Top 130 Time and Work questions in Hindi and English [ 100% free ]

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Top 130 Time and Work questions in Hindi and English :

81.When Pankaj finishes a certain work, he gets a total wage of Rs. 90. When Kamal finishes the same work, he gets total wage of Rs. 105. The daily wages of Pankaj and Kamal are Rs. 4.5 and Rs. 3.5 respectively. If both of them do it together, what is the cost of work?

जब पंकज एक निश्चित कार्य पूरा करता है, तो उसे कुल वेतन 90 रु. मिलता है। जब कमल उसी कार्य को पूरा करता है, तो उसे कुल वेतन 105 रु. मिलता है। पंकज और कमल की दैनिक मजदूरी क्रमशः 4.5 रु. और 3.5 रु. है। यदि वे दोनों इसे एक साथ करते हैं, तो कार्य की लागत कितनी है?


Option”D” is correct

The daily wage of Pankaj = Rs. 4.5

Total wage of Pankaj = Rs. 90

Number of days taken by Pankaj = 90/4.5 = 20 days

The daily wage of Kamal = Rs. 3.5

Total wage of Kamal = Rs. 105

Number of days taken by Kamal = 105/3.5 = 30 days

Number of days Taken by Pankaj and Kamal together = 1/(1/20 + 1/30) = 12 days

Cost of Pankaj for 12 days = 12 × 4.5 = Rs. 54

Cost of Kamal for 12 days = 12 × 3.5 = Rs. 42

∴ Total cost = 54 + 42 = Rs. 96

82.Three women Neha, Priya and Sneha are working on a task. Working alone, Neha, Priya and Sneha take 12, 15 and 20 hours to complete the task respectively. Neha and Priya worked for the first hour and then Neha and Sneha worked for the next hour. This pattern is continued until the work is finally finished. Determine the time taken to finish the task in this manner. (in hours)

तीन महिला नेहा, प्रिया और स्नेहा एक काम पर कार्य कर रहे हैं। अकेले काम करते हुए नेहा, प्रिया और स्नेहा काम को पूरा करने में क्रमशः 12, 15 और 20 घंटे लेते हैं। नेहा और प्रिया ने पहले घंटे के लिए काम किया और फिर नेहा और स्नेहा ने अगले घंटे के लिए काम किया। यह प्रक्रिया काम के खत्म होने तक जारी रहती है। तो इस प्रक्रिया में काम को खत्म करने में लिया गया समय (घंटे में) ज्ञात कीजिए।


Option”C” is correct

Work done by Neha and Priya in the first hour = 1/12 + 1/15 = 9/60th of the work

Work done by Neha and Sneha in the next hour = 1/12 + 1/20 = 8/60th of the work

Therefore, the total work completed by them in the first 2 hours = 9/60 + 8/60 = 17/60th of the work

Now in 2 × 3 = 6 hours work that will be finished = (17/60) × 3 = 51/60th of the work

Work done in 7 hours = work done in 6 hours + work done by Neha and Priya in the 7th hour = 51/60 + 9/60 = 60/60 = 1

Hence, time taken = 7 hours

83. If 30 persons take 10 days to complete a certain work working 8 hours a day, then 40 persons should work how many hours a day so that the work is completed in 6 days?

यदि 30 व्यक्ति एक दिन में 8 घंटे काम करते हुए एक विशिष्ट काम को पूरा करने के लिए 10 दिन लेते हैं, तो 40 व्यक्तियों को एक दिन में कितने घंटे काम करना चाहिए जिससे काम 6 दिनों में पूरा हो जाये?


Option”D” is correct

Men1 Days1 Hours1 = Men2 Days2 Hours2

30 10 8 = 40 6 Hours2

Hours2 = 10

40 persons should work 10 hours a day to complete the work in 6 days.

84. A and B can do a piece of work in 12 days, B and C in 15 days, C and A in 20 days. How long would A take separately to do the same work?

A और B एक काम को 12 दिनों में, B और C, 15 दिनों में, C और A, 20 दिनों में कर सकते हैं। तो समान काम को करने के लिए A ने अलग से कितना समय लिया होगा?


Option”C” is correct

One day work of A and B = 1/12

One day work of B and C = 1/15

One day work of C and A = 1/20

One day work of (A + B), (B + C) and (C + A) = 1/12 + 1/15 + 1/20

= 12/60 = 1/5

One day work of (A + B + C) = (1/2) × (1/5) = 1/10

One day work of A = One day work of (A + B + C) – One day work of (B + C)

= 1/10 – 1/15 = 2/60 = 1/30

∴ A takes 30 days alone to do the same work.

85. A and B together can do a certain work in x days. Working alone, A and B can do the same work in (x + 8) and (x + 18) days, respectively. A and B together will complete 5/6 of the same work in:

A और B एक साथ एक कार्य को x दिन में पूरा कर सकते हैं। A और B अकेले उस कार्य को क्रमशः (x + 8) और (x + 18)  दिन में पूरा कर सकते हैं। A और B एक साथ उस कार्य के 5/6 भाग को कितने दिन में पूरा करेंगे?


Option”D” is correct

A and B together can do the whole work in x days, then

According to the question

1/(x + 8) + 1/(x + 18) = 1/x

(x + 18 + x + 8)/(x2 + 26x + 144) = 1/x

x (2x + 26) = x2 + 26x + 144

2x2 + 26x = x2 + 26x + 144

x2 = 144

x = 12

So, 5/6 of the work done by A and B in = 12 × (5/6) = 10 days

Shortcut Trick If A and B alone can do the work in (x + 8) and (x + 18) days respectively.

A and B together can do the work in = √(8 × 18) = 12 days

So, x = 12 days

So, 5/6 of the work done by A and B in = 12 × (5/6) = 10 days

86. Pipes A and B together can fill a tank in 16 hours, whereas pipe C alone can empty the full tank in 24 hours. A and B were opened together for 10 hours and then closed. Pipe C was then opened. The tank will now be emptied by C in: 

पाइप A और B एक टैंक को 16 घंटे में भर सकते है, जबकि पाइप C अकेले पूरे टैंक को 24 घंटे में खाली कर सकता है। A और B को एक साथ 10 घंटे के लिए खोला गया और फिर बंद कर दिया गया। फिर पाइप C को खोला गया। अब C द्वारा टैंक कितने समय में खाली किया जा सकेगा?


Option”D” is correct

(A + B) fill a tank in 1 hour = 1/16

∴ (A + B) fill a tank in 10 hours = \(\large{\frac{1}{16}}\) × 10 = Available quantity in tank

C emptied the tank in 1 hour = 1/24

∴ Time taken by C in emptied the tank = (10/16)/(1/24)

Time taken by C = 240/16 = 15 hours.

87.Vaibhav can do a piece of work in 60 days. He works there for 15 days and then Sandeep alone finishes the remaining work in 30 days. In how many days will Vaibhav and Sandeep working together finish the work?

वैभव एक कार्य को 60 दिन में पूरा कर सकता है। वह वहाँ 15 दिन तक कार्य करता है और उसके बाद संदीप अकेले शेष कार्य को 30 दिन में पूरा करता है। वैभव और संदीप एक साथ कार्य करने पर उस कार्य को कितने दिन में पूरा करेंगे?


Option”B” is correct

Total work = 60

Let efficiency of Sandeep be x, then

15 + 30x = 60

30x = 60 – 15 = 45

x = 45/30 = 1.5

Vaibhav and Sandeep together can complete the whole work in = 60/(1 + 1.5) = 60/2.5 = 24 days

Alternate Method

Suppose Sandeep can complete the whole work in x days. 

According to the question,

15/60 + 30/x = 1

⇒ 30/x = 1 – 1/4

⇒ 30/x = 3/4

⇒ x = 40 days

Vaibhav and Sandeep together can complete the work in 1 day = 1/60 + 1/40

⇒ (2 + 3)/120 = 5/120 = 1/24

∴ Vaibhav and Sandeep together can complete the whole work in 24 days.

Alternate MethodCalculation:

Time taken by Vaibhav to complete the work = (60/15) = 4 days

Number of days Sandeep works = (1 – 1/4) = 3/4 days

Time taken by Sandeep to complete the work = (4/3 × 30) = 40 days

Now,

LCM of 60 and 40 is 120

Efficiency of Vaibhav = (120/60) = 2 units/day

Efficiency of Sandeep = (120/40) = 3 units/day

Time taken by Vaibhav and Sandeep together to complete a work = [120/(2 + 3)]

⇒ 120/5 days

⇒ 24 days

∴ The required days is 24 days

88. A and B, working together, can complete a work in d days. Working alone, A takes (8 + d) days and B takes (18 + d) days to complete the same work. A works for 4 days. The remaining work will be completed by B alone, in:

A और B, एक साथ काम करने पर, किसी कार्य को d दिनों में पूरा कर सकते हैं। अकेले A वह काम करने में (8 + d) दिन और B  उस कार्य को पूरा करने में (18 + d) दिन लगाता है। A, 4 दिन काम करता है। शेष कार्य अकेले B कितने दिनों में पूरा कर लेगा?


Option”C” is correct

According to the question

1/(8 + d) + 1/(18 + d) = 1/d

⇒ (18 + d + 8 + d)/(144 + 26d + d2) = 1/d

⇒ 144 + 26d + d2 = 26d + 2d2

⇒ d2 = 144

⇒ d = √144

⇒ d = 12 days

A and B together, can complete the whole work = 12 days

A alone can complete the whole work in = 12 + 8 = 20 days

B alone can complete the whole work in = 12 + 18 = 30 days.

Let the remaining work B complete in x days, then

According to the question

4/20 + x/30 = 1

⇒ x/30 = 1 – 1/5

⇒ x/30 = 4/5

⇒ x = 24 days

89.After completing a work together in 2 days, P and Q received Rs. 1200 and Rs. 400 respectively as wages. In how many days will Q alone complete the work?

2 दिनों में एक साथ एक काम पूरा करने के बाद, P और Q को क्रमशः 1200 रुपये और 400 रुपये वेतन मिला। Q अकेले कितने दिनों में काम पूरा करेगा?


“Option”C” is correct

Wages of P and Q are Rs. 1200 and Rs. 400 respectively.

⇒ Efficiency ratio of P and Q = 1200 : 400 = 3 : 1

⇒ Total work = (3 + 1) × 2 = 8 units

∴ Q alone can complete the whole work in = 8/1 = 8 days

90. P can do some work in 9 days. If Q is 50% more efficient than P, then how long will Q take to do the work?

P एक काम को 9 दिनों में कर सकता है। यदि Q, P की तुलना में 50% अधिक सक्षम है, तो Q को काम करने में कितना समय लगेगा?


Option”B” is correct

Let efficiency of P be 2 unit/day

⇒ Efficiency of Q = 2 × 3/2 = 3 units/day

Total work = 9 × 2 = 18 units

∴ Q alone can complete the whole work in = 18/3 = 6 days

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