BANK & INSURANCE (TIME AND WORK PIPE AND CISTERN) PART 3

Total Questions: 60

31. A & B together can complete a work in (80/9) days, B & C together can do the same work in (40/3) days, while A & C together can complete the work in (80/7) days. If all of them started working together, and A worked for 6 days and C left the work ___ days before the completion of work, then the whole work will be completed in __ days. The values given in which of the following options will fill the blanks in the same order in which it is given to make the above statement true:

A. 5, 10  B. 4, 13  C. 8, 11

Correct Answer: (d) Only A and C  
Solution:

Let total amount of work be 80 units (LCM of 80/9, 40/3 and 80/7)

Efficiency of A and B together = 9 units per day
Efficiency of B and C together = 6 units per day
Efficiency of A and C together = 7 units per day

Efficiency of A, B and C is 5 units per day, 4 units per day and 2 units per day respectively.

Amount of work done by A in 6 days = 6 × 5 = 30 units

Remaining work = 80 – 30 = 50 units

Let the work is completed in ‘x’ days and C left the work ‘y’ days before completion of work.

So, C worked for x – y days

Therefore, 2x (x – y) + 4x = 50
2x – 2y + 4x = 50
6x – 2y = 50

For A:
y = 5 and x = 10
6 × 10 – 2 × 5 = 50
So, A can be the answer.

For B:
y = 4 and x = 13
6 × 13 – 2 × 4 = 70
So, B cannot be the answer

For C:
x = 8 and x = 11
6 × 11 – 2 × 8 = 50
So, C can be the answer.

Hence, option d.

32. There are three persons ‘A’, ‘B’ and ‘C’ who can complete a work alone in (x + 20) days, (x - 5) days and ‘x’ days respectively. The efficiency of ‘A’ and ‘C’ together is 12.5% more than that of ‘B’. ‘A’ and ‘B’ started working together and joined by ‘C’ on 5th day. If at the end of 8th day, ‘A’ and ‘C’ both left and remaining work is completed by ‘B’ alone then total time taken to complete the work this way can be

Correct Answer: (b) (0.5x - 1) days
Solution:

According to the question,
1.125 × {1/(x – 5)} = {1/(x + 20)} + (1/x)

1.125x(x + 20) = (x – 5)(x + x + 20)

1.125x² + 22.5x = 2x² + 10x – 100

0.875x² – 12.5x – 100 = 0

0.875x² – 17.5x + 5x – 100 = 0

0.875x(x – 20) + 5(x – 20) = 0

(0.875x + 5)(x – 20) = 0

x = 20 (Since, number of days cannot be negative)

Therefore, time taken by ‘A’ to do the work alone = x + 20 = 40 days

Time taken by ‘B’ to do the work alone = x – 5 = 15 days

Time taken by ‘C’ to do the work alone = x = 20 days

Let total work = 120 units

Efficiency of ‘A’ = 120/40 = 3 units/day
Efficiency of ‘B’ = 120/15 = 8 units/day
Efficiency of ‘C’ = 120/20 = 6 units/day

Amount of work completed in 8 days = (8 + 3) × 4 + (3 + 8 + 6) × 4 = 68 + 44 = 112 units

Therefore, time taken by ‘B’ to do the rest amount of work alone = (120 – 112)/8 = 1 day

Total time taken = 8 + 1 = 9 days = (0.5x – 1) days

33. Ranjana can complete a task in 9 hours, Sanjana is 50% more efficient than Kangana. The time taken by Kangana alone to complete the task is 6 hours more than time taken by Sanjana alone to complete the task. Find the time taken by Ranjana, Sanjana and Kangana together to complete the task

Correct Answer: (b) 4 hours  
Solution:

Since, Sanjana is 50% more efficient than Kangana.

Let the efficiency of Kangana be ‘2x’.
So, the efficiency of Sanjana = ‘3x’

Since, efficiency is inversely proportional to time taken.

So, time taken by Kangana alone to complete the task = 3x hours

Time taken by Sanjana alone to complete the task = 2x hours

According to question,
3x – 2x = 6
x = 6 hours

So, time taken by Kangana alone to complete the task = 3 × 6 = 18 hours

Time taken by Sanjana alone to complete the task = 2 × 6 = 12 hours

Time taken by Ranjana alone to complete the task = 9 hours

Let the total work be LCM of (18, 12 and 9) = 36 units

Number of units of work completed by Kangana alone in one hour = 36/18 = 2 units

Number of units of work completed by Sanjana alone in one hour = 36/12 = 3 units

Number of units of work completed by Ranjana alone in one hour = 36/9 = 4 units

Number of units of work completed by Kangana, Sanjana and Ranjana together in one hour = 2 + 3 + 4 = 9 units

Required time taken to complete the task = 36/9 = 4 hours

Hence, option b

34. Directions [34-35]: Study the data carefully and answer the following questions:

Meena and Seema alone can complete the whole work in (9y + 3) days and 9z days, respectively and Reena and Kisan alone can complete the whole work in (2x + 2) days and (x - y) days, respectively. Reena and Chhaya together can complete the whole work in 18 days and Jaya and Payal together can complete the whole work in 24 days. Payal and Chhaya alone can complete the whole work in (10z + 2) days, and 6z days respectively. Kisan and Ira together can complete the whole work in 120/7 days and Ira and Jaya alone can complete the whole work in (x + y) days and 14z days, respectively.

Ques: If Meena and Reena started working together and after nine days they were replaced by Kisan and Chhaya, then they stopped working after five days, how much percentage of work is still remaining?

Correct Answer: (b) 31.25%  
Solution:

Jaya and Payal together can complete the whole work in 24 days.

⇒ 1/Jaya + 1/Payal = 1/24

⇒ 1/14z + 1/(10z + 2) = 1/24

⇒ (10z + 2 + 14z)/(14z(10z + 2)) = 1/24

⇒ 24(24z + 2) = 14z(10z + 2)

⇒ 140z² – 548z – 48 = 0

⇒ 35z² – 137z – 12 = 0

⇒ (35z + 3)(z – 4) = 0

⇒ z = –3/35 or 4 (neglecting negative value)

So, z = 4

Reena and Chhaya together can complete the whole work in 18 days

⇒ 1/Reena + 1/Chhaya = 1/18

⇒ 1/(2x + 2) + 1/6z = 1/18

⇒ 1/(2x + 2) = 1/18 – 1/24 = 1/72

⇒ 2x + 2 = 72

⇒ x = 35

Kisan and Ira together can complete the whole work in 120/7 days

⇒ 1/Kisan + 1/Ira = 7/120

⇒ 1/(x – y) + 1/(x + y) = 7/120

⇒ 2x/(x² – y²) = 7/120

⇒ 2 × 35 × 120/7 = 35² – y²

⇒ y² = 1225 – 1200

⇒ y² = 25

⇒ y = ±5 (neglecting negative value)

So, y = 5

Person

No of days

Meena

(9y + 3) = 9 × 5 + 3 = 48

Seema

9z = 9 × 4 = 36

Reena

(2x + 2) = 2 × 35 + 2 = 72

Kisan

(x – y) = 35 – 5 = 30

Payal

(10z + 2) = 10 × 4 + 2 = 42

Chhaya

6z = 6 × 4 = 24

Ira

(x + y) = 35 + 5 = 40

Jaya

14z = 14 × 4 = 56

Part of work done by Meena and Reena in 9 days
= 9(1/48 + 1/72) = 9 × 5/144 = 5/16

And part of work done by Kisan and Chhaya in 5 days
= 5(1/30 + 1/24) = 3/8

So, remaining percentage of work = (1 – 5/16 – 3/8) × 100 = 31.25%

35. Time taken by Ira to complete 75% of the work is how many days more or less than the time taken by Payal to complete 66(2/3)% of the work?

Correct Answer: (b) 2 days  
Solution:

Jaya and Payal together can complete the whole work in 24 days.

⇒ 1/Jaya + 1/Payal = 1/24
⇒ 1/14z + 1/(10z + 2) = 1/24
⇒ (10z + 2 + 14z)/(14z(10z + 2)) = 1/24
⇒ 24(24z + 2) = 14z(10z + 2)
⇒ 140z² – 548z – 48 = 0
⇒ 35z² – 137z – 12 = 0
⇒ (35z + 3)(z – 4) = 0
⇒ z = –3/35 or 4 (neglecting negative value)

So, z = 4

Reena and Chhaya together can complete the whole work in 18 days

⇒ 1/Reena + 1/Chhaya = 1/18
⇒ 1/(2x + 2) + 1/6z = 1/18
⇒ 1/(2x + 2) = 1/18 – 1/24 = 1/72
⇒ 2x + 2 = 72
⇒ x = 35

Kisan and Ira together can complete the whole work in 120/7 days

⇒ 1/Kisan + 1/Ira = 7/120
⇒ 1/(x – y) + 1/(x + y) = 7/120
⇒ 2x/(x² – y²) = 7/120
⇒ 2 × 35 × 120/7 = 35² – y²
⇒ y² = 1225 – 1200
⇒ y² = 25
⇒ y = ±5 (neglecting negative value)

So, y = 5

Person

No of days

Meena

(9y + 3) = 9 × 5 + 3 = 48

Seema

9z = 9 × 4 = 36

Reena

(2x + 2) = 2 × 35 + 2 = 72

Kisan

(x – y) = 35 – 5 = 30

Payal

(10z + 2) = 10 × 4 + 2 = 42

Chhaya

6z = 6 × 4 = 24

Ira

(x + y) = 35 + 5 = 40

Jaya

14z = 14 × 4 = 56

Time taken by Ira to complete 75% of the work
= 75/100 × 40 = 30 days

Time taken by Payal to complete 66 2/3% of the work
= 2/3 × 42 = 28 days

So, required difference = 30 – 28 = 2 days

36. Directions (36-37): Study the data carefully and answer the following questions:

Eight persons (Pankaj, Prakash, Pradeep, Piyush, Ashok, Anil, Anmol, and Aditya) engaged in a piece of work.

Prakash, and Pradeep alone can complete the work in 6a and 5c days respectively. Anil and Prakash together and Piyush and Prakash together can complete the work in 5a/2 and 4b days respectively. Piyush, Ashok and Anmol alone can complete the work in (9b + 2), (9a - 3) and 3c days respectively. Aditya alone, Prakash alone, and Pradeep and Anmol together can complete the work in (13a - 1), 42 and (2a + 1) days respectively.

Ques: Ashok and Pradeep together can complete how much percentage of the work in 3 Days?

Correct Answer: (d) 12.5%  
Solution:

Aditya alone, Prakash alone, and Pradeep and Anmol together can complete the work in (13a – 1), 42, (2a + 1) days respectively.

Prakash alone can complete the whole work in = 42 days

Prakash, and Pradeep alone can complete the work in 6a, 5c days respectively.
⇒ 42 = 6a
⇒ a = 7

Pradeep alone can complete the whole work in = 5c days

Aditya alone can complete the whole work in = 13a – 1 = 13 × 7 – 1 = 90 days

Anil and Prakash together and Piyush and Prakash together can complete the work in 5a/2, 4b days respectively.

Anil and Prakash together can complete the whole work = 5a/2 = 35/2 days
⇒ 1/Anil + 1/42 = 2/35
⇒ 1/Anil = 2/35 – 1/42
⇒ Anil = 30 days

Piyush, Ashok and Anmol alone can complete the work in (9b + 2), (9a – 3), 3c days respectively.

Anmol alone can complete the whole work in = 3c days

Piyush alone can complete the whole work in = (9b + 2) days

And Piyush and Prakash together can complete the work in = 4b days

⇒ 1/(9b + 2) + 1/42 = 1/4b
⇒ 1/42 = 1/4b – 1/(9b + 2)
⇒ 1/42 = (9b + 2 – 4b)/(36b² + 8b)
⇒ 36b² + 8b = 42 × (5b + 2)
⇒ 18b² + 4b = 105b + 42
⇒ 18b² – 101b – 42 = 0
⇒ (b – 6)(18b + 7) = 0

So, b = 6

Piyush alone can complete the whole work in = (9b + 2) days = 9 × 6 + 2 = 56 days

Pradeep and Anmol together can complete the whole work in = 2 × 7 + 1 = 15 days

⇒ 1/5c + 1/3c = 1/15
⇒ 8/15c = 1/15 ⇒ c = 8

Percentage of work done by Ashok and Pradeep together = 3 × (1/60 + 1/40) × 100 = 12.5%

37. The time taken by Prakash, Pradeep, and Piyush together to complete 20% of the work is how many more or less than the time taken by Ashok and Anil together to complete the 30% of the work?

Correct Answer: (d) 3 days  
Solution:

Aditya alone, Prakash alone, and Pradeep and Anmol together can complete the work in (13a – 1), 42, (2a + 1) days respectively.

Prakash alone can complete the whole work in = 42 days

Prakash, and Pradeep alone can complete the work in 6a, 5c days respectively.
⇒ 42 = 6a
⇒ a = 7

Pradeep alone can complete the whole work in
= 5c days

Aditya alone can complete the whole work in
= 13a – 1 = 13 × 7 – 1 = 90 days

Anil and Prakash together and Piyush and Prakash together can complete the work in 5a/2, 4b days respectively.

Anil and Prakash together can complete the whole work = 5a/2 = 35/2 days
⇒ 1/Anil + 1/42 = 2/35
⇒ 1/Anil = 2/35 – 1/42
⇒ Anil = 30 days

Piyush, Ashok and Anmol alone can complete the work in (9b + 2), (9a – 3), 3c days respectively.

Anmol alone can complete the whole work in
= 3c days

Piyush alone can complete the whole work in
= (9b + 2) days

And Piyush and Prakash together can complete the work in
= 4b days

⇒ 1/(9b + 2) + 1/42 = 1/4b
⇒ 1/42 = 1/4b – 1/(9b + 2)
⇒ 1/42 = (9b + 2 – 4b)/(36b² + 8b)
⇒ 36b² + 8b = 42 × (5b + 2)
⇒ 18b² + 4b = 105b + 42
⇒ 18b² – 101b – 42 = 0
⇒ (b – 6)(18b + 7) = 0

So, b = 6

Piyush alone can complete the whole work in
= (9b + 2) days = 9 × 6 + 2 = 56 days

Pradeep and Anmol together can complete the whole work in
= 2 × 7 + 1 = 15 days

⇒ 1/5c + 1/3c = 1/15
⇒ 8/15c = 1/15
⇒ c = 8

The time taken by Prakash, Pradeep, and Piyush together to complete 20% of the work = 20/100 × 1/(1/42 + 1/40 + 1/56) = 20/100 × 15 = 3 days

The time taken by Ashok and Anil together to complete the 30% of the work = 30/100 × 1/(1/60 + 1/30) = 30/100 × 20 = 6 days

So, required difference = 6 – 3 = 3 days

38. 12 men can finish some work in 15 days. They started working together but from 9th day onwards one additional man joins them every day. Find the number of days required to finish the work in this manner given that efficiency of each man is same.

Correct Answer: (e) 13.50 days
Solution:

Let the efficiency of each man be ‘10x’ units.

So total work = 12 × 15 × 10x = 1800x units

Amount of work done by 12 men in eight days = 12 × 10x × 8 = 960x units

Remaining work = 1800x – 960x = 840x units

Work done on:
Day 9 = 120x + 10x = 130x units
Day 10 = 130x + 10x = 140x units and so on

So, amount of work done in next 5 days = 130x + 140x + 150x + 160x + 170x = 750x units

Remaining amount of work = 840x – 750x = 90x units

Time taken to complete remaining work = 90x ÷ 180x = (1/2) days

Therefore, total time taken = 8 + 5 + (1/2) = 13.5 days

Hence, option e.

39. While working with their normal efficiency, ‘A’ alone can build a wall in 18 hours while ‘A’ and ‘B’ can together build it in 8.4 hours. If ‘A’ and ‘B’ work together for 5 hours where ‘A’ works at 120% his normal efficiency while ‘B’ works at 70% of his normal efficiency, then how much part of the wall will be built in the given time?

Correct Answer: (b) (5/9) part
Solution:

Let the total work done to build the wall = 126 units

Then, normal efficiency of ‘A’ = 126 ÷ 18
= 7 units/hour

Normal efficiency of ‘A’ and ‘B’ together = 126 ÷ 8.4
= 15 units/hour

So, normal efficiency of ‘B’ alone = 15 – 7 = 8 units/hour

120% of efficiency of ‘A’ = 7 × 1.2 = 8.4 units/hour
70% of efficiency of ‘B’ = 8 × 0.7 = 5.6 units/hour

So, work done by ‘A’ and ‘B’ together in 5 hours = (8.4 + 5.6) × 5 = 70 units

So, part of the wall completed = (70/126) = (5/9) part

Hence, option b.

40. B’ alone can complete a work in 20 days. ‘A’ and ‘B’ together can complete 75% of the same work in __ days. ‘A’ alone can complete the entire work in __ days. The values given in which of the following options will fill the blanks in the same order in which it is given so as to make the statement true?

I. 6, (40/3)  II. (80/7), (80/3)  III. 7, 12.5

Correct Answer: (d) Only I
Solution:

From I:
Let total work = L.C.M of 20 and 6 = 60 units

Then, efficiency of ‘B’ = (60/20) = 3 units/day

75% of the work = 60 × 0.75 = 45 units

Combined efficiency of ‘A’ and ‘B’ = 45 ÷ 6 = 7.5 units/day

So, efficiency of ‘A’ = 7.5 – 3 = 4.5 units/day

So, time taken by ‘A’ alone to complete the entire work
= 60 ÷ 4.5 = (40/3) days

So, I is true.

From II:
Let total work = L.C.M of 20 and (80/7) = 560 units

So, efficiency of ‘B’ = 560 ÷ 20 = 28 units/day

75% of total work = 560 × 0.75 = 420 units

Combined efficiency of ‘A’ and ‘B’ = 420 ÷ (80/7) = 36.75 units/day

So, efficiency of ‘A’ alone = 36.75 – 28 = 8.75 units/day

So, time taken by ‘A’ alone to complete the entire work
= 560 ÷ 8.75 = 64 days ≠ (80/3)

So, II is false.

From III:
Let the total work = L.C.M of 20 and 7 = 140 units

Then, efficiency of ‘B’ alone = 140 ÷ 20 = 7 units/day

75% of total work = 140 × 0.75 = 105 units/day

So, combined efficiency of ‘A’ and ‘B’ = 105 ÷ 7 = 15 units/day

So, efficiency of ‘A’ alone = 15 – 7 = 8 units/day

Time taken by ‘A’ alone to complete the entire work
= (140/8) days ≠ 12.5 days

So, III is not true.

Hence, option d.