Question

The length of a rectangular board is 15 cm more than its breadth. If the length is increased by 9 cm and the breadth is decreased by 6 cm, the area of the board remains the same as before. What is the ratio between the original length and breadth of the board?
1. 12 : 7
2. 21 : 16
3. 7 : 6
4. 4 : 3

Answer 1

Correct Answer - Option 2 : 21 : 16

Given:

length of a rectangular board is 15 cm more than its breadth.

length is increased by 9 cm and the breadth is decreased by 6 cm.

Let the breadth of the rectangular board be x

=> length of rectangular board = x + 15

Now

New, lenght of rectangular board be = x + 15 + 9

= x + 24

Breadth of rectangular board = x - 6

Given the area is equal. In both case

=> (x + 15) x = (x + 24) × (x - 6) 

x² + 15x = x² - 6x + 24x - 144

15x = 18x - 144

3x = 144

x = 144/3

x = 48

Thus breadth of the rectangular board = 48

length = (48 + 15)

length = 63 

Thus the ratio between the original length and breadth of the board = 63 : 48

= 21 : 16 

Hence, the correct answer is "21 : 16".