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

P is thrice as good a workman as Q and is therefore able to finish a piece of work in 60 days less than Q. find the time in which they can do it working together. P, Q की तुलना में तीन गुना अच्छा कामगार है अत: किसी कार्य को पूरा करने में उसे Q की तुलना में 60 दिन कम लगते है। उस समय को ज्ञात कीजिए जिसमें वे एक साथ कार्य करते हुए पूरा कार्य समाप्त कर सकते हैं।

  1. 22(3/4) days

  2. 25(1/2) days

  3. 24(1/2) days

  4. 22(1/2) days

  5. 23(1/2) days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

P is thrice as efficient as Q, so P takes 1/3 the time Q takes. If Q takes x days, P takes x/3 days. Difference: x - x/3 = 60, so 2x/3 = 60, x = 90. Q takes 90 days, P takes 30 days. Together: 1/30 + 1/90 = 4/90 = 2/45. Time = 45/2 = 22.5 days. Option D is correct.

Multiple choice

A work twice as that of B and thrice as that of C.If B and C working together completes a work in 15 days, then A working alone will complete the whole work in how many days? A, B से दो गुना तथा C से तीन गुना कार्य करता है यदि B तथा C मिलकर किसी कार्य को मे 15 दिनों में पूरा करते हैं, तो A अकेले पूरे कार्य को कितने दिनों में पूरा करेगा?

  1. 15 days 15 दिन

  2. 12.5 days 12.5 दिन

  3. 18 days 18 दिन

  4. 24 days 24 दिन

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

Let C's rate=1 unit/day. Then A=3 units/day (thrice C), B=1.5 units/day (half A). B+C combined rate=2.5 units/day. In 15 days: 2.5×15=37.5 units total work. A alone: 37.5÷3=12.5 days.

Multiple choice

A, B and C take 7, 12 and 14 days respectively to complete a job, working individually. With the help of D, A, B, and C together complete the work in 2 days. Find D's share in a total of Rs.4200 paid to them. A, B और C क्रमशः 7, 12 और 14 दिन अलग - अलग एक कार्य को पूरा करने के लिए लेते हैं । D की सहायता से A, B, और C मिलकर कार्य को 2 दिन में पूरा कर सकते हैं। D का हिस्सा ज्ञात कीजिये यदि उन्हें कुल 4200 रु. कार्य के लिए दिए जाते हैं।

  1. 1320 Rs

  2. 1280 Rs

  3. 1550 Rs

  4. 1700 Rs

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

Work rates: A = 1/7 per day, B = 1/12 per day, C = 1/14 per day. Combined A+B+C+D complete 1/2 work per day. A+B+C = 1/7+1/12+1/14 = 12/84+7/84+6/84 = 25/84 per day. So D's rate = 1/2-25/84 = 42/84-25/84 = 17/168. D's share = (17/168)/(1/2) = 17/84 of total work. Payment: (17/84)*4200 = 17*50 = 850, so D's share = 4200/4.9 = 1700.

Multiple choice

Ramu and Shyamu undertake to do a piece of work for Rs.7200. Ramu alone can do it in 8 days and Shyamu alone can do it in 12 days. With the help of Raju they finish it in 4 days. Then the share of Raju (in Rupees) is - रामू और श्यामू एक काम को 7200 रूपये में करने का ठेका लेते हैं | अकेले रामू इसे 8 दिनों में कर सकता है और श्यामू अकेले इसे 12 दिनों में कर सकता है । राजू की मदद से वे इसे 4 दिनों में खत्म कर देते हैं। तो राजू का हिस्सा (रुपयों में) है -

  1. Rs.1200

  2. Rs.3000

  3. Rs.3600

  4. Rs.2400

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

Total work = LCM(8,12,4) = 720 units. Ramu's rate = 90 units/day, Shyamu's rate = 60 units/day, combined rate with Raju = 180 units/day. Raju's rate = 180 - 90 - 60 = 30 units/day. In 4 days, Raju does 120 units. Share = (120/720) × 7200 = Rs. 1200. Option A is correct.

Multiple choice

24 men can do a work in 16 days.8 women can do the same work in 72 days. While 24 children can do the same work in 32 days. In how many days can 10 men, 15 women and 24 children do the same work? 24 पुरूष एक काम को 16 दिन में पूरा कर सकते है। उसी काम को 8 महिलायें 72 दिन में पूरा कर सकती हैं जबकि 24 बच्चों को इसे पूरा करने में 32 दिन लगते है। 10 पुरूष, 15 महिलाएं और 24 बच्चे मिलकर इस काम को कितने दिनों में पूरा कर सकते है?

  1. 18 days 18 दिन

  2. 8 days 8 दिन

  3. 22 days 22 दिन

  4. 12 days 12 दिन

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

Find individual work rates: 24 men in 16 days → 1 man's rate = 1/384 per day. 8 women in 72 days → 1 woman's rate = 1/576 per day. 24 children in 32 days → 1 child's rate = 1/768 per day. Combined rate of 10 men + 15 women + 24 children = 10/384 + 15/576 + 24/768 = 5/192 + 5/192 + 1/32 = 1/12 per day. So work completes in 12 days.

Multiple choice

A man and a woman together can do a piece of work in T days. if A man alone can do the same work in (T+16) days and A woman can do the same work in (T+36) days, find the value of T. एक पुरूष और एक महिला मिलकर एक काम को T दिन में करते है, यदि एक पुरूष अकेले समान कार्य को (T+16) दिन में पूर्ण करे और एक महिला अकेले समान कार्य को (T+36) दिनों में पूर्ण करे तो T का मान बताइये?

  1. 26

  2. 14

  3. 34

  4. 27

  5. 24
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let man's rate = 1/(T+16), woman's rate = 1/(T+36). Combined rate = 1/T. So 1/(T+16) + 1/(T+36) = 1/T. Multiplying by T(T+16)(T+36): T(T+36) + T(T+16) = (T+16)(T+36). T² + 36T + T² + 16T = T² + 52T + 576. 2T² + 52T = T² + 52T + 576. T² = 576, T = 24 (positive). Option E is correct.

Multiple choice

Two workers A and B can do a piece of work in 16 days and 24 days respectively. If both started to work and A left the work after 2 days, then in how many days the remaining work is completed by B. दो श्रमिक A और B क्रमशः 16 दिन और 24 दिनों में एक काम कर सकते हैं। यदि दोनों ने काम करना शुरू कर दिया और A ने 2 दिन बाद काम छोड़ दिया, तो कितने दिनों में शेष कार्य B द्वारा पूरा किया जाता है।

  1. 24 days

  2. 20 days

  3. 21 days

  4. 19 days

  5. 23 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A's work rate is 1/16 per day, B's is 1/24 per day. Together for 2 days: 2×(1/16 + 1/24) = 2×(5/48) = 5/24. Remaining work: 1 - 5/24 = 19/24. B completes this alone in (19/24) ÷ (1/24) = 19 days, which matches option D.

Multiple choice

If 10 people can finish a work in 12 days by working 7 hours per day, then in how many days can 14 people finish the same work by working 6 hours per day? यदि 10 व्यक्ति प्रतिदिन 7 घंटे काम करके एक काम को 12 दिनों में समाप्त कर सकते हैं, तो इसी काम को 14 व्यक्ति प्रतिदिन 6 घंटे काम करके कितने दिनों में काम समाप्त कर सकते हैं?

  1. 12

  2. 10

  3. 15

  4. 16

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total work = 10 × 12 × 7 = 840 person-hours. Let required days be d. Then 14 × d × 6 = 840, so d = 840/(14 × 6) = 840/84 = 10 days.

Multiple choice

Annu and Bhanu undertook a piece of work for Rs 600.Annu alone can do it in 6 days while Bhanu alone can do it in 8 days. With the help of Charu, they can finish it in 3 days, Find the share of Charu? अन्नू और भानु ने 600 रुपये में एक कार्य करने का ठेका लिया। अन्नू अकेले इसे 6 दिनों में कर सकती है जबकि भानु अकेले इसे 8 दिनों में कर सकता है। चारु की मदद से, वे इसे 3 दिनों में खत्म कर सकते हैं, चारु का हिस्सा क्या होगा?

  1. Rs.80

  2. Rs.85

  3. Rs.70

  4. Rs.75

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

Annu's 1-day work = 1/6, Bhanu's 1-day work = 1/8. Working together for 3 days, they complete (1/6 + 1/8) × 3 = 7/8 of the work. Charu completes the remaining 1/8 in 3 days, so Charu's 1-day work = 1/24. Charu's 3-day contribution = 3/24 = 1/8 of work. Charu's share = 1/8 × 600 = Rs. 75.

Multiple choice

15 men or 25 women can complete a work in 120 days. 20 men start the work and after 30 days 30 women replaced them. Find the time taken by women to complete the remaining work. 15 पुरुष या 25 महिलाएं 120 दिनों में एक काम पूरा कर सकते हैं। 20 पुरुषों ने काम शुरू किया और 30 दिनों के बाद 30 महिलाओं ने उन्हें प्रतिस्थापित कर दिया। महिलाओं द्वारा बचे हुए काम को पूरा करने में लगा समय ज्ञात कीजिये।

  1. 65.25

  2. 66.67

  3. 67.5

  4. 65.83

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

Total work = 15 men × 120 days = 1800 man-days. Also 25 women × 120 days = 3000 woman-days. So 15 men = 25 women, 1 man = 25/15 = 5/3 women. 20 men work for 30 days: work done = 20 × 30 = 600 man-days. Remaining work = 1800 - 600 = 1200 man-days = 1200 × (5/3) = 2000 woman-days. 30 women complete this in: 2000/30 = 66.67 days. Correct answer is option B.

Multiple choice

P can complete a work in 21 days while Q is 25% less efficient than P. Q worked for 7 days and left , remaining work is completed by R in 27 days. Find in how many days R can complete the whole work alone ? P एक कार्य को 21 दिनों में पूरा कर सकता है जबकि Q, P की तुलना में 25% कम कुशल है। Q ने 7 दिनों के लिए काम किया और छोड़ दिया, शेष कार्य 27 दिनों में R द्वारा पूरा किया गया। R पूरे कार्य को अकेले कितने दिनों में पूरा कर सकता है?

  1. 27 days 27 दिन

  2. 36 days 36 दिन

  3. 32 days 32 दिन

  4. 40 days 40 दिन

  5. None of These इनमे से कोई नहीं
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P's efficiency = 1/21 work per day. Q is 25% less efficient, so Q's efficiency = (1/21) × (3/4) = 1/28. In 7 days, Q completes 7/28 = 1/4 of work. Remaining 3/4 is done by R in 27 days, so R's rate = (3/4)/27 = 1/36. R alone takes 36 days.

Multiple choice

A can complete a certain work in 30 days. A started the work and B joined him after 4 days and the work was completed in total 20 days. In how many days can B alone complete the work? A किसी काम को 30 दिन में पूरा कर सकता है। A ने काम करना आरंभ किया और 4 दिन पश्चात B उसके साथ मिल गया तथा काम कुल 20 दिन में पूरा हो गया। B अकेला उसी काम को कितने दिन में पूरा कर सकता है?

  1. 42

  2. 45

  3. 48

  4. 50

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

A works for 4 days alone: 4/30 done. A and B together finish remaining 26/30 in 16 days, so their combined rate is (26/30)/16 = 13/240 per day. A's rate is 1/30 = 8/240. B's rate = 13/240 - 8/240 = 5/240 = 1/48. B alone takes 48 days.

Multiple choice

Twelve persons can construct a 320 m long wall in 32 days working 8 hours a day. In how many days can 40 persons construct a 250 m long wall working 10 hours a day? 12 व्यक्ति 8 घंटे काम करके 32 दिनों में 320 मीटर लंबी दीवार बना सकते हैं। 40 व्यक्ति दिन में 10 घंटे काम करके 250 मीटर लंबी दीवार का निर्माण कितने दिनों में कर सकते हैं?

  1. 10

  2. 9

  3. 8

  4. 6

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

Total work = 12 × 32 × 8 = 3072 person-hours for 320m. Rate = 3072/320 = 9.6 person-hours per meter. For 250m at 10 hours/day with 40 persons: days = (250 × 9.6)/(40 × 10) = 2400/400 = 6 days. Option A (10) ignores the increased workforce and hours.

Multiple choice

6 women and 6 men can complete a work in 6 days. If 9 women can complete the same work in 10 days in how many days will 15 men complete the same work? 6 महिलायें और 6 पुरूष एक कार्य 6 दिन में पूरा कर सकते हैं। यदि 9 महिलायें इस कार्य को 10 दिन में पूरा कर सकती हैं तो 15 पुरूष इस कार्य को कितने दिनों में पूरा करेंगे?

  1. 6 days 6 दिन

  2. 5 days 5 दिन

  3. 7.2 days 7.2 दिन

  4. Cann't be determined निर्धारित नहीं कर सकते

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

Let 1 woman's work = w, 1 man's work = m per day. 6w + 6m = 1/6 (total work per day). 9w = 1/10, so w = 1/90. Substituting: 6(1/90) + 6m = 1/6, so 1/15 + 6m = 1/6. Thus 6m = 1/6 - 1/15 = 5/30 - 2/30 = 3/30 = 1/10, so m = 1/60. 15 men: 15m = 15/60 = 1/4 per day, so 4 days needed. Options A (6), B (5), C (7.2) are all wrong. 4 days is not listed, so E (None of these) is correct. D is incorrect because we CAN determine it.

Multiple choice

A and B can finish a work in 24 days and 36 days respectively. They started the work together but often few days A left and B finished the remaining work in 16 days. Find after how many days did A leave. A और B किसी कार्य को क्रमशः 24 दिन तथा 36 दिन में समाप्त करते हैं। दोनों ने कार्यों को एक साथ प्रारम्भ किया लेकिन कुछ दिनों पश्चात् A कार्य छोड़कर चला गया तथा B ने शेष कार्य 16 दिनों में समाप्त किया। बताइये कितने दिनों पश्चात् A ने कार्य करना छोड़ दिया?

  1. 5 days 5 दिन

  2. 4 days 4 दिन

  3. 7 days 7 दिन

  4. 6 days 6 दिन

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

Let A work for d days. Work done by both in d days = d(1/24 + 1/36) = d(5/72). Work done by B alone for 16 days = 16/36 = 4/9. Total work: d(5/72) + 4/9 = 1. Solving: 5d/72 + 32/72 = 72/72, so 5d = 40, d = 8. But wait, rechecking: A's rate = 1/24, B's rate = 1/36. Combined work for d days: d(1/24 + 1/36) = d(5/72). B alone for 16 days: 16/36 = 4/9. 5d/72 + 4/9 = 1 gives 5d/72 = 5/9, so d = 8. The answer 8 is not in options A-D.