51. Satyam and Shivam can do a work in 10 days and 15 days respectively. Both start the work together, after 4 days Satyam left the work. Shivam has to complete the remaining work. In how many days, does the total work get completed?

सत्यम और शिवम क्रमशः 10 दिन और 15 दिन में एक कार्य कर सकते हैं। दोनों एक साथ कार्य शुरू करते हैं, 4 दिनों के बाद सत्यम ने कार्य छोड़ दिया। शेष कार्य शिवम को पूरा करना है। कितने दिनों में, कुल कार्य पूरा हो जायेगा?


Option”A” is correct

LCM of 10, 15 = 30

Let the total work = 30 units

Efficiency of Satyam = 30/10 = 3 units/day

Efficiency of Shivam = 30/15 = 2 units/day

When they work together = 3 + 2 = 5 units/day

According to question:

Work completed in 4 days = 5 × 4 = 20 units

Remaining work = 30 – 20 = 10 units

Shivam can complete remaining work in = 10/2 = 5 days

∴ Total time taken to complete the work = 4 days + 5 days = 9 days

52. 40 mechanics can repair a bike in 56 days. In how many days 32 mechanics will do the same work?

40 मैकेनिक 56 दिनों में एक बाइक की मरम्मत कर सकते हैं। 32 मैकेनिक उसी कार्य को कितने दिनों में करेंगे?


Option”D” is correct

Time taken by 40 mechanics = 56 days

So, 1 mechanic will take = 56 × 40 days

∴ 32 mechanic will take

⇒ (56 × 40)/32

⇒ 70 days

∴ 32 mechanics will do the same work in 70 days.

53. A alone can complete a work in 10 days and B alone can complete the same work in 20 days. In how many days both A and B together can complete half of the total work?

A अकेले एक कार्य को 10 दिनों में पूरा कर सकता है और B अकेले उसी कार्य को 20 दिनों में पूरा कर सकता है। A और B मिलकर कुल कार्य के आधे भाग को कितने दिनों में पूरा कर सकते हैं?


Option”C” is correct

Amount of work done by A in a single day = 1/10

Amount of work done by B in a single day = 1/20

Amount of work done by A and B in a single day = 1/10 + 1/20 = 3/20

To complete the half of the total work, the amount of time taken will be = 0.5 / (3/20) = 10/3 days.

Alternate method:

LCM of 10, 20 = 20

Let the total work be 20 units

Efficiency of A = 20/10 = 2 units

Efficiency of B = 20/20 = 1 unit

According to question

Work to be done half of the initial work i.e. 20/2 = 10 units

Total efficiency of A and B when work together = 2 + 1 = 3 units

Time to be completed by A and B = (10/3) days

54. Two articians M and N are prevented from doing one work. If M works alone it takes 8 hours more than the working together and if N works alone it takes 4.5 hours more than the working together then how long will it take them both to work together?

दो कलाकारों M और N को एक काम करने से रोका जाता है। यदि M अकेले काम करता है तो उसे एक साथ काम करने की तुलना में 8 घंटे अधिक लगते हैं और यदि N अकेले काम करता है तो उसे एक साथ काम करने की तुलना में 4.5 घंटे अधिक लगते हैं तो उन दोनों को एक साथ काम करने में कितना समय लगेगा?


Option”B” is correct

⇒ √(8 × 4.5)

⇒ √36 = 6

∴ M and N both will complete work together in 6 hours.

55. Rahul alone can complete a work in 10 days, Sunil alone can complete the same work in 15 days. Find the time taken by Ankit to do the same work if efficiency of Ankit is equal to the efficiency of Rahul and Sunil.

अकेले राहुल 10 दिनों में एक काम पूरा कर सकता हैं, अकेले सुनील 15 दिनों में एक काम पूरा कर सकता हैं। यदि अंकित की दक्षता राहुल और सुनील की दक्षता के बराबर है, तो अंकित द्वारा उसी कार्य को करने के लिए गया समय क्या है?


Option”D” is correct

Total work = 30 units [LCM of 10 and 15]

Efficiency of Rahul = 3 units/day

Efficiency of Sunil = 2 units/day

Efficiency of Ankit = 3 + 2 = 5 units/day

∴ Time taken by Ankit to complete the work = 30/5 = 6 days

56. Krishna does work in 8 days. Mufaad takes 4 more days than twice the time taken by Krishna. If they started working together in how many days they will do 7/8 work.

कृष्णा 8 दिनों में काम करता है। मुफ़द, कृष्ण द्वारा लिए गए समय के दोगुने से 4 दिन अधिक समय लेता है। यदि उन्होंने एक साथ काम करना शुरू किया तो 7/8 काम कितने दिनों में करेंगे?


Option”B” is correct

Mufaad does the work in 4 + 2 × 8 = 20 days

Together they will do the work in (8 × 20)/(8 + 20)

⇒ Together they will do the work in 160/28 days

⇒ Together they will do the work in 40/7 days

⇒ They will do 7/8 work in 7/8 of 40/7

∴ They will do 7/8 work in 5 days

57.B and C do a certain work in 35 days, while A, B & C can do the same work in 17.5 days. In how many days can A do the same work alone?

B और C एक निश्चित काम को 35 दिनों में करते हैं, जबकि A, B और C उसी काम को 17.5 दिनों में कर सकते हैं। A अकेले उसी काम को कितने दिनों में कर सकता है?


Option”A” is correct

Let the total work be 35units.

Now, calculate one day work of:

B + C = 35/35 = 1 unit

A + B + C = 35/17.5 = 2units

Subtract equation (i) – (ii)

⇒ A = 1 unit

Time taken to complete the work by A alone = Total work/Work done in day

⇒ 35/1 = 35 days

58. A can do a piece of work is 8 hours while B alone can do it in 12 hours. Both A and B working together can finish the work in time?

A अकेले एक कार्य को 8 घंटे में पूरा कर सकता है जबकि B अकेले उस कार्य को 12 घंटे में पूरा कर सकता है। A और B दोनों एक साथ कार्य करते हुए कार्य को कितने समय में पूरा कर सकते हैं?


Option”C” is correct

Let A and B together can finish the work in x hours

A can complete the work in 8 hours

∴ 1 day work of A = 1/8 units

B can complete the work in 12 hours

∴ 1 day work of B = 1/12 units

According to the question,

⇒ x(1/8 + 1/12) = 1

⇒ x × (3 + 2)/24 = 1

⇒ x = 24/5

∴ A and B together can finish the work in 24/5 hours

59. A can paint a house in 55 days and B can do it in 66 days. Along with C, they did the job in 12 days only. In how many days C alone can do the job?

A एक घर की रंगाई को 55 दिनों में कर सकता है और B 66 दिनों में कर सकता है। C के साथ, वे उस कार्य को केवल 12 दिनों में कर सकते हैं। केवल C कार्य को कितने दिनों में कर सकता है?


Option”D” is correct

​A and B take 55 and 66 days respectively to finish the entire work.

Part of work done by A in 1 day = 1/55

Part of work done by B in 1 day = 1/66

When they work together, part of work finished by both in one day = 1/55 + 1/66 = 11/330

Let C alone can paint a house in ‘x’ days

Part of work done by C in 1 day = 1/x

When the work together, they finished the entire work in 12 days

12 × (1/55 + 1/66 + 1/x) = 1

⇒ 1/x = 1/12 – 11/330

⇒ x = 20

∴ C alone can do the job in 20 days

Alternate method

Let total work = LCM of (55 and 66) = 330 units

Hence, work done by A in 1 day = 6 units

Work done by B in 1 day = 5 units

Now, work done by A, B and C in 1 day = 330/12 = 55/2 = 27.5 units

Hence, work done by C in 1 day = 27.5 – (5+ 6) = 16.5 units

∴ Time taken by C = 330/16.5 = 20 days

60. 10 people could complete a task in 8 days. After 4 days, 2 of the workers left. How many days from then did it take to complete the remaining task?

10 व्यक्ति एक कार्य को 8 दिनों में पूर्ण कर सकते हैं। 4 दिनों के बाद, 2 कर्मचारी कार्य को छोड़ देते हैं। अब शेष कार्य को पूर्ण होने में कितना समय लगेगा?


Option”D” is correct

10 people could complete a task in 8 days,

⇒ Total work = 80 units

After 4 days, 2 of the workers left,

⇒ Work done by 10 people in 4 days = 40

⇒ Remaining work = 40 and remaining people = 8

⇒ Days required = 40/8 = 5

∴ 5 days from then it takes to complete the task.

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