Two painters can paint a house faster than one. But how much faster? Time and Work problems answer that. The key idea is simple: think of work per day, not days per job.
Read the Article: Time and Work: Formulas, Shortcuts and Solved Examples →
0 / 25 correct · click an option to check it · +0 pts today
Q1. Irfan and Divya together can complete a piece of work in 19 days, and Divya alone can do it in 38 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: B
Let Irfan and Divya’s combined rate be 1/19 per day. Divya alone works at 1/38 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/19 – 1/38 = 1/38 of the job per day. So Irfan alone takes 38 days. Check: 1/38 + 1/38 = 1/19, one whole job in 19 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q2. Irfan and Divya together can complete a piece of work in 10 days, and Divya alone can do it in 20 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: D
Let Irfan and Divya’s combined rate be 1/10 per day. Divya alone works at 1/20 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/10 – 1/20 = 1/20 of the job per day. So Irfan alone takes 20 days. Check: 1/20 + 1/20 = 1/10, one whole job in 10 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q3. Irfan and Divya together can complete a piece of work in 20 days, and Divya alone can do it in 25 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: A
Let Irfan and Divya’s combined rate be 1/20 per day. Divya alone works at 1/25 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/20 – 1/25 = 1/100 of the job per day. So Irfan alone takes 100 days. Check: 1/100 + 1/25 = 1/20, one whole job in 20 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q4. Irfan and Divya together can complete a piece of work in 5 days, and Divya alone can do it in 6 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: D
Let Irfan and Divya’s combined rate be 1/5 per day. Divya alone works at 1/6 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/5 – 1/6 = 1/30 of the job per day. So Irfan alone takes 30 days. Check: 1/30 + 1/6 = 1/5, one whole job in 5 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q5. Irfan and Divya together can complete a piece of work in 13 days, and Divya alone can do it in 14 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: B
Let Irfan and Divya’s combined rate be 1/13 per day. Divya alone works at 1/14 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/13 – 1/14 = 1/182 of the job per day. So Irfan alone takes 182 days. Check: 1/182 + 1/14 = 1/13, one whole job in 13 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q6. Irfan and Divya together can complete a piece of work in 10 days, and Divya alone can do it in 12 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: C
Let Irfan and Divya’s combined rate be 1/10 per day. Divya alone works at 1/12 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/10 – 1/12 = 1/60 of the job per day. So Irfan alone takes 60 days. Check: 1/60 + 1/12 = 1/10, one whole job in 10 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q7. Irfan and Divya together can complete a piece of work in 6 days, and Divya alone can do it in 18 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: A
Let Irfan and Divya’s combined rate be 1/6 per day. Divya alone works at 1/18 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/6 – 1/18 = 1/9 of the job per day. So Irfan alone takes 9 days. Check: 1/9 + 1/18 = 1/6, one whole job in 6 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q8. Irfan and Divya together can complete a piece of work in 16 days, and Divya alone can do it in 17 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: D
Let Irfan and Divya’s combined rate be 1/16 per day. Divya alone works at 1/17 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/16 – 1/17 = 1/272 of the job per day. So Irfan alone takes 272 days. Check: 1/272 + 1/17 = 1/16, one whole job in 16 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q9. Irfan and Divya together can complete a piece of work in 22 days, and Divya alone can do it in 26 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: C
Let Irfan and Divya’s combined rate be 1/22 per day. Divya alone works at 1/26 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/22 – 1/26 = 1/143 of the job per day. So Irfan alone takes 143 days. Check: 1/143 + 1/26 = 1/22, one whole job in 22 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q10. Irfan and Divya together can complete a piece of work in 13 days, and Divya alone can do it in 26 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: B
Let Irfan and Divya’s combined rate be 1/13 per day. Divya alone works at 1/26 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/13 – 1/26 = 1/26 of the job per day. So Irfan alone takes 26 days. Check: 1/26 + 1/26 = 1/13, one whole job in 13 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q11. Irfan and Divya together can complete a piece of work in 18 days, and Divya alone can do it in 21 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: D
Let Irfan and Divya’s combined rate be 1/18 per day. Divya alone works at 1/21 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/18 – 1/21 = 1/126 of the job per day. So Irfan alone takes 126 days. Check: 1/126 + 1/21 = 1/18, one whole job in 18 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q12. Irfan and Divya together can complete a piece of work in 7 days, and Divya alone can do it in 8 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: A
Let Irfan and Divya’s combined rate be 1/7 per day. Divya alone works at 1/8 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/7 – 1/8 = 1/56 of the job per day. So Irfan alone takes 56 days. Check: 1/56 + 1/8 = 1/7, one whole job in 7 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q13. Irfan and Divya together can complete a piece of work in 15 days, and Divya alone can do it in 24 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: C
Let Irfan and Divya’s combined rate be 1/15 per day. Divya alone works at 1/24 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/15 – 1/24 = 1/40 of the job per day. So Irfan alone takes 40 days. Check: 1/40 + 1/24 = 1/15, one whole job in 15 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q14. Irfan and Divya together can complete a piece of work in 4 days, and Divya alone can do it in 6 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: B
Let Irfan and Divya’s combined rate be 1/4 per day. Divya alone works at 1/6 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/4 – 1/6 = 1/12 of the job per day. So Irfan alone takes 12 days. Check: 1/12 + 1/6 = 1/4, one whole job in 4 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q15. Irfan and Divya together can complete a piece of work in 15 days, and Divya alone can do it in 30 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: A
Let Irfan and Divya’s combined rate be 1/15 per day. Divya alone works at 1/30 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/15 – 1/30 = 1/30 of the job per day. So Irfan alone takes 30 days. Check: 1/30 + 1/30 = 1/15, one whole job in 15 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q16. Irfan and Divya together can complete a piece of work in 16 days, and Divya alone can do it in 24 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: C
Let Irfan and Divya’s combined rate be 1/16 per day. Divya alone works at 1/24 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/16 – 1/24 = 1/48 of the job per day. So Irfan alone takes 48 days. Check: 1/48 + 1/24 = 1/16, one whole job in 16 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q17. Irfan and Divya together can complete a piece of work in 12 days, and Divya alone can do it in 18 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: B
Let Irfan and Divya’s combined rate be 1/12 per day. Divya alone works at 1/18 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/12 – 1/18 = 1/36 of the job per day. So Irfan alone takes 36 days. Check: 1/36 + 1/18 = 1/12, one whole job in 12 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q18. Irfan and Divya together can complete a piece of work in 22 days, and Divya alone can do it in 23 days. In how many days can Irfan alone complete the work?
Show answer and explanation
Answer: D
Let Irfan and Divya’s combined rate be 1/22 per day. Divya alone works at 1/23 per day. Irfan’s own rate is the combined rate minus Divya’s rate. Irfan’s rate = 1/22 – 1/23 = 1/506 of the job per day. So Irfan alone takes 506 days. Check: 1/506 + 1/23 = 1/22, one whole job in 22 days together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q19. Ganesh and Lata can together complete a work in a combination where Ganesh takes 10 days alone and Lata takes 20 days alone. They work together for 2 days, after which Ganesh leaves. How many more days will Lata take to finish the remaining work?
Show answer and explanation
Answer: B
Let Ganesh’s rate be 1/10 and Lata’s rate be 1/20 of the job per day. Their combined rate is 1/10 + 1/20 = 3/20 per day. In 2 days together, they complete 2 x 3/20 = 3/10 of the job. Work remaining is 1 – 3/10 = 7/10. Lata alone now works at 1/20 per day. Time needed = 7/10 x 20 = 14 days. Check: 3/10 plus 14/20 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q20. Ganesh and Lata can together complete a work in a combination where Ganesh takes 8 days alone and Lata takes 24 days alone. They work together for 3 days, after which Ganesh leaves. How many more days will Lata take to finish the remaining work?
Show answer and explanation
Answer: D
Let Ganesh’s rate be 1/8 and Lata’s rate be 1/24 of the job per day. Their combined rate is 1/8 + 1/24 = 1/6 per day. In 3 days together, they complete 3 x 1/6 = 1/2 of the job. Work remaining is 1 – 1/2 = 1/2. Lata alone now works at 1/24 per day. Time needed = 1/2 x 24 = 12 days. Check: 1/2 plus 12/24 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q21. Ganesh and Lata can together complete a work in a combination where Ganesh takes 21 days alone and Lata takes 14 days alone. They work together for 6 days, after which Ganesh leaves. How many more days will Lata take to finish the remaining work?
Show answer and explanation
Answer: A
Let Ganesh’s rate be 1/21 and Lata’s rate be 1/14 of the job per day. Their combined rate is 1/21 + 1/14 = 5/42 per day. In 6 days together, they complete 6 x 5/42 = 5/7 of the job. Work remaining is 1 – 5/7 = 2/7. Lata alone now works at 1/14 per day. Time needed = 2/7 x 14 = 4 days. Check: 5/7 plus 4/14 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q22. Ganesh and Lata can together complete a work in a combination where Ganesh takes 12 days alone and Lata takes 28 days alone. They work together for 3 days, after which Ganesh leaves. How many more days will Lata take to finish the remaining work?
Show answer and explanation
Answer: C
Let Ganesh’s rate be 1/12 and Lata’s rate be 1/28 of the job per day. Their combined rate is 1/12 + 1/28 = 5/42 per day. In 3 days together, they complete 3 x 5/42 = 5/14 of the job. Work remaining is 1 – 5/14 = 9/14. Lata alone now works at 1/28 per day. Time needed = 9/14 x 28 = 18 days. Check: 5/14 plus 18/28 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q23. Ganesh and Lata can together complete a work in a combination where Ganesh takes 11 days alone and Lata takes 22 days alone. They work together for 7 days, after which Ganesh leaves. How many more days will Lata take to finish the remaining work?
Show answer and explanation
Answer: D
Let Ganesh’s rate be 1/11 and Lata’s rate be 1/22 of the job per day. Their combined rate is 1/11 + 1/22 = 3/22 per day. In 7 days together, they complete 7 x 3/22 = 21/22 of the job. Work remaining is 1 – 21/22 = 1/22. Lata alone now works at 1/22 per day. Time needed = 1/22 x 22 = 1 days. Check: 21/22 plus 1/22 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q24. Ganesh and Lata can together complete a work in a combination where Ganesh takes 6 days alone and Lata takes 10 days alone. They work together for 3 days, after which Ganesh leaves. How many more days will Lata take to finish the remaining work?
Show answer and explanation
Answer: C
Let Ganesh’s rate be 1/6 and Lata’s rate be 1/10 of the job per day. Their combined rate is 1/6 + 1/10 = 4/15 per day. In 3 days together, they complete 3 x 4/15 = 4/5 of the job. Work remaining is 1 – 4/5 = 1/5. Lata alone now works at 1/10 per day. Time needed = 1/5 x 10 = 2 days. Check: 4/5 plus 2/10 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q25. Ganesh and Lata can together complete a work in a combination where Ganesh takes 30 days alone and Lata takes 20 days alone. They work together for 9 days, after which Ganesh leaves. How many more days will Lata take to finish the remaining work?
Show answer and explanation
Answer: B
Let Ganesh’s rate be 1/30 and Lata’s rate be 1/20 of the job per day. Their combined rate is 1/30 + 1/20 = 1/12 per day. In 9 days together, they complete 9 x 1/12 = 3/4 of the job. Work remaining is 1 – 3/4 = 1/4. Lata alone now works at 1/20 per day. Time needed = 1/4 x 20 = 5 days. Check: 3/4 plus 5/20 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Leave a Reply