61. A and B together can complete a task in 10 days, B and C can do in 15 days, and C and A together can do it in 12 days. How long will they take to complete the task working together?

A और B एकसाथ एक काम को 10 दिनों में, B और C इसे 15 दिनों में और C और A इसे 12 दिनों में पूरा कर सकते हैं। एकसाथ काम करते हुए उन्हें काम पूरा करने में कितना समय लगेगा?


Option”B” is correct

We have,

⇒ (1/A) + (1/B) = (1/10)

⇒ (1/B) + (1/C) = (1/15)

⇒ (1/A) + (1/C) = (1/12)

Adding all these equations,

⇒ 2{(1/A) + (1/B) + (1/C)} = (1/10) + (1/15) + (1/12)

⇒ 2{(1/A) + (1/B) + (1/C)} = (6 + 4 + 5)/60

⇒ 2{(1/A) + (1/B) + (1/C)} = 15/60

⇒ {(1/A) + (1/B) + (1/C)} = 1/8

62.The ratio of the efficiencies of A, B and C is 2 : 5 : 3. Working together, they can complete a work in 27 days. B and C together can complete 4/9th part of that work in:

A, B और C की दक्षता का अनुपात 2 : 5 : 3 है। एक साथ काम करते हुए, वे एक काम को 27 दिनों में पूरा कर सकते हैं। B और C एक साथ काम का 4/9 भाग कितने समय में पूरा कर सकते हैं:


Option”A” is correct

The ratio of the efficiency of A, B and C = 2 : 5 : 3

Total work = (2 + 5 + 3) × 27 = 270

⇒ 4/9th part of the total work = 270 × [4/9] = 120

∴ Required time = 120/(5 + 3) = 120/8 = 15 days

63. A is 40% more efficient than B and C is 20% less efficient than B. Working together, they can finish a work is 5 days. In how many days will A alone complete 70% of that work?

A, B की तुलना में 40% अधिक कुशल है और C, B की तुलना में 20% कम कुशल है। साथ में काम करने से, वे कार्य को 5 दिन में पूरा कर सकते हैं। A अकेले कितने दिनों में उसका 70% कार्य पूरा करेगा?


Option”B” is correct

Let efficiency of B be 100

Efficiency of A will be = 100 × [140/100] = 140

Efficiency of C will be = 100 × [80/100] = 80

Efficiency ratio of A, B and C = 140 : 100 : 80 = 7 : 5 : 4

Total work = (7 + 5 + 4) × 5 = 80

70% of total work = 80 × [70/100] = 56

70% of total work A will complete in = 56/7 = 8 days

64. Efficiency ratio of A to B is 2 : 3 while the efficiency ratio of B to C is 4 : 5. Working together they can complete the work in 8 days. 80% of the total work will be completed by A alone in:

A और B की दक्षता का अनुपात 2 : 3 है जबकि B और C की दक्षता का अनुपात 4 : 5 है। एकसाथ कार्य करते हुए वह एक कार्य को 8 दिनों में पूरा कर सकते हैं। तो केवल A द्वारा कुल कार्य का 80% कितने दिनों में पूरा किया जा सकता है?


Option”B” is correct

Efficiency ratio of A to B = 2 : 3      —-(1)

Efficiency ratio of B to C = 4 : 5      —-(2)

Multiply equation (1) by 4 and multiply equation (2) by 3

Efficiency ratio of A, B and C = 8 : 12 : 15

Altogether they complete the work in 8 days.

Total work = (8 + 12 + 15) × 8 = 35 × 8 = 280

80% of the total work = 280 × (80/100) = 224

Time taken by A to complete the the 80% of the total work = 224/8 days

⇒ 28 days

∴ 80% of the total work will be completed in 28 days

65.If 49 men working 12 hours a day can complete a work in 8 days, then how many men working 4 hours a day can complete the same work in 24 days?

यदि 49 पुरुष एक दिन में 12 घंटे कार्य करने पर एक कार्य को 8 दिन पूरा कर सकते हैं, तो कितने पुरुष एक दिन में 4 घंटे कार्य करने पर उसी कार्य 24 दिन में पूरा कर सकते हैं?


Option”D” is correct

From MDH rule-

49 × 12 × 8 = m × 4 × 24

⇒ m = 49 men

66. To do a certain work, the ratio of the efficiencies of X and Y is 5 ∶ 4 Working together, they can complete the same work in 10 days. Y alone starts work and leaves after 5 days. The remaining work completed by X alone in

किसी विशिष्ट काम को करने के लिए X और Y की दक्षता का अनुपात 5 ∶ 4 है। एकसाथ काम करते हुए, वे समान काम को 10 दिनों में पूरा कर सकते हैं। Y अकेले काम प्रारंभ करता है और 5 दिनों के बाद काम छोड़ देता है। शेष काम अकेले X द्वारा कितने समय में पूरा किया जायेगा?


Option”D” is correct

Total work = (5 + 4) × 10 = 90 unit

Work done by Y in 5 days = 4 × 5 = 20 unit

Remaining work when Y leaves = 90 – 20 = 70 unit

∴ Time taken to complete remaining work by X = Remaining work/Efficiency of X = 70/5 = 14 days

67.A and B can do a piece of work in 25 days and 20 days respectively. If A and B worked for 5 days and then B left the work. Find the time taken by A to complete the remaining work.

A और B क्रमश 25 दिनों और 20 दिनों में एक काम कर सकते हैं। यदि A और B ने 5 दिन काम किया और फिर B ने काम छोड़ दिया। बचे हुए काम को पूरा करने के लिए A द्वारा लिया गया समय ज्ञात कीजिए।


Option”D” is correct

Let total work = LCM of 25 and 20 = 100 units

Hence, efficiency of A = 100/25 = 4 units

Efficiency of B = 100/20 = 5 units

Work done by A and B in 5 days = (4 + 5) × 5 = 45 units

Hence, remaining work = 100 – 45 = 55 units

∴ Required time = Remaining work/Efficiency of A = 55/4 days

68. E, F and G together can complete a work in 12 days and E and F together can complete the same work in 30 days. Then in how many days can G alone complete the same work?

E, F और G मिलकर एक काम को 12 दिनों में पूरा कर सकते हैं तथा E और F मिलकर समान काम को 30 दिनों में पूरा कर सकते हैं। तो समान काम को केवल G कितने दिनों में पूरा कर सकता है?


Option”B” is correct

Work done by E, F and G together in 1 day = 1/12

And, work done by E and F together in 1 day = 1/30

⇒ The work done by G in 1 day = 1/12 – 1/30 = 1/20

∴ The time taken by G to do the whole work is 20 days

69. A can finish a work in 15 days and B can do the same work in twice the time taken by A. Then, working together, what part of the same work they can finish in five days?

A, 15 दिनों में एक कार्य पूरा कर सकता है और B उसी कार्य को A द्वारा लिए गए समय के दो गुने समय में कर सकता है। तो, एक साथ काम करते हुए, उसी कार्य के कितने हिस्से को वे पाँच दिनों में पूरा कर सकते हैं?


Option”A” is correct

A can finish a work in = 15 days

A’s 1 day’s work = 1/15

B can finish the same work in = 2 × 15 = 30 days

B’s 1 day’s work = 1/30

A and B’s 1 day’s work = (1/15 + 1/30)

A and B’s 5 day’s work = 5 × (1/15 + 1/30) = 1/3 + 1/6 = 1/2

70. If A, B and C can do a task working alone in 12, 18 and 36 days respectively. They all work together for 2 days, then B quits. How many days A and C working together will take to complete the remainder of the task?

यदि A, B और C क्रमशः 12, 18 और 36 दिनों में एक कार्य कर सकते हैं। वे सभी 2 दिनों के लिए एक साथ कार्य करते हैं, फिर B कार्य छोड़ देता है। शेष कार्य को एक साथ पूरा करने में A और C को कितने दिन लगेंगे?


Option”A” is correct

A can do a task in = 12 day

∴ A’s 1 day’s task = 1/12

B can do a task in = 18 day

∴ B’s 1 day’s task = 1/18

C can do a task in = 36 day

∴ C’s 1 day’s task = 1/36

Let, A and C will take x days to complete the remainder of the task

According to the question,

⇒ (x + 2) × 1/12 + 2/18 + (x + 2) × 1/36 = 1

⇒ x/12 + 1/6 + 1/9 + x/36 + 1/18 = 1

⇒ (3x + x)/36 = 1 – (3 + 2 + 1)/18

⇒ x/9 = 1 – 1/3

⇒ x/9 = 2/3

⇒ x = 6

∴ A and C will take 6 days to complete the remainder of the task.

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