2026 · Q25
An alloy (X) of gold and silver is taken in the ratio 1 : 2 and another alloy (Y) of gold and silver is taken in the ratio 2 : 3. How many parts of X and Y must be taken to obtain a new alloy Z consisting of gold and silver in the ratio 4 : 7?
Elementary MathematicsRatio and Proportion
- A5 : 6
- B2 : 1
- C3 : 5
- D6 : 5
Explanation
Use alligation on the gold fraction: X has gold fraction 1/3, Y has 2/5, and Z must have 4/11. With x parts of X and y parts of Y, (x/3 + 2y/5)/(x + y) = 4/11. Clearing denominators gives 55x + 66y = 60x + 60y, i.e. 5x = 6y, so x : y = 6 : 5, option D. Check: 6 parts of X contribute 2 units of gold and 5 parts of Y contribute 2 units, making 4 gold in 11 total — the ratio 4 : 7. The distractor 2 : 1 would give 16 : 29, not 4 : 7.