Length of a rectangular field is increased by 10 meters and breadth is decreased by 4 meters, area of the field remains unchanged. If the length decreased by 5 meters and breadth is increased by 7 meters, again the area remains unchanged. Find the length and breadth of the rectangular field.a)12, 11b)13, 12c)13,11d)14,12e)None of theseCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b

Answer

Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b

Answer

Length = l and breadth = b,
(l +10)*(b-4) = lb and (l-5)*(b+7) = lb
Solve both equation to get l and b

Answer

Let's assume the initial length of the rectangular field is L meters and the initial breadth is B meters.

First condition:
According to the given condition, when the length is increased by 10 meters and the breadth is decreased by 4 meters, the area of the field remains unchanged.

So, the new length becomes L + 10 meters and the new breadth becomes B - 4 meters.

The area of the field is given by the formula:
Area = Length * Breadth

Since the area remains unchanged, we can write the equation as:
L * B = (L + 10) * (B - 4)

Expanding the equation:
LB = LB + 10B - 4L - 40

Simplifying the equation:
10B - 4L = 40

Second condition:
According to the given condition, when the length is decreased by 5 meters and the breadth is increased by 7 meters, the area of the field remains unchanged.

So, the new length becomes L - 5 meters and the new breadth becomes B + 7 meters.

Using the same formula for area, we can write the equation as:
L * B = (L - 5) * (B + 7)

Expanding the equation:
LB = LB - 5B + 7L - 35

Simplifying the equation:
7L - 5B = 35

Solving the equations:
We now have two equations:
10B - 4L = 40
7L - 5B = 35

To solve these equations, we can multiply the first equation by 5 and the second equation by 4 to eliminate the variable B.

Multiplying the first equation by 5:
50B - 20L = 200

Multiplying the second equation by 4:
28L - 20B = 140

Adding the two equations:
50B - 20L + 28L - 20B = 200 + 140
30B + 8L = 340

Dividing the equation by 2:
15B + 4L = 170

Now we have two equations:
15B + 4L = 170
7L - 5B = 35

Solving these equations gives us:
L = 13 meters
B = 11 meters

Therefore, the length of the rectangular field is 13 meters and the breadth is 11 meters.

Similar Quant Doubts

If the length, breadth and height of a cube are decreased, decreased and increased by 5%, 5% and 20%, respectively, then what will be the impact on the surface area of the cube (in percentage terms)?

If the length and breadth of a rectangular plot are increased by 20% and 50% respectively, Then the new area is how many times the original area?

If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 192m2. What is the area of the original rectangle?

If each side pair of opposite sides of a square is increased by 20 m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?

The area of a rectangle gets reduced by 9 square units,if its length is reduced by 5 units and breadth is increased by 3 units.If we increase the length by 3 units and breadth by 2 units, then the area is increased by 67 square units. Find the length and breadth of the rectangle.

Top Courses for Quant

Suggested Free Tests

Related Content

Quant Courses

Related Exams

Related Question Answers

Related Searches

Company