71.Amit and Sunil together can complete a work in 9 days, Sunil and Dinesh together can complete the same work in 12 days, and Amit and Dinesh together can complete the same work in 18 days. In how many days will they complete the work if Amit, Sunil and Dinesh work together?

अमित और सुनील मिलकर एक काम को 9 दिनों में पूरा कर सकते हैं, सुनील और दिनेश मिलकर समान काम को 12 दिनों में पूरा कर सकते हैं, तथा अमित और दिनेश मिलकर समान काम को 18 दिनों में पूरा कर सकते हैं। यदि अमित, सुनील और दिनेश मिलकर काम करते हैं, तो वे काम को कितने दिनों में पूरा करेंगे?


Option”C” is correct

A = Amit, S = Sunil and D = Dinesh

Total work = LCM of (9, 12 and 18) = 36

Hence, efficiency of A + S = 4

Efficiency of S + D = 3

Efficiency of A + D = 2

Now, Efficiency of A + S + D = (4 + 3 + 2)/2 = 9/2

∴ A, S and D together work in = 36/(9/2) = 4 × 2 = 8 days

72.30 men working 5 hours a day can do a task in 16 days. In how many days will 40 men working 6 hours a day do the same task?

एक दिन में 5 घंटा कार्य करने वाले 30 पुरुष 16 दिन में एक कार्य पूरा कर सकते हैं। एक दिन में 6 घंटा कार्य करने वाले 40 पुरुषों को उसी कार्य को पूरा करने के लिए कितने दिन लगेंगे?

A. 12 days

B. 10 days

C. 15 days

D. 18 days


Option”B” is correct

Let, work will be completed in x days

According to the question,

⇒ 30 × 5 × 16 = 40 × 6 × x

⇒ 240x = 2400

⇒ x = 10

∴ Work will be completed in = 10 days

73. 50 men can finish a work in 20 days. After completing half work, 50 more men join them, in how many days, they complete the remaining work?

50 व्यक्ति 20 दिनों में एक काम पूरा कर सकते हैं। आधा काम पूरा करने के बाद, 50 और पुरुष उनके साथ जुड़ते हैं, कितने दिनों में वे शेष काम पूरा करते हैं?


Option”B” is correct

According to the question

Total work = 50 × 20

Half work = (50 × 20)/2

Let half work complete 100 men in x days, then

100 × x = 50 × 10

⇒ x = (50 × 10)/100

⇒ x = 5 days

74. A can paint a house in 18 days and B can do it in 36 days. Along with C, they did the job in 6 days only. Then in how many days, C alone can do the job?

A ,18 दिनों में एक घर की रंगाई कर सकता है और B इसे 36 दिनों में कर सकता है। C के साथ, उन्होंने केवल 6 दिनों में यह कार्य किया। तो कितने दिनों में, C अकेले यह कार्य कर सकता है?


Option”D” is correct

1/6 = 1/36 + 1/18 + 1/C

⇒ 1/C = 1/6 – 1/12 = 1/12

∴ C can alone do the same work in 12 days

75. 12 persons can complete half of a work in 9 days. How many persons can complete the same work (whole) in 6 days?

12 व्यक्ति किसी कार्य के आधे हिस्से को 9 दिनों में पूरा कर सकते हैं। उसी कार्य (सम्पूर्ण) को कितने व्यक्ति 6 दिनों में पूरा कर सकते हैं?


Option”A” is correct

Let the person required to complete the work in 6 days be x

According to formula,

12 × 9 / (w / 2) = x × 6 / (w)

⇒ 6x = 24 × 9

⇒ x = 36

∴ Number of persons required to complete the work in 6 days = 36

76. Working together, A, B and C can complete a work in 36 days. If the efficiency of A, B and C are in the ratio 5 : 6 : 9, then B alone will complete the same work in:

एक साथ काम करने पर, A, B और C, 36 दिनों में एक काम पूरा कर सकतें है। यदि A, B और C की दक्षता 5 : 6 : 9 के अनुपात में है, तो B अकेले उसी कार्य को पूरा करेगा:


Option”A” is correct

According to question,

Time taken by A to complete the work = x/5

Time taken by B to complete the work = x/6

Time taken by C to complete the work C = x/9

Thus, A, B and C can complete a work in 36 days.

(1/x/5) + (1/x/5) + (1/x/5) = 1/36

(5/x) + (6/x) + (9/x) = 1/36

x = 20 × 36 = 720

∴ Time Taken by B alone will be 120 days

Alternate solution

Let work done per day by A, B and C be 5 units, 6 units and 9 units respectively.

Total work = (5 + 6 + 9) × 36 = 20 × 36 = 720 units

∴ Required time taken by B = 720/6 = 120 days.

77.If C alone can complete two-third part of a work in 12 days, then in how many days C can complete the whole work?

यदि C अकेले किसी काम के दो-तिहाई भाग को 12 दिनों में पूरा कर सकता है, तो कितने दिनों में C संपूर्ण काम को पूरा कर सकता है?


Option”D” is correct

2/3 part → 12 days

⇒ 1 part → 12 × (3/2) = 18 days

∴ C can complete the whole work in 18 days

78. Sheeta and Gita can complete a work in 12 days, Gita and Rita can complete the same work in 15 days and Rita and Sheeta can complete the same work in 20 days. Find time taken by Sheeta, Gita and Rita to do the same work.

शीता और गीता 12 दिनों में एक काम पूरा कर सकती हैं, गीता और रीता इसी काम को 15 दिनों में पूरा कर सकती हैं और रीता और शीता 20 दिनों में इसी काम को पूरा कर सकती हैं। शीता, गीता और रीता द्वारा समान कार्य करने के लिए गया समय ज्ञात कीजिये।


Option”C” is correct

Total work = 60 units (L.C.M of 12, 15 and 20)

Efficiency of Sheeta and Gita = 5 units/day

Efficiency of Gita and Rita = 4 units/day

Efficiency of Rita and Sheeta = 3 units/day

Efficiency of Sheeta, Gita and Rita = (5 + 4 + 3)/2 = 6 units/day

∴ Time taken by Sheeta, Gita and Rita to complete the whole work = 60/6 = 10 days

79. If the worker of a Factory is reduced by 20% and efficiency of the rest worker is increased by 30%; Find percentage change in total work?

यदि किसी कारखाने के श्रमिकों को 20% कम कर दिया जाता है और शेष श्रमिकों की दक्षता 30% तक बढ़ जाती है; कुल कार्य में प्रतिशत परिवर्तन ज्ञात कीजिये?


Option”D” is correct

et the total number of workers be x and the efficiency of one worker be y

Total initial work = xy      —-(i)

Total final work = (80% of x) × (130% of y)      —-(ii)

⇒ Total final work = 0.8x × 1.3y = 1.04xy

So from equation (i) and (ii) 

Increase in total work = 1.04xy – xy = 0.04xy

∴ Percentage increase in total work = 0.04xy × 100/xy = 4%

80. A certain number of men can finish a piece of work in 50 days. If however, there were 4 men less, it would take 20 more days for the work to be finished. How many men were there originally?

पुरुषों की एक निश्चित संख्या 50 दिनों में एक काम खत्म कर सकती है। यदि लेकिन, 4 पुरुष कम थे, तो काम पूरा होने में 20 और दिन लगेंगे। मूल रूप से वहां कितने आदमी थे?


Option”B” is correct

Let that certain number of men be ‘y’

⇒ y × 50 = (y – 4) × 70

⇒ 50y = 70y – 280

⇒ 20y = 280

⇒ y = 14

∴ The number of men initially is 14.

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