Quantitative Aptitude

Time and Work

2,195 Questions
All Pairwise rates and staged schedules 440 Workers-days-hours chain rule 439 LCM units and efficiency ratios 409 Different worker categories 311 Combined rates and an unknown worker 257 Division of wages 219 Alternate work 110 Opposing rates 10

Time and Work Questions

Multiple choice

In the following questions three equations numbered I, II and III are given. You have to solve all the equations either together or separately, or two together and one separately, or by any other method. A man can complete a piece of work in 8 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. x = If 5 men, 4 women and 10 children work together, in how many days can the work be completed y = If 4 men, 5 women and 10 children work together, in how many days can the work be completed z = If 3 men, 4 women and 12 children work together, in how many days can the work be completed

  1. x < y < z

  2. x > y > z

  3. x > y = z

  4. x z

  5. Relationship cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

One man's rate is 1/8 work per day, one woman's rate is 1/16, and one child's rate is 1/20. The combined rates for x, y, and z are 1.375, 1.3125, and 1.225 work per day respectively. Higher rate means fewer days, so x < y < z.

Multiple choice

Passage

Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

In how many days can 20 women finish the work? I. 20 men finish the work in 8 days. II. 20 men and 20 women finish the work in 24/7 days.

  1. Either I or II

  2. Only II

  3. Only I

  4. Both I and II

  5. Neither I nor II
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M and W be the work rates of a man and a woman. From I: 20M * 8 = 1 => M = 1/160. From II: 20M + 20W = 1 / (24/7) = 7/24. Substituting M: 20(1/160) + 20W = 7/24 => 1/8 + 20W = 7/24 => 20W = 7/24 - 3/24 = 4/24 = 1/6. So 20W = 1/6, meaning 20 women take 6 days. Both statements are required.

Multiple choice

Passage

Directions: In this problem, a question is followed by three statements, labelled as (A), (B) and (C). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question.

Eight men and six women together can compete a piece of work in 6 days. If Rs. 60 is given to a woman per day for her contribution towards work, then what is the amount received by a man per day? (A) Five men and six women together can compete the same work in 8 days. (B) Ten men and twelve women can complete the same work in 4 days. (C) The work done by a man in two days is equal to the work done by a woman in three days.

  1. Only A and C together are sufficient.

  2. Any one of A, B and C is sufficient.

  3. Only A and B together are sufficient.

  4. Any two statements together are sufficient.

  5. All statements together are necessary.
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

Directions: In this problem, a question is followed by three statements, labelled as (A), (B) and (C). Read the statements carefully and determine which of them is/are sufficient/necessary to answer the question.

In how many days can a piece of work be completed by Reema, Seema and Peema together? (A) 60% of the work is completed by Reema alone in 6 days. (B) The ratio of work efficiencies of Reema, Seema and Peema is 3 : 2 : 1. (C) Peema works for 5 days and then leaves the job, and the remaining work is done by Reema and Seema together.

  1. Only A and B together are sufficient.

  2. Any one of A, B and C is sufficient.

  3. Only A and C together are sufficient.

  4. Any two of A, B and C are sufficient.

  5. All of them together are necessary.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement A tells us Reema's efficiency (60% in 6 days means 100% in 10 days). Statement B provides the ratio of efficiencies for Reema, Seema, and Peema (3:2:1). With both, we can calculate the total work rate and the time taken by all three together.

Multiple choice

Passage

Directions: The question below contains a statement followed by Quantity I and Quantity II. Find both the quantities to determine the relationship among them and mark your answer accordingly.

Govind and Rahul can do a piece of work in 20 days, Rahul and Pankaj can complete the same work in 30 days, and Pankaj and Govind can complete half of that work in 25 days. Quantity I: Number of days required to complete the work by Govind alone Quantity II: Number of days required to complete the work by Pankaj alone

  1. Quantity I ≥ Quantity II

  2. Quantity I ≤ Quantity II

  3. Quantity I < Quantity II

  4. Quantity I > Quantity II

  5. Quantity I = Quantity II, or the relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

1/G + 1/R = 1/20, 1/R + 1/P = 1/30, 1/P + 1/G = 1/50 (since half work in 25 days). Sum: 2(1/G + 1/R + 1/P) = 1/20 + 1/30 + 1/50 = (15+10+6)/300 = 31/300. 1/G + 1/R + 1/P = 31/600. 1/P = 31/600 - 1/20 = (31-30)/600 = 1/600 => P=600. 1/G = 31/600 - 1/30 = (31-20)/600 = 11/600 => G=54.54. G < P.

Multiple choice

Passage

Directions: The following question is accompanied by three statements, (A) or (I), (B) or (II) and (C) or (III). Determine the statement(s) sufficient/necessary to answer the question.

X, Y and Z together can complete a work in 15 days. How long will it take for Y alone to complete the same job? A. X is 50% more efficient than Y. B. X and Y together can complete the work in 25 days. C. X and Z together can complete the work in 30 days.

  1. Either A and B together or C alone is sufficient.

  2. All A, B and C are not sufficient.

  3. Only A and B are sufficient.

  4. Only A and C are sufficient.

  5. Only C is sufficient.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X+Y+Z = 1/15. A: X=1.5Y. B: X+Y=1/25. C: X+Z=1/30. Using A and B: 1.5Y+Y = 1/25 -> 2.5Y = 1/25 -> Y = 1/62.5. Using C: Since X+Y+Z=1/15 and X+Z=1/30, Y = 1/15 - 1/30 = 1/30. Both paths lead to a unique value for Y.

Multiple choice

Passage

Directions: Read the given information carefully and answer the following question. The amounts of work done by a man, woman and a child are in the ratio of 3 : 2 : 1. There are 20 men, 30 women and 36 children in the factory, whose daily wages amount to Rs. 234.

How many days should 18 men, 27 women and 15 children work together to earn total wages of Rs. 19,188?

  1. 52

  2. 104

  3. 112

  4. 126

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The ratio of work is 3:2:1. Total daily work = 20*3 + 30*2 + 36*1 = 60+60+36 = 156 units. Wages for 156 units = 234, so 1 unit = 1.5 Rs. New group work = 18*3 + 27*2 + 15*1 = 54 + 54 + 15 = 123 units. Daily wage = 123 * 1.5 = 184.5. Days = 19188 / 184.5 = 104.

Multiple choice

Passage

Directions: The question contains a statement that is followed by quantities I, II and III. Read the information clearly and answer your question accordingly. The options represent the relations between these three quantities K) > L) < M) = N) ≤ O) ≥ For example: Quantity I = 200 Quantity II = 300 Quantity III = 100 (a) K, L (b) L, M (c) L, K (d) O, L (e) L, N Quantity I < Quantity II > Quantity III So, answer is (c)

P, Q, R and S together can complete a job in 16/3 days. P and Q together can complete the same job in 20/3 days. R and S together can complete the same job in 80/3 days. P and S alone can complete the same job in 10 days and 80 days, respectively. The work is started by P and Q together. They worked for 4 days and left and then, R alone worked for 5 days. Time taken by S to complete the remaining job is Y days. Quantity I: Value of Y. Quantity II: The number of days taken by Love and Kush together to complete the whole work, if Love can complete the same work in 15 days and Kush can complete the same work in (Y + 8) days. Quantity III: The number of days taken by Sandy and Linde together to complete the whole work, if Sandy alone can complete the same job in (Y + 3) days and Linde alone can complete the same job in (Y - 2) days.

  1. e

  2. d

  3. a

  4. b

  5. c
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P+Q+R+S = 3/16, P+Q = 3/20, R+S = 3/80. P=1/10, S=1/80. From P+Q=3/20, Q=3/20-1/10=1/20. From R+S=3/80, R=3/80-1/80=2/80=1/40. Work done by P+Q in 4 days = 4*(1/20) = 1/5. Work done by R in 5 days = 5*(1/40) = 1/8. Remaining work = 1 - 1/5 - 1/8 = 27/40. S completes this in (27/40)/(1/80) = 54 days. Y=54. Quantity I=54. Quantity II: Love=15, Kush=62, together = (15*62)/(77) approx 12. Quantity III: Sandy=57, Linde=52, together = (57*52)/(109) approx 27. I > II > III.

Multiple choice

Passage

Directions: Read the following to answer the question. Priya, Jyoti, Pooja, Kajol, Neha and Khushi alone need a unique time to do a job. Priya can complete the job in 10 days, Jyoti alone takes 20 days less than the time taken by Pooja alone to complete the same job and Pooja alone takes 30 days more than the time taken by Priya alone. If Neha, Khushi and Kajol work together, then the total job can be completed in days, if Khushi is 50% more efficient than Neha and Kajol is 100% more efficient than Khushi.

The time taken by Jyoti and Khushi together to complete the same job is how many days more than the time taken by Priya and Kajol together to complete the same job?

  1. 6 days

  2. 8 days

  3. 10 days

  4. 12 days

  5. 9 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Passage

Directions : Study the given information and answer the following question. Reema, Mahesh and Suresh are working together as a team to complete the treasure hunt task in fun activities organised during college fest. Reema takes 5 more days than Mahesh and 9 more days than Suresh to complete the task alone. Reema and Mahesh together can complete the task in the same time as Suresh alone can.

How many days would Reema take to complete the task when she is working alone?

  1. 13 days

  2. 16 days

  3. 15 days

  4. 20 days

  5. None of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let M, R, S be days taken by Mahesh, Reema, and Suresh. R = M+5, R = S+9. 1/R + 1/M = 1/S. Substituting M = R-5 and S = R-9 gives 1/R + 1/(R-5) = 1/(R-9). Solving this quadratic equation: (R-5+R)/(R(R-5)) = 1/(R-9) => (2R-5)(R-9) = R^2-5R => 2R^2 - 23R + 45 = R^2 - 5R => R^2 - 18R + 45 = 0. Roots are 15 and 3. Since R must be > 9, R = 15.

Multiple choice

Passage

Directions: The question given below is followed by three statements (A), (B) and (C). You have to determine which statement(s) is/are sufficient/necessary to answer the question.

What is the number of days in which Aman can complete the work? A. Aman is 75% more efficient than Gaurav, who alone can complete the work in 15 days. B. If the efficiency of Aman is decreased by 50%, he will complete the work in 120/7 days. C. Aman and Raghav together can complete the work in 10 days.

  1. Only A is sufficient.

  2. Only B is sufficient.

  3. Both options 1 and 2 are correct.

  4. Only C is sufficient.

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A gives Aman's efficiency relative to Gaurav, allowing calculation of Aman's time. B gives Aman's efficiency directly, allowing calculation of his time. C relates Aman and Raghav, but without Raghav's efficiency, it is insufficient. Both A and B are sufficient independently.

Multiple choice

Passage

Directions: Read the given information carefully and answer the question. There are four different types of project coded such that project 1 = P 1 , project 2 = P 2 , project 3 = P 3 , and project 4 = P 4 . The following information gives the number of days taken by three different persons to complete a particular project alone. Anisha completes the projects P 1 , P 2 , P 3 and P 4 in 20 days, 30 days, 15 days and 10 days, respectively. Radha completes the projects P 1 , P 2 , P 3 and P 4 in x days, (x + 5) days, (x + 5) days and (x + 10) days, respectively. Veena completes the projects P 1 , P 2 , P 3 and P 4 in (y - 5) days, (y + 5) days, (y - 15) days and z days, respectively. Anisha and Radha together can complete the project P 4 in 7.5 days, Radha and Veena together can complete the project P 1 in 12 days, and Anisha and Veena together can complete the project P 4 in 5 days.

A = Time taken (in days) by Radha and Veena to complete the project P2 B = Time taken (in days) by Anisha and Radha to complete the project P4 Which of the following options is correct considering the above statements?

  1. A : B = 39 : 64

  2. A : B = 80 : 39

  3. A : B = 36 : 83

  4. A : B = 42 : 65

  5. A : B = 42 : 83
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

In each of the following questions, a question & then two statements – I & II are given. You have to determine that the data provided in these statements is enough to answer the question or not. Study both the statement: निम्नलिखित प्रत्येक प्रश्न में एक प्रश्न और फिर दो कथन I और II दिए गए हैं। आपको यह निर्धारित करना है कि इन कथनों में प्रदान किया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों का अध्ययन करें:

There are three people P, Q and R. Find the time taken by R to complete the whole work. तीन व्यक्ति P, Q और R हैं। R द्वारा पूरे कार्य को पूरा करने में लिया गया समय ज्ञात कीजिए। Statement I : P and Q together can complete the work in 20 days while Q and R can complete the whole work in 16 days. Statement II : P and Q together can complete the work in 20 days. Efficiency of P and Q is same. कथन I: P और Q मिलकर काम को 20 दिनों में पूरा कर सकते हैं जबकि Q और R पूरे काम को 16 दिनों में पूरा कर सकते हैं। कथन II: P और Q मिलकर कार्य को 20 दिनों में पूरा कर सकते हैं। P और Q की दक्षता समान है।

  1. Only Statement I alone. केवल कथन I

  2. Only Statement II alone. केवल कथन II

  3. Both Statements I and II together. दोनों कथन I और II एक साथ

  4. Neither Statement I nor II is sufficient. न तो कथन I और न ही II पर्याप्त है।

  5. Either Statement I or II. या तो कथन I या II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

From Statement I, P+Q = 1/20 and Q+R = 1/16. Subtracting gives R - P = 1/16 - 1/20 = 1/80. From Statement II, P = Q, and P+Q = 1/20, so 2P = 1/20, giving P = 1/40. Substituting back, R = 1/40 + 1/80 = 3/80, meaning R completes the work in 80/3 ≈ 26.67 days. Both statements together are required to find R's individual time.

Multiple choice

Passage

In each of the following questions, a question & then two statements – I & II are given. You have to determine that the data provided in these statements is enough to answer the question or not. Study both the statement: निम्नलिखित प्रत्येक प्रश्न में एक प्रश्न और फिर दो कथन I और II दिए गए हैं। आपको यह निर्धारित करना है कि इन कथनों में प्रदान किया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों का अध्ययन करें:

How many days A, B and C can complete the work together? A, B और C मिलकर कितने दिनों में कार्य पूरा कर सकते हैं? Statement I – Ratio of efficiency of A and B is 2:1. B and C can complete the work in 12 days. Statement II – Ratio of efficiency of A and C is 3:1. C can alone complete the work in 30 days. कथन I - A और B की दक्षता का अनुपात 2:1 है। B और C उस कार्य को 12 दिनों में पूरा कर सकते हैं। कथन II - A और C की दक्षता का अनुपात 3:1 है। C अकेले कार्य को 30 दिनों में पूरा कर सकता है।

  1. Only Statement I alone. केवल कथन I

  2. Only Statement II alone. केवल कथन II

  3. Both Statements I and II together. दोनों कथन I और II एक साथ

  4. Neither Statement I nor II is sufficient. न तो कथन I और न ही II पर्याप्त है।

  5. Either Statement I or II. या तो कथन I या II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement I alone: A:B = 2:1, B+C=12 days. Insufficient - three unknowns, need more relationships. Statement II alone: A:C=3:1, C=30 days. Can find A=90 days, but B's rate unknown. Together: From II, A=90, C=30. From I, A:B=2:1 so B=45. Combined rate = 1/90+1/45+1/30 = 1/15, giving 15 days together. Both statements needed.

Multiple choice

Passage

In each of the following questions, a question & then two statements – I & II are given. You have to determine that the data provided in these statements is enough to answer the question or not. Study both the statement: निम्नलिखित प्रत्येक प्रश्न में एक प्रश्न और फिर दो कथन I और II दिए गए हैं। आपको यह निर्धारित करना है कि इन कथनों में प्रदान किया गया डेटा प्रश्न का उत्तर देने के लिए पर्याप्त है या नहीं। दोनों कथनों का अध्ययन करें:

In how many days 1 man and 2 women complete the work? 1 पुरुष और 2 महिलाएं उस कार्य को कितने दिनों में पूरा करेंगे? Statement I – 10 women complete the work in 40 days and 15 men take 15 days to complete the work. Statement II – 6 women and 3 men can complete the work in 10 days and 3 women and 7 men takes 10 days to complete the work. कथन I - 10 महिलाएं 40 दिनों में कार्य पूरा करती हैं और 15 पुरुष कार्य को पूरा करने में 15 दिन लेते हैं। कथन II - 6 महिलाएं और 3 पुरुष 10 दिनों में कार्य को पूरा कर सकते हैं और 3 महिलाएं और 7 पुरुष कार्य को पूरा करने में 10 दिन का समय लेते हैं।

  1. Only Statement I alone. केवल कथन I

  2. Only Statement II alone. केवल कथन II

  3. Both Statements I and II together. दोनों कथन I और II एक साथ

  4. Neither Statement I nor II is sufficient. न तो कथन I और न ही II पर्याप्त है।

  5. Either Statement I or Iदोनों कथन I और II एक साथI. या तो कथन I या II
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statement I: 10W=40 days → 1W=400 days. 15M=15 days → 1M=225 days. 1M+2W rate = 1/225+2/400 = (8+9)/1800 = 17/1800. Time = 1800/17 ≈ 106 days. Sufficient. Statement II: 6W+3M=10 days and 3W+7M=10 days. Two equations, two unknowns (rates of W and M). Can solve uniquely. Sufficient. Either statement alone is sufficient.