The Length of a Blackboard is 7 Cm More Than its Breadth GMAT Problem Solving

Question: The length of a blackboard is 7 cm more than its breadth. If the length is increased by 9 cm and breadth is decreased by 3 cm, then the area remains the same. What is the length and breadth of the blackboard (in cm) ?

(A) 13, 6
(B) 14, 7
(C) 15, 8
(D) 16, 9
(E) 17, 19

Correct Answer: C
Solution and Explanation:
Approach Solution 1:

The problem statement states that:

Given:

• The length of a blackboard is 7 cm more than its breadth.
• If the length is increased by 9 cm and the breadth is decreased by 3 cm, then the area remains the same.

Find out:

• The length and breadth of the blackboard (in cm)

Let the length be L and the breadth of the blackboard be B
As per the condition of the question we get:
L = 7 + B
Area of the board, L × B = (7 + B) × B
If its length is increased by 9 cm and breadth is decreased by 3 cm, its area remains the same.
=> (L + 9)(B − 3) = L × B

However, L = 7 + B
=> (7 + B + 9)(B − 3) = (7 + B) × B
=> (16 + B)(B − 3) = (7 + B) × B
=> 16B − 48 + B^2 − 3B = 7B + B^2
=> 6B = 48
=> B = 8 cm
Therefore, Length = 7 + 8 = 15 cm

Hence, the length and breadth of the blackboard are 15cm and 8cm respectively.

Approach Solution 2:

The problem statement informs that:

Given:

• The length of a blackboard is 7 cm more than its breadth.
• If the length is increased by 9 cm and the breadth is decreased by 3 cm, then the area remains the same.

Find out:

• The length and breadth of the blackboard (in cm)

The problem can be solved by an easier and quicker approach.

Let’s solve the question by analysing the options.

Let’s consider option (A) 13, 6.
Here the length is 7cm more than the breadth.
Area = 13 * 6 = 78.
As per the given condition, new length = 13 + 9 = 22 and new breadth = 6 – 3 = 3
New area= 22 * 3 = 66.
Therefore, it contradicts the condition of the question since the new area is not the same as the previous area. Hence, option A is wrong.

Let’s consider option (B) 14, 7.
Here the length is 7cm more than the breadth.
Area = 14 * 7 = 98.
As per the given condition, new length = 14 + 9 = 23 and new breadth = 7 – 3 = 4
New area= 23 * 4 = 92.
Therefore, it contradicts the condition of the question since the new area is not the same as the previous area. Hence, option B is wrong.

Let’s consider option (C) 15, 8.
Here the length is 7cm more than the breadth.
Area = 15 * 8 = 120.
As per the given condition, new length = 15 + 9 = 24 and new breadth = 8 – 3 = 5
New area= 24 * 5 = 120.
Therefore, it agrees with the condition of the question since the area remains the same.
Hence option C satisfies each and every condition. Thus it is the correct answer.

Consequently, the rest of the options gets eliminated.
Hence, the length and breadth of the blackboard are 15cm and 8cm respectively.

“The length of a blackboard is 7 cm more than its breadth”- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. The candidate needs to examine every data and fact of the GMAT Problem Solving questions to solve quantitative problems. GMAT Quant practice papers help the candidates to get aware of different types of questions that will enable them to score better in the exam.

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