A, B and C are boxes containing marbles in the ratio 1 : 2 : 3. Total number of marbles is 60. The above ratio can be changed to 3 : 4 : 5 by transferring

### Concept & Ratio Mapping When a total quantity is redistributed, the total sum remains constant while the ratio parts change. Map both initial and final ratios to the fixed total to find individual changes. ### Step-by-Step Solution * The initial ratio of marbles in boxes $A$, $B$, and $C$ is $1 : 2 : 3$. * Total ratio parts = $1 + 2 + 3 = 6$. * The total number of marbles is 60. So, 1 ratio part = $\frac{60}{6} = 10$ marbles. * Initial marbles: $A = 10$, $B = 2 \times 10 = 20$, $C = 3 \times 10 = 30$. * The new target ratio is $3 : 4 : 5$. * Total new ratio parts = $3 + 4 + 5 = 12$. * Since the total marbles (60) stay the same, 1 new ratio part = $\frac{60}{12} = 5$ marbles. * Target marbles: $A = 3 \times 5 = 15$, $B = 4 \times 5 = 20$, $C = 5 \times 5 = 25$. * Comparing initial and target: $A$ needs $+5$ (from 10 to 15), $B$ needs $0$ (stays at 20), $C$ needs $-5$ (from 30 to 25). * This means 5 marbles must be transferred from box $C$ to box $A$. ### Exam Strategy & Shortcut Calculate the actual number of marbles for $A$, $B$, and $C$ in both scenarios. Initial: 10, 20, 30. Final: 15, 20, 25. The difference is immediately apparent: $A$ goes up by 5, $C$ goes down by 5, and $B$ remains unchanged. Hence, move 5 from $C$ to $A$. ### Common Pitfall Assuming the total number of marbles changes or miscalculating the value of one ratio part for the second scenario. ### Final Answer Therefore, the correct answer is **5 marbles from C to A**.