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. Ganesh and Lata can together complete a work in a combination where Ganesh takes 24 days alone and Lata takes 18 days alone. They work together for 4 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 1/24 and Lata’s rate be 1/18 of the job per day. Their combined rate is 1/24 + 1/18 = 7/72 per day. In 4 days together, they complete 4 x 7/72 = 7/18 of the job. Work remaining is 1 – 7/18 = 11/18. Lata alone now works at 1/18 per day. Time needed = 11/18 x 18 = 11 days. Check: 7/18 plus 11/18 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q2. Ganesh and Lata can together complete a work in a combination where Ganesh takes 21 days alone and Lata takes 24 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 1/21 and Lata’s rate be 1/24 of the job per day. Their combined rate is 1/21 + 1/24 = 5/56 per day. In 7 days together, they complete 7 x 5/56 = 5/8 of the job. Work remaining is 1 – 5/8 = 3/8. Lata alone now works at 1/24 per day. Time needed = 3/8 x 24 = 9 days. Check: 5/8 plus 9/24 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q3. Ganesh and Lata can together complete a work in a combination where Ganesh takes 14 days alone and Lata takes 7 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 1/14 and Lata’s rate be 1/7 of the job per day. Their combined rate is 1/14 + 1/7 = 3/14 per day. In 2 days together, they complete 2 x 3/14 = 3/7 of the job. Work remaining is 1 – 3/7 = 4/7. Lata alone now works at 1/7 per day. Time needed = 4/7 x 7 = 4 days. Check: 3/7 plus 4/7 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q4. Ganesh and Lata can together complete a work in a combination where Ganesh takes 21 days alone and Lata takes 18 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: C
Let Ganesh’s rate be 1/21 and Lata’s rate be 1/18 of the job per day. Their combined rate is 1/21 + 1/18 = 13/126 per day. In 7 days together, they complete 7 x 13/126 = 13/18 of the job. Work remaining is 1 – 13/18 = 5/18. Lata alone now works at 1/18 per day. Time needed = 5/18 x 18 = 5 days. Check: 13/18 plus 5/18 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q5. Ganesh and Lata can together complete a work in a combination where Ganesh takes 18 days alone and Lata takes 9 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: A
Let Ganesh’s rate be 1/18 and Lata’s rate be 1/9 of the job per day. Their combined rate is 1/18 + 1/9 = 1/6 per day. In 2 days together, they complete 2 x 1/6 = 1/3 of the job. Work remaining is 1 – 1/3 = 2/3. Lata alone now works at 1/9 per day. Time needed = 2/3 x 9 = 6 days. Check: 1/3 plus 6/9 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q6. Ganesh and Lata can together complete a work in a combination where Ganesh takes 8 days alone and Lata takes 10 days alone. They work together for 4 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 1/8 and Lata’s rate be 1/10 of the job per day. Their combined rate is 1/8 + 1/10 = 9/40 per day. In 4 days together, they complete 4 x 9/40 = 9/10 of the job. Work remaining is 1 – 9/10 = 1/10. Lata alone now works at 1/10 per day. Time needed = 1/10 x 10 = 1 days. Check: 9/10 plus 1/10 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q7. Ganesh and Lata can together complete a work in a combination where Ganesh takes 7 days alone and Lata takes 21 days alone. They work together for 5 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 1/7 and Lata’s rate be 1/21 of the job per day. Their combined rate is 1/7 + 1/21 = 4/21 per day. In 5 days together, they complete 5 x 4/21 = 20/21 of the job. Work remaining is 1 – 20/21 = 1/21. Lata alone now works at 1/21 per day. Time needed = 1/21 x 21 = 1 days. Check: 20/21 plus 1/21 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q8. Ganesh and Lata can together complete a work in a combination where Ganesh takes 15 days alone and Lata takes 12 days alone. They work together for 5 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 1/15 and Lata’s rate be 1/12 of the job per day. Their combined rate is 1/15 + 1/12 = 3/20 per day. In 5 days together, they complete 5 x 3/20 = 3/4 of the job. Work remaining is 1 – 3/4 = 1/4. Lata alone now works at 1/12 per day. Time needed = 1/4 x 12 = 3 days. Check: 3/4 plus 3/12 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q9. Ganesh and Lata can together complete a work in a combination where Ganesh takes 18 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: C
Let Ganesh’s rate be 1/18 and Lata’s rate be 1/20 of the job per day. Their combined rate is 1/18 + 1/20 = 19/180 per day. In 9 days together, they complete 9 x 19/180 = 19/20 of the job. Work remaining is 1 – 19/20 = 1/20. Lata alone now works at 1/20 per day. Time needed = 1/20 x 20 = 1 days. Check: 19/20 plus 1/20 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q10. Ganesh and Lata can together complete a work in a combination where Ganesh takes 12 days alone and Lata takes 18 days alone. They work together for 4 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 1/12 and Lata’s rate be 1/18 of the job per day. Their combined rate is 1/12 + 1/18 = 5/36 per day. In 4 days together, they complete 4 x 5/36 = 5/9 of the job. Work remaining is 1 – 5/9 = 4/9. Lata alone now works at 1/18 per day. Time needed = 4/9 x 18 = 8 days. Check: 5/9 plus 8/18 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q11. Ganesh and Lata can together complete a work in a combination where Ganesh takes 10 days alone and Lata takes 28 days alone. They work together for 5 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 1/28 of the job per day. Their combined rate is 1/10 + 1/28 = 19/140 per day. In 5 days together, they complete 5 x 19/140 = 19/28 of the job. Work remaining is 1 – 19/28 = 9/28. Lata alone now works at 1/28 per day. Time needed = 9/28 x 28 = 9 days. Check: 19/28 plus 9/28 equals one whole job.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q12. Karan can do a piece of work in 21 days and Fatima can do the same work in 5 days. They complete it together and receive a combined wage of Rs. 130. What is Fatima’s share?
Show answer and explanation
Answer: D
Let Karan’s rate be 1/21 and Fatima’s rate be 1/5 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/21 : 1/5, which simplifies to 5:21. So Karan gets 5 parts and Fatima gets 21 parts of the total wage. Fatima’s share = 21/(5+21) x Rs. 130 = Rs. 105. Check: Karan’s share plus Fatima’s share adds up to Rs. 130.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q13. Karan can do a piece of work in 21 days and Fatima can do the same work in 17 days. They complete it together and receive a combined wage of Rs. 798. What is Fatima’s share?
Show answer and explanation
Answer: C
Let Karan’s rate be 1/21 and Fatima’s rate be 1/17 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/21 : 1/17, which simplifies to 17:21. So Karan gets 17 parts and Fatima gets 21 parts of the total wage. Fatima’s share = 21/(17+21) x Rs. 798 = Rs. 441. Check: Karan’s share plus Fatima’s share adds up to Rs. 798.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q14. Karan can do a piece of work in 16 days and Fatima can do the same work in 6 days. They complete it together and receive a combined wage of Rs. 385. What is Fatima’s share?
Show answer and explanation
Answer: A
Let Karan’s rate be 1/16 and Fatima’s rate be 1/6 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/16 : 1/6, which simplifies to 3:8. So Karan gets 3 parts and Fatima gets 8 parts of the total wage. Fatima’s share = 8/(3+8) x Rs. 385 = Rs. 280. Check: Karan’s share plus Fatima’s share adds up to Rs. 385.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q15. Karan can do a piece of work in 6 days and Fatima can do the same work in 4 days. They complete it together and receive a combined wage of Rs. 140. What is Fatima’s share?
Show answer and explanation
Answer: B
Let Karan’s rate be 1/6 and Fatima’s rate be 1/4 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/6 : 1/4, which simplifies to 2:3. So Karan gets 2 parts and Fatima gets 3 parts of the total wage. Fatima’s share = 3/(2+3) x Rs. 140 = Rs. 84. Check: Karan’s share plus Fatima’s share adds up to Rs. 140.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q16. Karan can do a piece of work in 9 days and Fatima can do the same work in 24 days. They complete it together and receive a combined wage of Rs. 253. What is Fatima’s share?
Show answer and explanation
Answer: C
Let Karan’s rate be 1/9 and Fatima’s rate be 1/24 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/9 : 1/24, which simplifies to 8:3. So Karan gets 8 parts and Fatima gets 3 parts of the total wage. Fatima’s share = 3/(8+3) x Rs. 253 = Rs. 69. Check: Karan’s share plus Fatima’s share adds up to Rs. 253.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q17. Karan can do a piece of work in 12 days and Fatima can do the same work in 13 days. They complete it together and receive a combined wage of Rs. 300. What is Fatima’s share?
Show answer and explanation
Answer: D
Let Karan’s rate be 1/12 and Fatima’s rate be 1/13 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/12 : 1/13, which simplifies to 13:12. So Karan gets 13 parts and Fatima gets 12 parts of the total wage. Fatima’s share = 12/(13+12) x Rs. 300 = Rs. 144. Check: Karan’s share plus Fatima’s share adds up to Rs. 300.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q18. Karan can do a piece of work in 13 days and Fatima can do the same work in 16 days. They complete it together and receive a combined wage of Rs. 957. What is Fatima’s share?
Show answer and explanation
Answer: A
Let Karan’s rate be 1/13 and Fatima’s rate be 1/16 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/13 : 1/16, which simplifies to 16:13. So Karan gets 16 parts and Fatima gets 13 parts of the total wage. Fatima’s share = 13/(16+13) x Rs. 957 = Rs. 429. Check: Karan’s share plus Fatima’s share adds up to Rs. 957.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q19. Karan can do a piece of work in 9 days and Fatima can do the same work in 15 days. They complete it together and receive a combined wage of Rs. 80. What is Fatima’s share?
Show answer and explanation
Answer: C
Let Karan’s rate be 1/9 and Fatima’s rate be 1/15 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/9 : 1/15, which simplifies to 5:3. So Karan gets 5 parts and Fatima gets 3 parts of the total wage. Fatima’s share = 3/(5+3) x Rs. 80 = Rs. 30. Check: Karan’s share plus Fatima’s share adds up to Rs. 80.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q20. Karan can do a piece of work in 21 days and Fatima can do the same work in 22 days. They complete it together and receive a combined wage of Rs. 559. What is Fatima’s share?
Show answer and explanation
Answer: B
Let Karan’s rate be 1/21 and Fatima’s rate be 1/22 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/21 : 1/22, which simplifies to 22:21. So Karan gets 22 parts and Fatima gets 21 parts of the total wage. Fatima’s share = 21/(22+21) x Rs. 559 = Rs. 273. Check: Karan’s share plus Fatima’s share adds up to Rs. 559.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q21. Karan can do a piece of work in 21 days and Fatima can do the same work in 20 days. They complete it together and receive a combined wage of Rs. 369. What is Fatima’s share?
Show answer and explanation
Answer: D
Let Karan’s rate be 1/21 and Fatima’s rate be 1/20 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/21 : 1/20, which simplifies to 20:21. So Karan gets 20 parts and Fatima gets 21 parts of the total wage. Fatima’s share = 21/(20+21) x Rs. 369 = Rs. 189. Check: Karan’s share plus Fatima’s share adds up to Rs. 369.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q22. Karan can do a piece of work in 5 days and Fatima can do the same work in 10 days. They complete it together and receive a combined wage of Rs. 87. What is Fatima’s share?
Show answer and explanation
Answer: A
Let Karan’s rate be 1/5 and Fatima’s rate be 1/10 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/5 : 1/10, which simplifies to 2:1. So Karan gets 2 parts and Fatima gets 1 parts of the total wage. Fatima’s share = 1/(2+1) x Rs. 87 = Rs. 29. Check: Karan’s share plus Fatima’s share adds up to Rs. 87.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q23. Karan can do a piece of work in 5 days and Fatima can do the same work in 22 days. They complete it together and receive a combined wage of Rs. 567. What is Fatima’s share?
Show answer and explanation
Answer: B
Let Karan’s rate be 1/5 and Fatima’s rate be 1/22 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/5 : 1/22, which simplifies to 22:5. So Karan gets 22 parts and Fatima gets 5 parts of the total wage. Fatima’s share = 5/(22+5) x Rs. 567 = Rs. 105. Check: Karan’s share plus Fatima’s share adds up to Rs. 567.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q24. Karan can do a piece of work in 7 days and Fatima can do the same work in 14 days. They complete it together and receive a combined wage of Rs. 81. What is Fatima’s share?
Show answer and explanation
Answer: D
Let Karan’s rate be 1/7 and Fatima’s rate be 1/14 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/7 : 1/14, which simplifies to 2:1. So Karan gets 2 parts and Fatima gets 1 parts of the total wage. Fatima’s share = 1/(2+1) x Rs. 81 = Rs. 27. Check: Karan’s share plus Fatima’s share adds up to Rs. 81.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q25. Karan can do a piece of work in 19 days and Fatima can do the same work in 21 days. They complete it together and receive a combined wage of Rs. 160. What is Fatima’s share?
Show answer and explanation
Answer: C
Let Karan’s rate be 1/19 and Fatima’s rate be 1/21 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/19 : 1/21, which simplifies to 21:19. So Karan gets 21 parts and Fatima gets 19 parts of the total wage. Fatima’s share = 19/(21+19) x Rs. 160 = Rs. 76. Check: Karan’s share plus Fatima’s share adds up to Rs. 160.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples