Meena keeps coins in two jars, M and N. If she moves 9 coins from jar N to jar M, the numbers of coins in the two jars are interchanged. If instead she moves 3 coins from jar M to jar N, jar N then has twice as many coins as jar M. How many coins are in M and N respectively?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 18 and 27
Moving 9 from jar N to jar M swaps the counts only if jar N has 9 more than jar M. The second move then gives one equation.
Let jar M have \(a\); then jar N has \(a+9\)
After 3 are moved from jar M to jar N: jar M has \(a-3\), jar N has \(a+12\)
\(a+12=2(a-3)\), so \(a+12=2 a-6\)
\(a=18\), and jar N \(=18+9=27\)
Check: moving 3 gives 15 and 30, and 30 is twice 15
Jar M has 18 and jar N has 27 coins.
Why the other options are incorrect
Option (2) 28 and 37 — Incorrect. Moving 3 from jar M to jar N gives 25 and 40, and 40 is not twice 25.
Option (3) 23 and 32 — Incorrect. Moving 3 from jar M to jar N gives 20 and 35, and 35 is not twice 20.
Option (4) 27 and 18 — Incorrect. Moving 9 from jar N to jar M gives 36 and 9, not interchanged.