Raman has two urns, A and B, each holding some pebbles. If 20 pebbles are moved from urn B to urn A, the numbers of pebbles in the two urns are interchanged. If instead 10 pebbles are moved from urn A to urn B, urn B then has twice as many pebbles as urn A. How many pebbles do A and B have respectively?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50 and 70
Moving 20 pebbles swaps the counts only if B has 20 more than A. The second move then gives one equation in A.
Let A have \(a\) pebbles; then B has \(a+20\)
After 10 move from A to B: A has \(a-10\), B has \(a+30\)
\(a+30=2(a-10)\), so \(a+30=2a-20\)
\(a=50\), and B \(=50+20=70\)
Check: moving 10 gives 40 and 80, and 80 is twice 40
Urn A has 50 pebbles and urn B has 70.
Why the other options are incorrect
Option (1) 60 and 40 — Incorrect. Moving 20 from B to A gives 80 and 20, not swapped.
Option (2) 80 and 100 — Incorrect. Moving 10 from A to B gives 70 and 110, and 110 is not twice 70.
Option (4) 70 and 90 — Incorrect. Moving 10 from A to B gives 60 and 100, and 100 is not twice 60.