 So, in this question, 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 and the breadth by 2 units, the area increases by 67 square units. Find the dimension of the rectangle. Okay. So, let us start with some assumptions. So, let us say, so this is the solution. Let the length of the rectangle be L and similarly, let the breadth of the rectangle be B. Therefore, area of rectangle would be length into breadth that is L into B. Okay. Now, they say the area of a rectangle gets reduced by 9, so that means LB minus 9, so reduced by 9 when if its length is reduced by 5 units, so L minus 5 and breadth is increased by 3 units, so B plus 3, right? This is the first equation. You can simplify it and write LB minus 9 is equal to LB plus 3L minus 5B minus 15, right? So this LB and this LB will get cancelled and you will get what 3L minus 5B and this minus 9 goes on to the right-hand side becomes minus 15 plus 9 equals 0, so simplifying you will get 3L minus 5B minus 6 equals 0. Let it be equation number 1, okay? On the other hand, they say if we increase the length by 3, so L plus 3 and the breadth by 2, so that means B plus 2, so this will be the new area and the new area they are saying will be original area plus 67 square units. So let us again simplify this, LB plus 3B plus 2L plus 6 is equal to LB plus 67, so LB and LB gets cancelled and you will get 3B plus 2L minus 61 equals 0, so these are the two equation number 2. So what can we do? We can eliminate, use the method of elimination. So let us multiply this equation by 2, so that we get 6L minus 10B minus 12 equals 0 and let us multiply this equation by 3. So we will multiply the first equation by 2 to get 6L minus 10B minus 12 equals to 0 and multiply the second equation by 3 to get 6L and then 9B plus 9B, right? 6L plus 9B minus 183 equals 0 and then subtract, so this is minus minus plus, so it will become 19B minus 19B and this is plus 171 equals 0. So hence B is 171 upon 19 to give you B equals as equal to 9, okay? Now when B is 9, you can find out L, so let us use the first equation, so 3L minus 5 into 9. This is the first equation here, minus 6 equals 0, so 3L will be equal to 51, right? 95 is 45 plus 651, so L is 51 upon 3 that is 17, okay? So hence dimension of the rectangle is 17 and breadth is 9. Let us check if this is true or not, so hence if I reduce, so what is the area now? LB is nothing but 17 into 9 which is 153, right? 17 or 9 is 153 square units. Now if I reduce the length by 5, so it will become 12 and then the question was if I reduce the length by 5 and increase the breadth by 3, so it will be 12 and this is 144, right? Which is nothing but 153 minus 9, that's correct, first condition is met and the second condition is increase length by 3, so it will be 20 and increase breadth by 2, so 11, so it will be 220 which is 220 is nothing but 153 plus 67, right? Yeah, so hence both the conditions are met, right? So hence our solution is correct, so L is 17 and B is 9.