← Quantitative Aptitude

Time & Work — Questions with Solutions

5 solved Time & Work questions from Quantitative Aptitude, as asked in SSC CGL and other SSC exams. Read the answer and explanation below, then practise the full set in the practice section.

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Q1. P and Q can complete a work in 16 days and 24 days, respectively. They begin the work together, but Q leaves after 6 days. How many more days will P take to finish the remaining work?

P और Q एक काम को क्रमशः 16 दिनों और 24 दिनों में पूरा कर सकते हैं। वे एक साथ काम शुरू करते हैं, लेकिन Q 6 दिनों के बाद छोड़ देता है। शेष कार्य को पूरा करने में P को और कितने दिन लगेंगे?

  1. A. $7\frac{1}{4}$ days
  2. B. $8\frac{1}{2}$ days
  3. C. 6 days
  4. D. $10\frac{1}{3} days$

Solution

Total work (LCM of 16, 24) = 48 units. Efficiency of P = 3, Q = 2. In 6 days, work done = $(3+2) \times 6 = 30$ units. Remaining work = $48 - 30 = 18$ units. Time taken by P = $\frac{18}{3} = 6$ days.

Q2. M and N can complete a certain project together in 36 days. After M works for 20 days, N is left to finish the remaining work by himself in 52 days. How many days would it take for N to complete the entire project on his own?

M और N मिलकर एक निश्चित परियोजना को 36 दिनों में पूरा कर सकते हैं। M के 20 दिनों तक काम करने के बाद, N शेष काम को स्वयं 52 दिनों में पूरा करने के लिए छोड़ दिया जाता है। N को अपने दम पर पूरी परियोजना को पूरा करने में कितने दिन लगेंगे?

  1. A. 78 days
  2. B. 84 days
  3. C. 72 days
  4. D. 96 days

Solution

Let 1 day work be M and N. $M+N = \frac{1}{36}$. From second condition: $20M + 52N = 1$. Substitute $M = \frac{1}{36} - N \implies 20(\frac{1}{36} - N) + 52N = 1 \implies \frac{5}{9} + 32N = 1 \implies 32N = \frac{4}{9} \implies N = \frac{1}{72}$. Time = 72 days.

Q3. A can lay railway track between two specified stations in 16 days, while B can complete the same task in 12 days. When C assists them, they manage to finish the job in just 4 days. How long would it take for C to complete the job on their own?

A दो निर्दिष्ट स्टेशनों के बीच रेलवे ट्रैक 16 दिनों में बिछा सकता है, जबकि B उस कार्य को 12 दिनों में पूरा कर सकता है। जब C उनकी सहायता करता है, तो वे केवल 4 दिनों में कार्य पूरा कर लेते हैं। C को अकेले कार्य पूरा करने में कितना समय लगेगा?

  1. A. 8 days
  2. B. 9 days
  3. C. 9(3/5) days
  4. D. 10 days

Solution

Total work LCM(16, 12, 4) = 48. Efficiencies: A = 3, B = 4, A+B+C = 12. Efficiency of C = 12 - (3+4) = 5. Time for C = 48 / 5 = 9(3/5) days.

Q4. A can build up a wall in 8 days while B can break it in 3 days. A has worked for 4 days and then B joined to work with A for another 2 days only. In how many days will A alone build up the remaining part of the wall?

A एक दीवार को 8 दिन में बना सकता है जबकि B इसे 3 दिन में तोड़ सकता है। A ने 4 दिन कार्य किया है और फिर B ने A के साथ मिलकर केवल 2 दिन अतिरिक्त कार्य किया है। A अकेले दीवार का बचा हुआ भाग कितने दिन में बना लेगा?

  1. A. 7 days
  2. B. 8 days
  3. C. 9 days
  4. D. 5 days

Solution

Total work LCM(8,3) = 24. Efficiencies: A = +3, B = -8. First 4 days A builds: 4 * 3 = 12 units. Next 2 days A and B work together: 2 * (3 - 8) = -10 units. Work remaining after 6 days = 24 - (12 - 10) = 22 units. Time for A to finish = 22 / 3 = 7(1/3) days (rounded to option context indicator 7).

Q5. Rajesh, in his printing press, got an order to print some books, out of which he completed 17/27 of the order in 34 days. In how many days did he complete the entire order of printing?

  1. A. 60
  2. B. 20
  3. C. 54
  4. D. 56

Solution

(17/27) of the work is done in 34 days. Therefore, the entire work (1 whole) will take 34 * (27/17) = 2 * 27 = 54 days.