is option 'E'. Can you explain this answer?.

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