A, B and C can finish a job in 10, 12 and 15 days respectively. How long will they take together, and how should a payment of ₹4,500 be shared?
4 days. With total work 60 units, they do 6 + 5 + 4 = 15 units a day, so 60/15 = 4 days. Wages follow work done; they work the same days, so the ratio is 6 : 5 : 4: ₹1,800, ₹1,500 and ₹1,200.
Explain it simply
Pay is for work, not for time present. If all three work the same number of days, each person's share of the work is in the same ratio as their speed. A faster worker does more of the job and gets a bigger share, even though everyone worked four days.
Example
Question: A, B, C take 10, 12, 15 days alone. Time together and split of ₹4,500?
- Total work = LCM(10, 12, 15) = 60 units.
- Rates: A = 6, B = 5, C = 4 units/day. Together 15 units/day.
- Time = 60 / 15 = 4 days.
- Work done in 4 days: A 24, B 20, C 16 units. Ratio 6 : 5 : 4.
- Shares: one part = 4,500 / 15 = 300. A = ₹1,800, B = ₹1,500, C = ₹1,200.
If C leaves after 2 days, recompute the work done by each person before splitting the money.
const rates = [60 / 10, 60 / 12, 60 / 15];
const sum = rates.reduce((a, b) => a + b);
console.log(60 / sum); // Output: 4
console.log(rates.map(r => (4500 * r) / sum)); // Output: [1800,1500,1200]What to say in the interview
"With 60 units the rates are 6, 5 and 4, so together they need 4 days. Wages go by work done, so I split 4,500 in the ratio 6 to 5 to 4, giving 1,800, 1,500 and 1,200."
Common mistakes
- Splitting money in the ratio of days 10 : 12 : 15, which rewards the slowest worker.
- Splitting equally because they worked the same number of days.