By Pathantu · Published 6 October 2026 · Original practice, not PYQ
Method
One job in d days means a rate of 1/d job per day. Add rates, not completion times.
Take the LCM of individual times as total work units. Time = remaining units ÷ combined daily rate.
Subtract a leak’s rate. If it equals or exceeds filling, an initially empty tank cannot fill under those constant conditions.
Six questions: try first, then open the solution
1. A takes 10 days and B 15. Find their time together.
Show worked solution
Take 30 units: daily rates 3 and 2. Time=30/(3+2)=6 days.
2. A takes 12 days, B 18. A works alone for 3 days, then B joins. Find total time.
Show worked solution
Take 36 units. A completes 9; 27 remain. Joint rate=5. Total=3+27/5=8.4 days.
3. Together A and B need 8 days; A alone needs 24. Find B’s time.
Show worked solution
B’s rate=1/8−1/24=1/12. B needs 12 days.
4. A pipe fills in 6 hours; a leak empties in 9. How long with both open?
Show worked solution
Net rate=1/6−1/9=1/18 tank/hour. Filling takes 18 hours.
5. A is twice as efficient as B. Together they need 6 days. Find individual times.
Show worked solution
Rates 2:1, total work 18 units. A needs 18/2=9 days; B needs 18/1=18.
6. After 4 days on a 10-day job, what fraction remains?
Show worked solution
Completed=4/10=2/5. Remaining=1−2/5=3/5.
Check your reasoning
Convert hours and days to one unit. Twice the efficiency means half the time for the same job.
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