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. Karan can do a piece of work in 4 days and Fatima can do the same work in 7 days. They complete it together and receive a combined wage of Rs. 363. What is Fatima’s share?
Show answer and explanation
Answer: A
Let Karan’s rate be 1/4 and Fatima’s rate be 1/7 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/4 : 1/7, which simplifies to 7:4. So Karan gets 7 parts and Fatima gets 4 parts of the total wage. Fatima’s share = 4/(7+4) x Rs. 363 = Rs. 132. Check: Karan’s share plus Fatima’s share adds up to Rs. 363.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q2. Karan can do a piece of work in 22 days and Fatima can do the same work in 23 days. They complete it together and receive a combined wage of Rs. 540. What is Fatima’s share?
Show answer and explanation
Answer: B
Let Karan’s rate be 1/22 and Fatima’s rate be 1/23 of the job per day. Wages split in the same ratio as the work each person does. That ratio is 1/22 : 1/23, which simplifies to 23:22. So Karan gets 23 parts and Fatima gets 22 parts of the total wage. Fatima’s share = 22/(23+22) x Rs. 540 = Rs. 264. Check: Karan’s share plus Fatima’s share adds up to Rs. 540.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q3. Karan can do a piece of work in 8 days and Fatima can do the same work in 15 days. They complete it together and receive a combined wage of Rs. 161. What is Fatima’s share?
Show answer and explanation
Answer: C
Let Karan’s rate be 1/8 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 1/8 : 1/15, which simplifies to 15:8. So Karan gets 15 parts and Fatima gets 8 parts of the total wage. Fatima’s share = 8/(15+8) x Rs. 161 = Rs. 56. Check: Karan’s share plus Fatima’s share adds up to Rs. 161.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q4. Karan can do a piece of work in 21 days and Fatima can do the same work in 15 days. They complete it together and receive a combined wage of Rs. 456. What is Fatima’s share?
Show answer and explanation
Answer: D
Let Karan’s rate be 1/21 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 1/21 : 1/15, which simplifies to 5:7. So Karan gets 5 parts and Fatima gets 7 parts of the total wage. Fatima’s share = 7/(5+7) x Rs. 456 = Rs. 266. Check: Karan’s share plus Fatima’s share adds up to Rs. 456.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q5. Sachin can do a certain job in 30 days. Priya is 20% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: C
Let Sachin’s rate be 1/30 of the job per day. Priya is 20% more efficient than Sachin. So Priya’s rate is (100+20)/100 times Sachin’s rate. Priya’s rate = (100+20)/100 x 1/30 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 30 x 100/(100+20) = 25 days. Check: 25 days is less than 30 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q6. Sachin can do a certain job in 12 days. Priya is 100% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: C
Let Sachin’s rate be 1/12 of the job per day. Priya is 100% more efficient than Sachin. So Priya’s rate is (100+100)/100 times Sachin’s rate. Priya’s rate = (100+100)/100 x 1/12 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 12 x 100/(100+100) = 6 days. Check: 6 days is less than 12 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q7. Sachin can do a certain job in 6 days. Priya is 100% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: A
Let Sachin’s rate be 1/6 of the job per day. Priya is 100% more efficient than Sachin. So Priya’s rate is (100+100)/100 times Sachin’s rate. Priya’s rate = (100+100)/100 x 1/6 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 6 x 100/(100+100) = 3 days. Check: 3 days is less than 6 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q8. Sachin can do a certain job in 20 days. Priya is 100% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: D
Let Sachin’s rate be 1/20 of the job per day. Priya is 100% more efficient than Sachin. So Priya’s rate is (100+100)/100 times Sachin’s rate. Priya’s rate = (100+100)/100 x 1/20 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 20 x 100/(100+100) = 10 days. Check: 10 days is less than 20 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q9. Sachin can do a certain job in 24 days. Priya is 100% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: B
Let Sachin’s rate be 1/24 of the job per day. Priya is 100% more efficient than Sachin. So Priya’s rate is (100+100)/100 times Sachin’s rate. Priya’s rate = (100+100)/100 x 1/24 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 24 x 100/(100+100) = 12 days. Check: 12 days is less than 24 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q10. Sachin can do a certain job in 6 days. Priya is 50% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: B
Let Sachin’s rate be 1/6 of the job per day. Priya is 50% more efficient than Sachin. So Priya’s rate is (100+50)/100 times Sachin’s rate. Priya’s rate = (100+50)/100 x 1/6 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 6 x 100/(100+50) = 4 days. Check: 4 days is less than 6 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q11. Sachin can do a certain job in 24 days. Priya is 50% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: D
Let Sachin’s rate be 1/24 of the job per day. Priya is 50% more efficient than Sachin. So Priya’s rate is (100+50)/100 times Sachin’s rate. Priya’s rate = (100+50)/100 x 1/24 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 24 x 100/(100+50) = 16 days. Check: 16 days is less than 24 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q12. Sachin can do a certain job in 30 days. Priya is 50% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: A
Let Sachin’s rate be 1/30 of the job per day. Priya is 50% more efficient than Sachin. So Priya’s rate is (100+50)/100 times Sachin’s rate. Priya’s rate = (100+50)/100 x 1/30 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 30 x 100/(100+50) = 20 days. Check: 20 days is less than 30 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q13. Sachin can do a certain job in 20 days. Priya is 25% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: C
Let Sachin’s rate be 1/20 of the job per day. Priya is 25% more efficient than Sachin. So Priya’s rate is (100+25)/100 times Sachin’s rate. Priya’s rate = (100+25)/100 x 1/20 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 20 x 100/(100+25) = 16 days. Check: 16 days is less than 20 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q14. Sachin can do a certain job in 30 days. Priya is 100% more efficient than Sachin. How many days does Priya alone take to do the same job?
Show answer and explanation
Answer: B
Let Sachin’s rate be 1/30 of the job per day. Priya is 100% more efficient than Sachin. So Priya’s rate is (100+100)/100 times Sachin’s rate. Priya’s rate = (100+100)/100 x 1/30 per day. Priya’s time is the reciprocal of that rate. Priya’s time = 30 x 100/(100+100) = 15 days. Check: 15 days is less than 30 days, matching Priya’s higher speed.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q15. Rahul is twice as good a workman as Manick, and together they can finish a piece of work in 12 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: D
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is twice as efficient, so Rahul’s rate is 2/b per day. Together their combined rate is (2+1)/b per day. This must equal 1/12, since together they finish in 12 days. So b = 3 x 12 = 36 days for Manick. Rahul alone takes b/2 = 36/2 = 18 days. Check: 1/18 + 1/36 = 1/12, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q16. Rahul is thrice as good a workman as Manick, and together they can finish a piece of work in 3 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: C
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is thrice as efficient, so Rahul’s rate is 3/b per day. Together their combined rate is (3+1)/b per day. This must equal 1/3, since together they finish in 3 days. So b = 4 x 3 = 12 days for Manick. Rahul alone takes b/3 = 12/3 = 4 days. Check: 1/4 + 1/12 = 1/3, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q17. Rahul is thrice as good a workman as Manick, and together they can finish a piece of work in 6 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: A
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is thrice as efficient, so Rahul’s rate is 3/b per day. Together their combined rate is (3+1)/b per day. This must equal 1/6, since together they finish in 6 days. So b = 4 x 6 = 24 days for Manick. Rahul alone takes b/3 = 24/3 = 8 days. Check: 1/8 + 1/24 = 1/6, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q18. Rahul is thrice as good a workman as Manick, and together they can finish a piece of work in 9 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: D
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is thrice as efficient, so Rahul’s rate is 3/b per day. Together their combined rate is (3+1)/b per day. This must equal 1/9, since together they finish in 9 days. So b = 4 x 9 = 36 days for Manick. Rahul alone takes b/3 = 36/3 = 12 days. Check: 1/12 + 1/36 = 1/9, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q19. Rahul is twice as good a workman as Manick, and together they can finish a piece of work in 4 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: B
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is twice as efficient, so Rahul’s rate is 2/b per day. Together their combined rate is (2+1)/b per day. This must equal 1/4, since together they finish in 4 days. So b = 3 x 4 = 12 days for Manick. Rahul alone takes b/2 = 12/2 = 6 days. Check: 1/6 + 1/12 = 1/4, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q20. Rahul is four times as good a workman as Manick, and together they can finish a piece of work in 8 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: C
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is four times as efficient, so Rahul’s rate is 4/b per day. Together their combined rate is (4+1)/b per day. This must equal 1/8, since together they finish in 8 days. So b = 5 x 8 = 40 days for Manick. Rahul alone takes b/4 = 40/4 = 10 days. Check: 1/10 + 1/40 = 1/8, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q21. Rahul is twice as good a workman as Manick, and together they can finish a piece of work in 6 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: A
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is twice as efficient, so Rahul’s rate is 2/b per day. Together their combined rate is (2+1)/b per day. This must equal 1/6, since together they finish in 6 days. So b = 3 x 6 = 18 days for Manick. Rahul alone takes b/2 = 18/2 = 9 days. Check: 1/9 + 1/18 = 1/6, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q22. Rahul is twice as good a workman as Manick, and together they can finish a piece of work in 8 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: C
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is twice as efficient, so Rahul’s rate is 2/b per day. Together their combined rate is (2+1)/b per day. This must equal 1/8, since together they finish in 8 days. So b = 3 x 8 = 24 days for Manick. Rahul alone takes b/2 = 24/2 = 12 days. Check: 1/12 + 1/24 = 1/8, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q23. Rahul is four times as good a workman as Manick, and together they can finish a piece of work in 4 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: D
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is four times as efficient, so Rahul’s rate is 4/b per day. Together their combined rate is (4+1)/b per day. This must equal 1/4, since together they finish in 4 days. So b = 5 x 4 = 20 days for Manick. Rahul alone takes b/4 = 20/4 = 5 days. Check: 1/5 + 1/20 = 1/4, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q24. Rahul is twice as good a workman as Manick, and together they can finish a piece of work in 2 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: A
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is twice as efficient, so Rahul’s rate is 2/b per day. Together their combined rate is (2+1)/b per day. This must equal 1/2, since together they finish in 2 days. So b = 3 x 2 = 6 days for Manick. Rahul alone takes b/2 = 6/2 = 3 days. Check: 1/3 + 1/6 = 1/2, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples
Q25. Rahul is twice as good a workman as Manick, and together they can finish a piece of work in 10 days. In how many days can Rahul alone finish the work?
Show answer and explanation
Answer: B
Let Manick’s time alone be b days, so Manick’s rate is 1/b of the job per day. Rahul is twice as efficient, so Rahul’s rate is 2/b per day. Together their combined rate is (2+1)/b per day. This must equal 1/10, since together they finish in 10 days. So b = 3 x 10 = 30 days for Manick. Rahul alone takes b/2 = 30/2 = 15 days. Check: 1/15 + 1/30 = 1/10, one whole job together.
Related topics: Time and Work: Formulas, Shortcuts and Solved Examples