101.A can do 40% of a work in 6 days and B can do 30% of the same work in 3 days. They started the work together but B left after 2 days and A continued to work. In how many days was the entire work completed?

A एक काम के 40% भाग को 6 दिनों में और B समान काम के 30% भाग को 3 दिनों में पूरा कर सकता है। वे एक साथ काम प्रारंभ करते हैं लेकिन 2 दिनों के बाद B काम छोड़ देता है और A काम में लगा रहता है। पूरा काम कितने दिनों में पूरा होता है?


Option”B” is correct

A can do 40% of a work in 6 days

∴ A can do 100% of the work in 15 days

B can do 30% of the same work in 3 days

∴ B can do 100% of the same work in 10 days

Total work = LCM of (15 and 10) = 30

Efficiency of A = 30/15 = 2

Efficiency of B = 30/10 = 3

Work done by A and B together in 2 days = 5 × 2 = 10

Remaining work = 30 – 10 = 20

Remaining work done by A = 20/2 = 10 days

∴ Total Number of days = 10 + 2 = 12 days

102.A alone can complete a work in 12 days and B alone can complete the work in 15 days. 3/5th of the work is completed by A and B together. The remaining work is completed by B alone. Find the total time taken to complete the work.

A अकेला 12 दिनों में कार्य पूरा कर सकता है और B अकेले 15 दिनों में कार्य पूरा कर सकता है। कार्य के 3/5 भाग को A और B मिलकर पूरा करते हैं। शेष कार्य अकेले B पूरा करता है। कार्य पूरा करने के लिए लिया गया कुल समय ज्ञात कीजिए।


Option”A” is correct

Given,

A’s 1 day’s work = 1/12

B’s 1 day’s work = 1/15

(A + B)’s 1 day’s work = 1/12 + 1/15 = 3/20

Time is taken by A and B to complete the 3/5th of the work

= 3/5 × 20/3 = 4 days

Remaining work = 1 – 3/5 = 2/5

Time is taken By B to complete remaining work = 2/5 × 15 = 6 days

Total time taken = 4 + 6 = 10 days

103. A can do a piece of work alone in 10 days, whereas B alone can do it in 15 days. They work together and get Rs. 2000 for their work. What is the share of B?

A अकेले 10 दिनों में एक काम कर सकता है, जबकि B अकेले इसे 15 दिनों में कर सकता है। वे एक साथ काम करते हैं और उसके लिए उन्हें 2000 रुपए मिलते हैं। B का हिस्सा क्या है?


Option”C” is correct

A = 10 days, B = 15 days

⇒ A : B = 10 : 15 = 2 : 3

We know, efficiency ∝ 1/Time

⇒ A : B = 3 : 2

⇒ Share of B = [2/ (2 + 3)] × 2000 = 2 × 400 = 800

∴ The share of B is Rs. 800

104. A can complete a certain work in 30 days. B is 25% more efficient than A and C is 20% more efficient than B. They all worked together for 3 days. B alone will complete the remaining work in:

A एक निश्चित कार्य को 30 दिनों में पूरा कर सकता है। B, A की तुलना में 25% अधिक कुशल और C, B की तुलना में 20% अधिक कुशल है। वे सभी 3 दिनों तक एक साथ काम करते थे। B अकेले शेष कार्य को कितने दिनों में पूरा कर लेगा?


Option”B” is correct

A can complete work in = 30 days

Efficiency of A (A’s 1 day’s work) = 1/30

Efficiency of B (B’s 1 day’s work) = 1/30 × (125/100) = 1/24

Efficiency of C (C’s 1 day’s work) = 1/24 × (120/100) = 1/20

Let the remaining work be complete by B in x days.

According to the question

3 (1/30 + 1/24 + 1/20) + x/24 = 1

⇒ 3 [(4 + 5 + 6)/120] + x/24 = 1

⇒ 15/40 + x/24 = 1

⇒ x/24 = 1 – 3/8 ×

⇒ x/24 = (8 – 3)/8

⇒ x/24 = 5/8

⇒ x = 5/8 × 24 = 15

Short Trick:

Let Efficiency of A = 4

Efficiency of B = 4 × 5/4 = 5

Efficiency of C = 5 × 6/5 = 6

Total work = 30 × 4 = 120

Work done by A, B and C in 3 days = (4 + 5 + 6) × 3 = 45

Remaining work = 120 – 45 = 75

∴ B completes the remaining work in = 75/5 = 15 days

105. If 20 men can build a wall 56 m long in 6 days, then what length of wall can be built by 35 men in 3 days?

यदि 20 पुरुष 56 मीटर लंबी एक दिवार को 6 दिनों में बना सकते हैं, तो 3 दिनों में 35 पुरुषों द्वारा कितनी लंबी दिवार को बनाया जा सकता है?


Option”C” is correct

Applying the above formula

⇒ (20 × 6)/56 = (35 × 3)W2

⇒ W2 = 105 × 56/120

⇒ W2 = 49 m

∴ The required length of wall will be 49 metre

106. 3 men and 5 boys can complete a task in 15 days, whereas 6 men and 7 boys can complete the same task in 9 days. Find the relationship between the task done by the boys and the task done by the men.

3 पुरुष और 5 लड़के एक कार्य को 15 दिनों में पूर्ण कर सकते हैं, जबकि 6 पुरुष और 7 लड़के उसी कार्य को 9 दिनों में पूर्ण कर सकते हैं। लड़कों द्वारा किए गए कार्य और पुरुषों द्वारा किए गए कार्य के बीच संबंध ज्ञात कीजिये।


Option”A” is correct

Let efficiency of 1 man and 1 boy be x and y respectively,

According to the question

(3x + 5y) × 15 = (6x + 7y) × 9

⇒ 45x + 75y = 54x + 63y

⇒ 54x – 45x = 75y – 63y

⇒ 9x = 12y

⇒ x : y = 4 : 3      —-(i)

Let’s check the option

Option 1: 3x = 4y

From (i), we get

3 × 4 = 4 × 3

⇒ 12 = 12

∴ Option 1 is correct 

107.P takes 50% more time than Q. If they work together, the work will work complete in 18 days. In how many days will Q alone complete the work?

P, Q से 50% अधिक समय लेता है। यदि वे मिलकर काम करते हैं, तो काम 18 दिनों में पूरा हो जायेगा। तो केवल Q काम को कितने दिनों में पूरा करेगा?


Option”A” is correct

Let time taken by Q be 2 days

Time taken by P = 2 × 3/2 = 3 days

⇒ Time ratio of Q to P = 2 : 3

As we know, efficiency is inversely proportional to time.

⇒ Efficiency ratio of P to Q = 2 : 3

Total work = (3 + 2) × 18 = 90 units

∴ Q alone can complete the whole work in = 90/3 = 30 days

108. Two people A and B alone can do a piece of work in 8 days and 12 days respectively. They undertook to do the piece of work for Rs. 3500 and with the help of C they can finish the work in 2.4 days, then what is the share of C?

दो व्यक्ति A और B अकेले क्रमशः 8 दिन और 12 दिनों में एक कार्य कर सकते हैं। उन्होंने उस काम को 3500 रुपए में करने का बीड़ा उठाया है और C की सहायता से वे 2.4 दिनों में कार्य समाप्त कर सकते हैं, तब C का हिस्सा क्या होगा?


Option”C” is correct

A alone can complete the work in 8 days

1 day work of A = 1/8 units

B alone can complete the work in 12 days

1 day work of B = 1/12 units

According to the question,

With the help of C total work is completed in 2.4 days

⇒ (1/8) + (1/12) + (1/C) = (1/2.4)

⇒ (1/C) = (1/2.4) – (1/8) – (1/12)

⇒ C = 4.8 days

Ratio of efficiency of A, B and C = (1/8): (1/12): (1/4.8) = 3: 2: 5

Share of C = 3500 × (5/10) = Rs. 1750

∴ Share of C is Rs. 1750.

109. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? 

A, B और C क्रमशः 20, 30 और 60 दिनों में काम कर सकते हैं। यदि A हर तीसरे दिन B और C द्वारा सहायता प्राप्त करता है तो A कितने दिनों में कार्य कर सकता है?


Option”B” is correct

Let total work be LCM of (20, 30 and 60) = 60 unit

Efficiency of A = 3 units

Efficiency of B = 2 units

Efficiency of C = 1 unit

According to the question

A is assisted by B and C together on every third day

Work done by A in first 2 days = 3 + 3 = 6 unit

Work done by A, B and C on third day = 3 + 2 + 1 = 6

Total work done by A, B and C in 3 days = 6 + 6 = 12 unit

12 units work done by A, B and C in 3 days

∴ 60 unit work A, B and C will be complete in 3/12 × 60 = 15 days

110. A, B and C can finish a work in 36/19 days. B and C can finish it in 36/7 days. A and B can finish it in 9/4 days. In how many days will B alone be able to finish the work?

A, B और C 36/19 दिनों में एक कार्य पूर्ण कर सकते हैं। B और C इसे 36/7 दिनों में पूर्ण कर सकते हैं। A और B इसे 9/4 दिनों में पूर्ण कर सकते हैं। B अकेले कितने दिनों में कार्य पूर्ण करेगा?


Option”D” is correct

Let the total work be 36 units (∵ LCM of 36, 36, 9)

Efficiency of A + B + C = 36/(36/19) = (36 × 19) / 36 = 19

Similarly Efficiency of B + C = 7

⇒ A + B = 16

Now, A + B + C = 19

⇒ A + 7 = 19 (Putting B + C = 7)

⇒ A = 12

Since, A + B = 16

⇒ B = 16 – 12 = 4

∴ B alone will take = 36/4 = 9 days

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