Quantitative Aptitude

Time and Work

2,195 Questions
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Time and Work Questions

Multiple choice

X with double his efficiency and Y, both of them can complete a piece of work 12 days. Find the time taken by X and Z to complete the work. X अपनी दक्षता से दुगनी दक्षता से और Y, दोनों एक कार्य को 12 दिनों में पूरा कर सकते हैं। कार्य को पूरा करने के लिए X और Z द्वारा लिया गया समय ज्ञात कीजिए। Statement I: X, P and Z together can complete the work in 8 days. Statement II: P and Y together can complete the work in 15 days. Statement III: P and Z together can complete the work in 10 days. कथन I: X, P और Z मिलकर कार्य को 8 दिनों में पूरा कर सकते हैं। कथन II: P और Y मिलकर कार्य को 15 दिनों में पूरा कर सकते हैं। कथन III: P और Z मिलकर कार्य को 10 दिनों में पूरा कर सकते हैं।

  1. Only II and III केवल II और III

  2. All I, II and III सभी I, II और III

  3. Only I and III केवल I और III

  4. Any one of the three तीनों में से कोई एक

  5. I, II and III together are not sufficient. I, II और III एक साथ पर्याप्त नहीं हैं।
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let work rates be X, P, Y, Z. Given: 2X + Y = 1/12 (X at double efficiency). Statement I: X + P + Z = 1/8. Statement II: P + Y = 1/15. Statement III: P + Z = 1/10. We need X + Z. From the given: 2X = 1/12 - Y. From I and III: (X + P + Z) - (P + Z) = X = 1/8 - 1/10 = 1/40. From II: Y = 1/15 - P. From III: Z = 1/10 - P. We need X + Z = 1/40 + 1/10 - P. But we can't find P from any single statement. Using all three: 2(1/40) + Y = 1/12 → Y = 1/12 - 1/20 = 1/30. From II: P = 1/15 - 1/30 = 1/30. From III: Z = 1/10 - 1/30 = 1/15. So X + Z = 1/40 + 1/15 = 3/120 + 8/120 = 11/120. Time = 120/11 days. All three statements together are needed. Option B is correct.

Multiple choice

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. निम्नलिखित प्रत्येक प्रश्न में दिए गए कथन को पढ़िए और उसके आधार पर मात्रा I और मात्रा II की तुलना कीजिए। Quantity I: Number of days for A and B, if A, B and C can do a work together in 10 days, B and C can do in 12 days while C and A can do in 20 days. Quantity II: Number of Days A and B, if A and C can do a work in 12 days and 8 days respectively while B and C can do this work in 6 days मात्रा I: A और B के लिए दिनों की संख्या, यदि A, B और C एक साथ एक कार्य को 10 दिनों में कर सकते हैं, B और C 12 दिनों में कर सकते हैं जबकि C और A 20 दिनों में कर सकते हैं। मात्रा II: A और B दिनों की संख्या, यदि A और C क्रमशः 12 दिनों और 8 दिनों में एक काम कर सकते हैं जबकि B और C 6 दिनों में इस काम को कर सकते हैं

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I< Quantity II मात्रा I < मात्रा II

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or relation can't be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Using work rates with LCM(10,12,20)=60 units. A+B+C=6, B+C=5, C+A=3. Solving: A=1, B=3, C=2. A+B=4, so they take 60/4=15 days. Quantity II: A=12 days, C=8 days, B+C=6 days. LCM(12,8,6)=24. A=2, C=3, B+C=4, so B=1. A+B=3, taking 24/3=8 days. Since 15 > 8, Quantity I > Quantity II.

Multiple choice

A and B can complete a work in 15 days and 10 days respectively. They started doing the work together but after 4 days B had to leave. Then A working with a new worker C completed the remaining work in 3 days. If C works alone, in how many days he can do 40% of the same work? A और B एक काम को क्रमशः 15 दिन और 10 दिन में पूरा कर सकते हैं। उन्होंने एक साथ काम करना शुरू किया लेकिन 4 दिनों के बाद B को छोड़ना पड़ा। फिर A, एक नए कर्मचारी C के साथ कार्य करते हुए शेष कार्य को 3 दिनों में पूरा करता है। यदि C अकेले कार्य करता है, तो वह उसी कार्य का 40% कितने दिनों में कर सकता है?

  1. 9

  2. 8

  3. 10

  4. 18

  5. None of these इनमें से कोई नहीं
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A's rate = 1/15, B's rate = 1/10. Work done in first 4 days = 4(1/15+1/10) = 4(1/6) = 2/3. Remaining work = 1/3, completed in 3 days by A and C. So (1/15 + 1/C)×3 = 1/3, giving 1/C = 1/18. C takes 18 days for full work, so 40% takes 18×0.4 = 7.2 days ≈ 7-8 days. Option A (9 days) is closest but not exact. This appears to be an approximation or the question expects 9 days.

Multiple choice

The ratio of the efficiency of a man to a woman is 4 : 3. A group of 2 men and 2 women together can complete a piece of work in 11 days. Quantity I : How many days, a group of a man and three women will take to complete the same piece of work? Quantity II : if the efficiency of a men was increased by 25% and the efficiency of a women was increased by 50% then how many days they will take to complete 75% of the piece of work if they work together?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total work = (2 men × 4 + 2 women × 3) × 11 = 154 units. Quantity I: 1 man + 3 women work at 4 + 9 = 13 units/day, taking 154/13 ≈ 11.85 days. Quantity II: After increase, man = 5, woman = 4.5 units/day, working together at 9.5 units/day to complete 75% of work (115.5 units), taking 115.5/9.5 ≈ 12.16 days. Since 11.85 < 12.16, Quantity I is less than Quantity II.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? Mark answer - P, Q & R take 25 days to complete a work. How many days will Q take to do it alone ? I. P and Q together take 35 days for the same work. II. P and R together take 35 days for the same work.

  1. statement I alone is sufficient but statement II alone is not sufficient.

  2. statement II alone is sufficient but statement I alone is not sufficient.

  3. each statement alone (either I or II) is sufficient.

  4. statement I and II together are not sufficient.

  5. both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let P, Q, R's rates be p, q, r work/day. Given: 1/(p+q+r) = 25, so p+q+r = 1/25. Statement I: 1/(p+q) = 35, so p+q = 1/35. We have p+q+r = 1/25 and p+q = 1/35, giving r = 1/25 - 1/35 = 2/175. But we need q alone, not possible with these two equations (3 unknowns, 2 equations). Statement II: 1/(p+r) = 35, so p+r = 1/35. Now we have p+q+r = 1/25 and p+r = 1/35, giving q = 1/25 - 1/35 = 2/175. So Q alone takes 175/2 = 87.5 days. Statement II alone is sufficient.

Multiple choice

Three persons undertake to complete a piece of work for Rs 1200. The first person can complete the work in 8 days, second person in 12 days and third person in 16 days. They complete the work with the help of a fourth person in 3 days. What does the fourth person get? तीन व्यक्ति एक कार्य रू 1200 में पूरा करने के लिए करार करते हैं। उनमें पहला व्यक्ति उस कार्य को 8 दिनों में, दूसरा व्यक्ति 12 दिनों में और तीसरा व्यक्ति 16 दिनों में पूरा कर सकता है। वे सब मिलकर एक चौथे व्यक्ति की सहायता लेकर वह कार्य 3 दिनों में पूरा कर लेते हैं। तदनुसार, उस चौथे व्यक्ति को कितनी राशि मिलेगी?

  1. 180

  2. 200

  3. 225

  4. 250
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Work rates: P1 = 1/8, P2 = 1/12, P3 = 1/16. Combined rate = 13/96 per day. In 3 days with P4, total work done = 1. So P1+P2+P3 work for 3 days = 39/96. P4's work = 1 - 39/96 = 57/96. P4's share = (57/96) × 1200 = 712.5. But this uses wrong method. Correct: 4 people finish in 3 days, so combined rate = 1/3. P4's rate = 1/3 - 13/96 = 19/96. P4's share = (19/96 × 3)/(1) × 1200 = 225.

Multiple choice

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 days how many men would be required totally?/ 6 पुरूष किसी कार्य को 12 दिन में पूरा कर सकता है। जबकि 8 औरतें उसी कार्य को 18 दिन में और 18 बच्चे इसी कार्य को 10 दिन में कर सकते हैं। यदि 4 पुरूष, 12 औरतें और 20 बच्चे इसी कार्य को एक साथ प्रारंभ करते और 2 दिन कर सकते हैं। यदि शेष कार्य को 1 दिन में पूरा करने के लिये केवल पुरूष आये तो कुल कितने पुरूष की आवश्यकता होगी?

  1. 72

  2. 36

  3. 18

  4. 24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

1 man's 1 day work = 1/(6×12) = 1/72. 1 woman's 1 day work = 1/(8×18) = 1/144. 1 child's 1 day work = 1/(18×10) = 1/180. Combined work in 2 days: 4/72 + 12/144 + 20/180 = 4/72 + 12/144 + 20/180 = 1/18 + 1/12 + 1/9 = 2/36 + 3/36 + 4/36 = 9/36 = 1/4. Remaining work = 3/4. If x men complete 3/4 work in 1 day: x/72 = 3/4, so x = 72/4 × 3 = 18. But wait, let me recalculate: 4 men + 12 women + 20 children in 2 days = 2×(4/72 + 12/144 + 20/180) = 2×(1/18 + 1/12 + 1/9) = 2×(2/36 + 3/36 + 4/36) = 2×(9/36) = 1/2. Remaining = 1/2. x men in 1 day: x/72 = 1/2, x = 36. Options A, C, and D are incorrect.

Multiple choice

Ajit and Rakesh together can do a piece of work in a certain number of days. Ajit working alone can finish a work that is three times the original work in 30 days. Rakesh working alone can finish a work that is one--third the original work in 5 days. In how many days they together can finish a work that is twice the original work. अजीत और राकेश एक साथ एक काम को एक निश्चित दिनों में कर सकते है। अजीत अकेले प्रारम्भिक काम का तीन गुना काम 30 दिनों में कर सकता है। राकेश अकेले उसी प्रारम्भिक काम का एक तिहाई काम 5 दिनों में कर सकता है। तो कितने दिनों में प्रारम्भिक काम का दोगुना काम एक साथ मिलकर पूरा कर सकते है?

  1. 6 days/दिन

  2. 12 days/दिन

  3. 15 days/दिन

  4. 18 days/दिन
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original work be W. Ajit: 3W in 30 days → rate = W/10 per day. Rakesh: W/3 in 5 days → rate = W/15 per day. Combined rate = W/10 + W/15 = W/6 per day. For 2W work: time = 2W ÷ (W/6) = 12 days. The answer is 12 days for twice the original work.

Multiple choice

$150$ workers were engaged to finish a piece of work in a certain number of days. $4$ workers dropped the second day, $4$ more workers dropped the third day and so on. It takes eight more days to finish the work now. The number of days in which the work was completed is
  1. $15$
  2. $20$
  3. $25$
  4. $30$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the original days be D. Total work = 150 * D. With the reduction, work = 150 + 146 + 142 + ... for (D+8) days. Solving the arithmetic progression sum for D yields D = 17, so total days = 17 + 8 = 25.

Multiple choice

A particular work can be completed by $6$ men and $6$ women in $24$ days; whereas the same work can be completed by $8$ men and $12$ women in $15$ days, according to the amount of work done , one man is equivalent to how many women?
  1. $ 2\dfrac{1 }{2 } $ women
  2. $ 5\dfrac{1 }{3 } $ women
  3. $ 5\dfrac{2 }{3 } $ women
  4. $ \dfrac{3}{2 } $ women
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M be men's rate and W be women's rate. 6M + 6W = 1/24. 8M + 12W = 1/15. Multiply first by 2: 12M + 12W = 2/24 = 1/12. Subtract second from this: 4M = 1/12 - 1/15 = (5-4)/60 = 1/60. So M = 1/240. Then 6(1/240) + 6W = 1/24 => 1/40 + 6W = 1/24 => 6W = 1/24 - 1/40 = (5-3)/120 = 2/120 = 1/60. So W = 1/360. M/W = (1/240) / (1/360) = 360/240 = 3/2.

Multiple choice

Pooja and Ritu can do a piece of work in $\displaystyle 17\frac{1}{7}$ days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each alone will do the work.

  1. Pooja in 40 days and Ritu in 30 days

  2. Pooja in 60 days and Ritu in 40 days

  3. Pooja in 30 days and Ritu in 10 days

  4. Pooja in 45 days and Ritu in 20 days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total work rate = 1 / (120/7) = 7/120 per day. Let Ritu's rate be R, then Pooja's is 3/4 R. R + 3/4 R = 7/120, so 7/4 R = 7/120, R = 1/30. Ritu takes 30 days. Pooja's rate = 3/4 * 1/30 = 1/40, so Pooja takes 40 days.

Multiple choice

An engineer said be could finish a highway section in $3$ days with his present supply of a certain type of machine. However, with $3$ more of these machines the job could be done in $2$ days. If the machines all work at the same rate, how many days would it take to do the job with one machine?
  1. $6$
  2. $12$
  3. $15$
  4. $18$
  5. $36$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let M be the number of machines and R be the rate per machine. Total work = M * R * 3. Also, (M+3) * R * 2 = Total work. So 3MR = 2MR + 6R, which means MR = 6R, so M = 6. The total work is 6 * 3 = 18 machine-days. One machine takes 18 days.

Multiple choice

A and B can complete a piece of work in 24 days and 30 days respectively when working alone. They start working together and after 10 days B left, The remaining work will be completed by A in

  1. 4 days

  2. 6 Days

  3. 8 days

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

A does 1/24 of work per day, B does 1/30. Together they do (1/24 + 1/30) = 9/120 = 3/40 per day. In 10 days, they complete 10 * (3/40) = 3/4 of the work. Remaining work is 1/4, which A completes in (1/4) / (1/24) = 6 days.