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

Total Questions: 60

11. A, B and C can do a certain piece of work in 40 days, 72 days and 90 days respectively. All of them started working together but after __ days, A and B left the job and the remaining work is done by C alone 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. 10, 45  B. 16, 18  C. 18, 10

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

Let the total work = 360 units (LCM of 40, 72 and 90)

Amount of work done by A alone in one day = 360/40 = 9 units
Amount of work done by B alone in one day = 360/72 = 5 units
Amount of work done by C alone in one day = 360/90 = 4 units

Amount of work done by A, B and C together in one day = 9 + 5 + 4 = 18 units

For option A:
Amount of work done by A, B and C together in 10 days = 10 × 18 = 180 units
Amount of work done by C in 45 days = 45 × 4 = 180 units
Total work done = 180 + 180 = 360 units
So, option A can be the answer.

For option B:
Amount of work done by A, B and C together in 16 days = 18 × 16 = 288 units
Amount of work done by C in 18 days = 18 × 4 = 72 units
Total work done = 288 + 72 = 360 units
So, option B can be the answer.

For option C:
Amount of work done by A, B and C together in 18 days = 18 × 18 = 324 units
Amount of work done by C in 10 days = 10 × 4 = 40 units
Total work done = 324 + 40 = 364 ≠ 360 units
So, option C can’t be the answer.

Hence, option d.

12. Directions (12-13): Answer the questions based on the information given below.

Time taken by Rajiv and Aritra together to complete a work is 4 days less than the time taken by Pankaj and Rajiv together to complete the work. Pankaj, Rajiv and Aritra together can complete the work in 9 days. Rajiv alone can complete the work in 28 4/5 days.

Ques: Find the time taken by Pankaj and Rajiv together to complete the work?

Correct Answer: (d) 16 days  
Solution:

Let the time taken by Pankaj and Rajiv together to complete the work = x days.

So, the time taken by Rajiv and Aritra together to complete the work = x – 4 days

According to question:
(1/x) + {1/(x – 4)} – (1/9) = 5/144

{(x – 4 + x)/(x² – 4x)} = (5/144) + (1/9)
{(2x – 4)/(x² – 4x)} = (21/144) = 7/48

7x² – 28x = 96x – 192
7x² – 124x + 192 = 0
7x² – 112x – 12x + 192 = 0
7x(x – 16) – 12(x – 16) = 0
(x – 16)(7x – 12) = 0

x = 16, 12/7

‘x’ can’t be (12/7) because x – 4 = (12/7) – 4 = (–16/7), and number of days can’t be negative.

So, ‘x’ = 16

So, the time taken by Pankaj and Rajiv together to complete the work = x = 16 days

Hence, option d.

13. Aritra is how much percent less/more efficient than Pankaj?

Correct Answer: (b) 75%  
Solution:

Let the time taken by Pankaj and Rajiv together to complete the work = x days.

So, the time taken by Rajiv and Aritra together to complete the work = x – 4 days

According to question:
(1/x) + {1/(x – 4)} – (1/9) = 5/144

{(x – 4 + x)/(x² – 4x)} = (5/144) + (1/9)
{(2x – 4)/(x² – 4x)} = (21/144) = 7/48

7x² – 28x = 96x – 192
7x² – 124x + 192 = 0
7x² – 112x – 12x + 192 = 0
7x(x – 16) – 12(x – 16) = 0
(x – 16)(7x – 12) = 0

x = 16, 12/7

‘x’ can’t be (12/7) because x – 4 = (12/7) – 4 = (–16/7), and number of days can’t be negative.

So, ‘x’ = 16

So, Pankaj and Rajiv together can complete the work in 16 days whereas Rajiv and Aritra together can complete the work in 12 days.

Let the total work = 144 units (LCM of 16, 12 and 144/5)

Amount of work done by Pankaj and Rajiv together in one day = 144/16 = 9 units
Amount of work done by Rajiv and Aritra together in one day = 144/12 = 12 units
Amount of work done by Rajiv alone in one day = {144/(144/5)} = 5 units
Amount of work done by Pankaj alone in one day = 9 – 5 = 4 units
Amount of work done by Aritra alone in one day = 12 – 5 = 7 units

Desired percentage = {(7 – 4)/4} × 100 = 75%

Hence, option b.

14. Directions (14-15): Answer the questions based on the information given below.

A, B, C and D are hired to do a certain piece of work. A and B together can complete the work in 90/7 days. A and C together can complete the work in 144/7 days. B and D together can complete the work in 120/11 days. A and D together can complete the work in 72/5 days.

Ques: What is the time taken by C to complete the work if he works alone?

Correct Answer: (b) 48 days  
Solution:

Let the total work = 720 units (LCM of 90, 120, 72, 144)

Amount of work done by A and B together in one day
= 720/(90/7) = 56 units

Amount of work done by B and D together in one day
= 720/(120/11) = 66 units

Amount of work done by A and D together in one day
= 720/(72/5) = 50 units

Amount of work done by A and C together in one day
= 720/(144/7) = 35 units

Amount of work done by A, B and D in one day
= (56 + 66 + 50)/2 = 86 units

Amount of work done by A alone in one day
= 86 – 66 = 20 units

Amount of work done by B alone in one day
= 86 – 50 = 36 units

Amount of work done by D alone in one day
= 86 – 56 = 30 units

Amount of work done by C alone in one day
= 35 – 20 = 15 units

Time taken by C alone to complete the work
= 720/15 = 48 days

Hence, option b.

15. E is 40% less efficient than D. What is the time taken by D and E to complete the work if they worked on alternate days starting from D?

Correct Answer: (c) 30 days  
Solution:

Let the total work = 720 units (LCM of 90, 120, 72, 144)

Amount of work done by A and B together in one day
= 720/(90/7) = 56 units

Amount of work done by B and D together in one day
= 720/(120/11) = 66 units

Amount of work done by A and D together in one day
= 720/(72/5) = 50 units

Amount of work done by A and C together in one day
= 720/(144/7) = 35 units

Amount of work done by A, B and D in one day
= (56 + 66 + 50)/2 = 86 units

Amount of work done by A alone in one day
= 86 – 66 = 20 units

Amount of work done by B alone in one day
= 86 – 50 = 36 units

Amount of work done by D alone in one day
= 86 – 56 = 30 units

Amount of work done by C alone in one day
= 35 – 20 = 15 units

Amount of work done by E in one day
= 30 × 0.60 = 18 units

Amount of work done by D and E in 2 days
= 30 + 18 = 48 units

Time taken by D and E to complete the work if they work on alternate days
= (720/48) × 2
= 30 days

Hence, option c.

16. Directions (16-17): Answer the questions based on the information given below.

Aarushi and Tarushi together can make a bed in 30 days while Tarushi and Parul together can make the same bed in 32 days. Aarushi and Parul together started the work and worked for ‘a’ days and made (55/3)% of the bed, after that Parul left the work and Tarushi joined Aarushi and made (400/7)% of the remaining part of the bed in (a + b) days and the rest of the bed is made by Aarushi alone in 28 days.

Ques: What is the value of (a – b)?

Correct Answer: (d) 2  
Solution:

Let the total amount of the work = 480 units (LCM of 30 and 32)

Amount of work done by Aarushi and Parul together in making (55/3)% of the bed
= 480 × (55/3)% = 88 units

Amount of work done by Aarushi and Tarushi together in making (400/7)% of the remaining part of the bed
= (480 – 88) × (400/7)% = 224 units

Amount of work done by Aarushi in making remaining share of bed
= 480 – 88 – 224 = 168 units

Time taken by Aarushi to make the remaining part of the bed = 28 days

Aarushi’s efficiency = 168/28 = 6 units per day

Efficiency of Aarushi and Tarushi together = 480/30
= 16 units per day

Tarushi’s efficiency = 16 – 6 = 10 units per day

Tarushi and Parul’s efficiency together = 480/32
= 15 units per day

Parul’s efficiency = 15 – 10 = 5 units per day

According to the question,
(6 + 5) × a = 88
11 × a = 88
a = 8

Again, according to the question,
(10 + 6) × (a + b) = 224
16 × (8 + b) = 224
8 + b = 14
b = 6

Required value of (a – b) = 8 – 6 = 2

Hence, option d.

17. If Aarushi, Tarushi and Parul started making the same bed together and worked for (b + c) days after that Parul left the work and remaining bed was made by Aarushi and Tarushi together in (a + 1) days, then find the value of ‘c’.

Correct Answer: (a) 10  
Solution:

Let the total amount of the work = 480 units (LCM of 30 and 32)

Amount of work done by Aarushi and Parul together in making (55/3)% of the bed
= 480 × (55/3)% = 88 units

Amount of work done by Aarushi and Tarushi together in making (400/7)% of the remaining part of the bed
= (480 – 88) × (400/7)% = 224 units

Amount of work done by Aarushi in making remaining share of bed
= 480 – 88 – 224 = 168 units

Time taken by Aarushi to make the remaining part of the bed = 28 days

Aarushi’s efficiency = 168/28 = 6 units per day

Efficiency of Aarushi and Tarushi together = 480/30
= 16 units per day

Tarushi’s efficiency = 16 – 6 = 10 units per day

Tarushi and Parul’s efficiency together = 480/32
= 15 units per day

Parul’s efficiency = 15 – 10 = 5 units per day

According to the question,
(6 + 5) × a = 88
11 × a = 88
a = 8

Again, according to the question,
(10 + 6) × (a + b) = 224
16 × (8 + b) = 224
8 + b = 14
b = 6

According to the question,
(6 + 10 + 5) × (b + c) + (10 + 6) × (a + 1) = 480
21 × (6 + c) + 16 × 9 = 480
126 + 21c + 144 = 480
21c = 210
c = 10

Hence, option a.

18. A’ alone can complete project ‘P’ in 55 days while ‘A’ and ‘B’ can together complete project ‘P’ in 20 days. 40% more work than project ‘P’ is to be done to complete Project ‘Q’. ‘B’ is hired to work on project ‘Q’ for 15 days. But ‘B’ works at ‘y’% of his original efficiency for 10 days and (y + 20)% of his original efficiency for remaining days such that ‘A’ takes 59.5 days to complete the remaining work in project ‘Q’. Find the value of ‘y’.

Correct Answer: (b) 60  
Solution:

Let the total work to be done to complete project ‘P’
= LCM of 55 and 20 = 220 units

Then, efficiency of ‘A’ alone = 220 ÷ 55 = 4 units/day

Combined efficiency of ‘A’ and ‘B’ = 220 ÷ 20 = 11 units/day
So, efficiency of ‘B’ alone = 11 – 4 = 7 units/day

Total work to be done to complete project ‘Q’
= 220 × 1.4 = 308 units

Work done by ‘A’ alone in 59.5 days = 59.5 × 4
= 238 units

So, work done by ‘B’ = 308 – 238 = 70 units

So, {7 × (y/100)} × 10 + {7 × (y + 20)/100} × 5
= 70

(7y/10) + {(7y + 140)/20} = 70
(14y + 7y + 140) = 1400
So, y = (1400 – 140) ÷ 21 = 60

Hence, option b.

19. Directions (19-21): Answer the questions based on the information given below.

8 women can complete a work in ‘3x’ days while 4 men can complete the same work in ‘6x’ days. 18 boys can complete the work in ‘y’ days and the time taken by 5 men and 7 women together to complete the same work is 25% less than the time taken by 18 boys. 5 men, 8 women and 14 boys can complete the work in (z + 5) days while 7 men, 3 women and 30 boys can complete the same work in (1.5z – 3) days. The work done by 4 men in (y + 6) days is equal to the time taken by 16 boys to complete the same work in (0.5y + 3) days.

Ques: 8z men were assigned to complete a work in 15 days. After working for 6 days, ‘a’ more men joined them such that the remaining work got completed in 5 days. Find the value of ‘a’.

Correct Answer: (e) 64
Solution:

According to the question,
8W × 3x = 4M × 6x
W = M

Therefore, (5M + 7W) = (5M + 7M) = 12M
12M × 0.75y = 18B × y
1M = 2B

Therefore,
(5M + 8W + 14B) = (5M + 8M + 7M) = 20M

Also,
(7M + 3W + 30B) = (7M + 3M + 15M) = 25M

According to the question,
20M × (z + 5) = 25M × (1.5z – 3)
4z + 20 = 7.5z – 15
z = 35/3.5 = 10

Therefore,
4M × 6x = 20M × (z + 5)
4M × 6x = 20M × 15
x = 12.5

Similarly,
4M × 6x = 12M × 0.75y
4M × 75 = 12M × 0.75y
y = 400/12 = (100/3)

Total men who have to complete the work in 15 days
= 8z = 80 men

Therefore, 80 × 15 = 80 × 6 + (80 + a) × 5
1200 – 480 = (80 + a) × 5
a = 144 – 80 = 64

Hence, option e.

20. A’ can complete a work in 1.2z days. ‘B’ is 25% less efficient than that of ‘A’. Both of them started working together but after 6 days ‘A’ left and ‘C’ joined the work such that the remaining work got completed in 1.2 days. Find the time taken by ‘A’ and ‘C’ to complete the whole work together.

Correct Answer: (b) 8 days  
Solution:

According to the question,
8W × 3x = 4M × 6x
W = M

Therefore, (5M + 7W) = (5M + 7M) = 12M
12M × 0.75y = 18B × y
1M = 2B

Therefore,
(5M + 8W + 14B) = (5M + 8M + 7M) = 20M

Also,
(7M + 3W + 30B) = (7M + 3M + 15M) = 25M

According to the question,
20M × (z + 5) = 25M × (1.5z – 3)
4z + 20 = 7.5z – 15
z = 35/3.5 = 10

Therefore,
4M × 6x = 20M × (z + 5)
4M × 6x = 20M × 15

4M × 6x = 20M × 15
x = 12.5

Similarly,
4M × 6x = 12M × 0.75y
4M × 75 = 12M × 0.75y
y = 400/12 = (100/3)

Time taken by ‘A’ to complete the work = 1.2z = 12 days
Time taken by ‘B’ to complete the work = 12/0.75 = 16 days

Let the total work = 48 units

Efficiency of ‘A’ = 48/12 = 4 units/day
Efficiency of ‘B’ = 48/16 = 3 units/day

Work completed by ‘A’ and ‘B’ in 6 days = 6 × (3 + 4)
= 42 units

Let the efficiency of ‘C’ be ‘a’ units/day

Therefore, (a + 3) × 1.2 = 48 – 42
a = 5 – 3 = 2 units/day

Therefore, required time taken = 48/(4 + 2) = 8 days

Hence, option b.