Two boxes, P and Q, hold some marbles. If 15 marbles are moved from box Q to box P, the numbers of marbles in the two boxes are interchanged. If instead 5 marbles are moved from box P to box Q, box Q then has twice as many marbles as box P. How many marbles do P and Q have respectively?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 30 and 45
Moving 15 from box Q to box P swaps the counts only if box Q has 15 more than box P. The second move then gives one equation.
Let box P have \(a\); then box Q has \(a+15\)
After 5 are moved from box P to box Q: box P has \(a-5\), box Q has \(a+20\)
\(a+20=2(a-5)\), so \(a+20=2 a-10\)
\(a=30\), and box Q \(=30+15=45\)
Check: moving 5 gives 25 and 50, and 50 is twice 25
Box P has 30 and box Q has 45 marbles.
Why the other options are incorrect
Option (1) 35 and 50 — Incorrect. Moving 5 from box P to box Q gives 30 and 55, and 55 is not twice 30.
Option (2) 40 and 55 — Incorrect. Moving 5 from box P to box Q gives 35 and 60, and 60 is not twice 35.
Option (3) 45 and 30 — Incorrect. Moving 15 from box Q to box P gives 60 and 15, not interchanged.