Question

The area of a rectangle gets reduced by 40 square units if its length is reduced by 7 units and breadth is increased by 2 units. If we increase the length by 4 units and breadth by 4 units, then the area is increased by 108 square units. Find the length and breadth.

• A. 8 units and 15 units respectively
• B. 12 units and 15 units respectively
• C. 15 units and 8 units respectively
• D. 15 units and 12 units respectively

Hint:

Always expand the modified area expression and compare it with the original area to form linear equations.

Answer 1

The Correct Option is D

Step 1: Use first condition.
\[ (L-7)(B+2)=LB-40 \] Expanding: \[ LB+2L-7B-14=LB-40 \] \[ 2L-7B=-26 \] \[ 2L-7B+26=0 \]

Step 2: Use second condition.
\[ (L+4)(B+4)=LB+108 \] \[ LB+4L+4B+16=LB+108 \] \[ 4L+4B=92 \] \[ L+B=23 \]

Step 3: Solve simultaneously.
\[ L=23-B \] Substitute: \[ 2(23-B)-7B=-26 \] \[ 46-9B=-26 \] \[ 9B=72 \] \[ B=8 \] \[ L=15 \]

Step 4: Final answer.
\[ {L=15,\;B=8} \] Hence option (C) is correct.