2021 · Q28
Let work done by (3n − 1) men in (2n + 1) days be x and work done by (3n + 1) men in (4n − 3) days be y. If x : y = 6 : 11, then what is the value of n ?
Elementary MathematicsTime and Work
- A6
- B7
- C8
- D9
Explanation
Work is proportional to men × days, so x : y = (3n−1)(2n+1) : (3n+1)(4n−3) = 6 : 11. Cross-multiplying: 11(6n² + n − 1) = 6(12n² − 5n − 3), i.e. 66n² + 11n − 11 = 72n² − 30n − 18. This gives 6n² − 41n − 7 = 0, i.e. (6n+1)(n−7) = 0, so n = 7. This is option (b).