41. The efficiencies of A, B and C are in the ratio of 5 : 3 : 2. Working together, they can complete a task in 21 hours. In how many hours will B alone complete 40% of that task?

A, B और C की दक्षताओं का अनुपात 5 : 3 : 2 हैं। एक साथ कार्य करते हुए, वे एक कार्य को 21 घंटे में पूरा कर सकते हैं। B अकेले कार्य करते हुए कितने घंटे में उस कार्य का 40% कार्य पूरा करेगा?


Option”B” is correct

The efficiencies of A, B and C are in the ratio of 5 : 3 : 2

Total work = (5 + 3 + 2) × 21 = 210

40% of the total work = 210 × 40/100 = 84

40% of the total work completed by B in = 84/3 = 28 hours

42. The efficiencies of A, B and C are in the ratio 5 : 6 : 8 working together, they can complete a piece of work in 120 hours. In how many hours will, B alone be able be to complete 40% of that work?

A, B और C की कार्यक्षमता का अनुपात 5 ∶ 6 ∶ 8 हैं। एकसाथ कार्य करने पर, वे एक कार्य को 120 घंटे में पूरा कर सकते हैं। B अकेले उस कार्य का 40% भाग कितने घंटे में पूरा करने में सक्षम है?


Option”D” is correct

The efficiencies ratios of A, B and C = 5 ∶ 6 ∶ 8

Total work = (5 + 6 + 8) × 120 = 19 × 120 = 2280

40% of the total work = 2280 × 40/100 = 912

B alone can complete the 40% of the total work = 912/6 = 152 days.

43. To do a certain work, the ratio of efficiency of P, Q and R is 6 ∶ 5 ∶ 4. Working together, they can complete the work in 20 days. They work together for 10 days. 50% of the remaining work will be completed by Q alone in∶

एक निश्चित कार्य करने के लिए, P, Q और R की दक्षता का अनुपात 6 ∶ 5 ∶ 4 है। एक साथ काम करने पर, वे 20 दिनों में इस कार्य को पूरा कर सकते हैं। वे 10 दिनों तक एक साथ कार्य करते हैं। शेष कार्य का 50% Q द्वारा अकेले कितने दिनों में पूरा किया जाएगा? 


Option”C” is correct

Efficiency ratio of P, Q and R = 6 ∶ 5 ∶ 4

Total work = (6 + 5 + 4) × 20 = 15 × 20 = 300

Work completed by three in 10 days = 15 × 10 = 150

Remaining work = 300 – 150 = 150

50% of the remaining work = 150 × (1/2) = 75

50% of the remaining work will complete Q alone in = 75/5 = 15 days

44. A and B can do a piece of work in 6 days and 8 days, respectively. With the help of C, they completed the work in 3 days and earned Rs. 1,848. What was the share of C?

A और B एक कार्य को क्रमशः 6 दिन और 8 दिनों में पूरा कर सकते हैं। C की सहायता से, वे कार्य को 3 दिनों में पूरा करते हैं और 1,848 रुपये अर्जित करते हैं। C का हिस्सा क्या था?


Option”C” is correct

Let C complete the whole wok in x days

According to the question

1/6 + 1/8 + 1/x = 1/3

⇒ 1/x = 1/3 – 1/6 – 1/8

⇒ 1/x = (8 – 4 – 3)/24

⇒ 1/x = 1/24

So, C alone can complete the whole work in = 24 days

Efficiency ratio of A, B and C = 1/6 ∶ 1/8 ∶ 1/24 = 4 ∶ 3 ∶ 1

Let share ratio of A, B and C be 4k ∶ 3k ∶ k

According to the question

⇒ 4k + 3k + k = 1848

⇒ 8k = 1848

⇒ k = 1848/8 = 231

∴ Share of C = 231

45.A , B and C can complete a work in 24, 15 and 10 days respectively. If A and B worked for 3 days and left the work then find the number of days taken by C to complete the remaining work.

A, B और C क्रमश 24, 15 और 10 दिनों में एक काम पूरा कर सकते हैं। यदि A और B ने 3 दिन काम किया और काम छोड़ दिया तो ज्ञात कीजिए कि शेष कार्य पूरा करने में C को कितने दिन लगेंगे?


Option”C” is correct

Let total work = LCM of 24, 15 and 10 = 120 units

Hence, efficiency of A = 5 units

Efficiency of B = 8 units

Efficiency of C = 12 units

Hence, work done by A and B in 3 days = (5 + 8) × 3 = 39 units

Now, remaining work = 120 – 39 = 81 units

∴ Time taken by C = 81/12 = 27/4 days

46. 9 men can finish a work in 12 days working 4 hours in a day and 12 children can finish the same work in 6 days working ‘x’ hours a day. What is the value of ‘x’ if a man is 1.5 times as efficient as of a boy?

9 पुरुष एक दिन में 4 घंटे कार्य करके 12 दिन में एक कार्य पूरा कर सकते हैं और 12 बच्चे ‘x’ घंटे प्रतिदिन कार्य करके 6 दिनों में कार्य पूरा कर सकते हैं। यदि एक पुरुष एक लड़के की तुलना में 1.5 गुना  कुशल है तो ‘x’ का मान क्या होगा?


Option”C” is correct

The ratio of efficiency of a man to a boy = 1.5 : 1 = 3 : 2

3 children = 2 men

12 children = 8 men

Now,

MDH = constant

9 × 12 × 4 = 8 × 6 × x

x = 9 hours

47.A alone can do a piece of work in 30 days. B alone can do the same work in 60 days. If they work together for five days, What fraction of the work will be left?

A अकेला 30 दिनों में एक कार्य कर सकता है। B अकेले उसी कार्य को 60 दिनों में कर सकता है। यदि वे दोनों एक साथ पांच दिनों के लिए कार्य करते हैं, तो कार्य का कौन सा भाग शेष बचेगा?


Option”C” is correct

A can do a work in 1 day = 1/30 part

⇒ A can do a work in 5 days = 5/30 = 1/6 part

⇒ B can do the same work in 1 day = 1/60 part

⇒ B can do the same work in 5 days = 5/60 = 1/12 part

⇒ Work done by A and B together in 5 days = 1/6 + 1/12 = 3/12 = 1/4 part

⇒ Remaining work = 1 – 1/4 = 3/4 part

∴ Remaining work is 3/4 part.

48. A can finish a work in 20 days and B can finish the same work in 25 days. They began together, but B left the work after 5 days. How many more days will A take to finish the remaining work?

A एक काम को 20 दिनों में खत्म कर सकता है और B समान काम को 25 दिनों में खत्म कर सकता है। वे मिलकर काम करना शुरू करते हैं, लेकिन B, 5 दिनों के बाद काम छोड़ देता है। तो शेष काम को खत्म करने के लिए A और कितने दिन लेगा?


Option”D” is correct

A can complete the whole work in = 20 days

A’s 1 day’s work = 1/20

B can complete the whole work in = 25 days

B’s 1 day’s work = 1/25

Let A complete the whole work in x days.

According to the question

⇒ 5/20 + 5/25 + x/20 = 1

⇒ 1/4 + 1/5 + x/20 = 1

⇒ (5 + 4 + x)/20 = 1

⇒ 9 + x = 20

⇒ x = 20 – 9

⇒ x = 11 days

49. Working together, P, Q and R reap a field in 6 days. If P can do it alone in 10 days and Q in 24 days, in how many days will R alone be able to reap the field?

एक साथ काम करते हुए, P, Q और R 6 दिन में एक खेत को काटते हैं। यदि P अकेले इसे 10 दिन में और Q 24 दिन में पूरा कर सकता है, तो R कितने दिन में अकेले खेत को काट सकेगा?

A. 32 days

B. 40 days

C. 45 days

D. 60 days


Option”D” is correct

Let, R alone can reap the field in x days

According to the question,

⇒ 1/10 + 1/24 + 1/x = 1/6

⇒ 1/x = 1/6 – 1/10 – 1/24

⇒ 1/x = (20 – 12 – 5)/120

⇒ 1/x = 3/120

⇒ x = 40

∴ R alone can reap the field in = 40 days

50. A can finish a work in 33 days and B can finish the same work in one-third of the time taken by A. By working together, how much of the same work can both of them finish in six days?

A एक काम को 33 दिनों में पूरा कर सकता है और B समान काम को A द्वारा लिए गए समय के एक-तिहाई समय में पूरा कर सकता है। मिलकर काम करते हुए समान काम के कितने भाग को वे दोनों छह दिनों में पूरा कर सकते हैं?


Option”A” is correct

Let the total work be 33units

⇒ A’s efficiency = 33/33 = 1 units/day

⇒ B’s efficiency = 33/11 = 3 units/day

Work done in 6 days = 6 × (1 + 3) = 6 × 4 = 24 units

∴ Required answer = 24/33 = 8/11

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