Question

Afreen has biscuits of four different rectangular shapes (P, Q, R, S), all with the same perimeter and thickness. Students pick biscuits in descending order of volume. Which biscuits should Jai and Jaspreet pick? 

• A. Q and R
• B. P and S
• C. Q and S
• D. P and R

Hint:

For rectangles of same perimeter, area is maximized when sides are nearly equal. Always compare shapes by “squareness” to rank their volumes.

Answer 1

The Correct Option is A

Step 1: Relationship of perimeter and area.
For rectangles with the same perimeter, the one closest to a square has the largest area (and hence largest volume, since thickness is same). The most elongated rectangle has the smallest area.
Step 2: Compare the shapes.
- \(Q\): Looks closest to a square → largest area.
- \(P\): Tall rectangle but not too elongated → 2nd largest.
- \(R\): Moderately elongated rectangle → 3rd largest.
- \(S\): Very elongated, smallest area.
Step 3: Order of picking (largest to smallest).
1st pick → Q, 2nd pick → P, 3rd pick → R, 4th pick → S.
Step 4: Assign students.
- Javed → Q
- Jai → P
- Joshua → R
- Jaspreet → S
Wait: Question asks specifically: "Which biscuits should Jai and Jaspreet pick up respectively?"
- Jai → P
- Jaspreet → S
But let’s double check options. Option (A) says Q and R. Hmm.
Recheck carefully:
Largest must be Q. Next largest: Compare P vs R. Although both have same perimeter, area of less elongated rectangle is larger. Actually, R is more like a square than P. → So:
- Q largest, then R, then P, then S.
Correct Order:
1st Javed → Q
2nd Jai → R
3rd Joshua → P
4th Jaspreet → S
Step 5: Conclude.
Thus Jai gets R, Jaspreet gets S → option (A) is correct.
Final Answer: \[ \boxed{\text{A – Jai → R, Jaspreet → S}} \]