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

Total Questions: 60

21. Which of the following cannot be determined using the information given above?

I. Ratio of efficiencies of man to woman

II. Value of (x + z)

III. Amount of work done by 5 men in ‘y’ days.

Correct Answer: (c) Only III
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)

For I:
Ratio of efficiencies of men and women = 1:1
Therefore, I can be determined

For II:
Value of (x + z) = (12.5 + 10) = 22.5
Therefore, II can be determined

For III:
Since, the efficiency of each man is not known, therefore, total work done by 5 men in ‘y’ days cannot be determined.
Therefore, III cannot be determined

Hence, option c.

22. 3 bulls working together for 3 days can complete 3/16 parts of the work. 2 cows and 2 goats working together can complete 100/3 of the same work in 8 days. 4 goats working together can complete (800/9)% of the same work in 24 days. If 1 bull 1 cow and 2 goats worked together for 15 days, and then 1 goat left, then what is the time taken by the remaining workers to finish the remaining work?

Correct Answer: (c) 17/3 days
Solution:

Let the efficiency of a bull = ‘x’ units/day
Efficiency of a cow = ‘y’ units/day
And efficiency of a goat = ‘z’ units/day

Given that,

Amount of work completed by 3 bulls working together for 3 days = 3x × 3 = (3/16) of total work
Total work = 9x × (16/3) = 48x units

Amount of work completed by 2 cows and 2 goats working together for 8 days = (2y + 2z) × 8 = (48x/3) units

So, 16y + 16z = 16x
y + z = x

Amount of work completed by 4 goats working together for 24 days = 4z × 24 = (48x × (8/9)) units
Amount of work completed by 4 goats working together for (24 × (9/8)) = 27 days = 108z units

So, 108z = 48x
9z = 4x

Therefore, efficiency ratio of goat to that of bull is 4:9
So, z = (4x/9)

So, y = x – (4x/9) = (5x/9)

Therefore, efficiency ratio of cow to that of bull is 5:9

Let total work = 48 × 9 = 432 units

Then, efficiency of bull, cow and goat are 9 units/days, 5 units/days and 4 units/days, respectively.

Total work completed by 1 bull, 1 cow and 2 goats working together for 15 days = (9 + 5 + 8) × 15 = 330 units

Remaining work = 432 – 330 = 102 units

Time taken by 1 bull 1 cow and 1 goat to complete this work = 102 ÷ (9 + 5 + 4) = (17/3) days

Hence, option c.

23. A, B and C together can complete the work in 35 days. A and B together can complete the work in 60 days. If B is ___ % less efficient than C, then A alone can complete the 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 to make the above statement true:
A. 20, 140  B. 30, 125  C. 40, 105

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

Let the total work = 420 units (LCM of 35 and 60)

Amount of work done by A, B and C together in one day = 420/35 = 12 units

Amount of work done by A and B together in one day = 420/60 = 7 units

Amount of work done by C alone in one day = 12 – 7 = 5 units

For option A:
Amount of work done by B alone in one day = 0.80 × 5 = 4 units
Amount of work done by A alone in one day = 7 – 4 = 3 units
Time taken by A alone to complete the work = 420/3 = 140 days
So option A can be the answer.

For option B:
Amount of work done by B alone in one day = 0.70 × 5 = 3.5 units
Amount of work done by A alone in one day = 7 – 3.5 = 3.5 units
Time taken by A alone to complete the work = 420/3.5 = 120 days
So option B cannot be the answer.

For option C:
Amount of work done by B alone in one day = 0.60 × 5 = 3 units
Amount of work done by A alone in one day = 7 – 3 = 4 units
Time taken by A alone to complete the work = 420/4 = 105 days

So option C can be the answer.
Hence, option c.

24. Working alone ‘A’ can complete project ‘P’ in (y + 14.8) days. When working together with ‘B’ on project ‘P’, A’s efficiency decreases by ‘z%’ such that ‘A’ and ‘B’ together can complete it in 15 days. ‘B’ alone and ‘A’ alone can complete project ‘Q’ in ‘y’ days and (y + 8) days, respectively while ‘A’ and ‘B’ together, working with their original efficiencies, can complete project ‘Q’ in (35/3) days. Find the value of ‘z’.

Correct Answer: (e) None of these
Solution:

We have,
(1/y) + (1/(y + 8)) = (3/35)

Or, (y + 8 + y) + (y² + 8y) = (3/35)
Or, 3y² + 24y – 70y – 280 = 0
Or, 3y² – 46y – 280 = 0
Or, 3y² – 60y + 14y – 280 = 0
Or, 3y(y – 20) + 14(y – 20) = 0
Or, (3y + 14)(y – 20) = 0

So, y = -14/3 or 20
Since efficiency cannot be negative, so y = 20

So, efficiency ratios of ‘A’ and ‘B’ respectively when working alone = 20:28 = 5:7

Now, time taken by ‘A’ alone to complete project ‘P’ = 20 + 14.8 = 34.8 days

Let total amount of work to done to complete project ‘P’ = 870 units (LCM of 174 and 15)

Efficiency of ‘A’ alone = 870/(174/5) = 25 units per day

Efficiency of ‘A’ while working with ‘B’ on project ‘P’ + efficiency of ‘B’ alone = (870/15) = 58 units per day

Now, efficiency of ‘B’ while working alone = (7/5) × 25 = 35 units per day

Efficiency of ‘A’ while working with ‘B’ on project ‘P’ = 58 – 35 = 23 units per day

Required percentage = [(25 – 23)/25] × 100 = 8%

Hence, option e.

25. Directions (25-26): Answer the questions based on the information given below.

Three persons ‘A’, ‘B’ and ‘C’ can complete a piece of work alone in ‘a’ days, ‘a + 6’ days and ‘a + 16’ days, respectively. ‘B’ started the work alone and worked for ‘d’ days and after that ‘A’ and ‘C’ joined them. They all worked together for ‘d + 2’ days and after that ‘B’ left them and the remaining work is completed by ‘A’ and ‘C’ together in ‘d + 3’ days. The work done by ‘A’ in 6 days is equal to the work done by ‘C’ in 10 days.

Ques: Find the value of a + d.

Correct Answer: (c) 27
Solution:

Given, the work done by ‘A’ in 6 days is equal to the work done by ‘C’ in 10 days.

So, A × 6 = C × 10
(Efficiency of ‘A’) : (efficiency of ‘C’) = 5:3
(Time taken by ‘A’) : (Time taken by ‘C’) = 3/5

According to the question,
a/(a + 16) = 3/5

5a = 3a + 48
2a = 48
a = 24

Time taken by ‘A’ to complete the work = 24 days
Time taken by ‘B’ to complete the work = (24 + 6) = 30 days
Time taken by ‘C’ to complete the work = (24 + 16) = 40 days

Let total amount of the work = 120 units (LCM of 24, 30 and 40)

The efficiency of ‘A’ = 120/24 = 5 units per day
The efficiency of ‘B’ = 120/30 = 4 units per day
The efficiency of ‘C’ = 120/40 = 3 units per day

According to the question,
4 × d + 12(d + 2) + 8(d + 3) = 120

4d + 12d + 24 + 8d + 24 = 120
24d + 48 = 120
24d = 72
d = 3

Required value of a + d = 24 + 3 = 27

Hence, option c.

26. If ‘B’ started the work alone and was joined by ‘C’ after 12 days and they together worked for 4 days. After that ‘B’ left the work and ‘D’ joined ‘C’ and completed the remaining work in 8 days. In how many days ‘D’ alone can complete the whole work?

Correct Answer: (a) 48 days  
Solution:

Given, the work done by ‘A’ in 6 days is equal to the work done by ‘C’ in 10 days.
So, A × 6 = C × 10
(Efficiency of ‘A’) : (efficiency of ‘C’) = 5:3
(Time taken by ‘A’) : (Time taken by ‘C’) = 3/5

According to the question,
a/(a + 16) = 3/5

5a = 3a + 48
2a = 48
a = 24

Time taken by ‘A’ to complete the work = 24 days
Time taken by ‘B’ to complete the work = (24 + 6) = 30 days
Time taken by ‘C’ to complete the work = (24 + 16) = 40 days

Let total amount of the work = 120 units (LCM of 24, 30 and 40)

The efficiency of ‘A’ = 120/24 = 5 units per day
The efficiency of ‘B’ = 120/30 = 4 units per day
The efficiency of ‘C’ = 120/40 = 3 units per day

According to the question,
4 × d + 12(d + 2) + 8(d + 3) = 120

4d + 12d + 24 + 8d + 24 = 120
24d + 48 = 120
24d = 72
d = 3

Work done by ‘B’ in 12 days = 4 × 12 = 48 units
Work done by ‘B’ and ‘C’ together in 4 days = 7 × 4 = 28 units

Remaining amount of the work = 120 – 48 – 28
= 44 units

Remaining work is done by ‘C’ and ‘D’ together in 8 days. So,
The efficiency of ‘C’ and ‘D’ together = 44/8 = 5.5 units

The efficiency of ‘D’ = 5.5 – 3 = 2.5 units

Time taken by ‘D’ alone to complete the work
= 120/2.5 = 48 days

Hence, option a.

27. Directions (27-28): Answer the questions based on the information given below.

In a company there are two project works, project-‘A’ and project-‘B’. Some men are required to complete the project in a certain time working some hours in a day.

Project-A: (X + 6) men can complete the work in ‘2Y’ days working 5 hours per day while (X + 10) men can complete the same work in (Y + 10) days working 7 hours per day.

Project-B: (X + 10) men can complete the work in (Y – 5) days working 9 hours per day while ‘2X’ men can complete the same work in (Y – 5) days working 6 hours per day.

Note: ‘Y’ is multiple of 7 and is greater than 14 but less than 56.

Ques: What is the value of (2X + Y)?

Correct Answer: (c) 95
Solution:

Project-A:
According to the question,
(X + 6) × 2Y × 5 = (X + 10) × (Y + 10) × 7 ....(1)

Project-B:
According to the question,
(X + 10) × (Y – 5) × 9 = 2X × (Y – 5) × 6

3(X + 10) = 4X
3X + 30 = 4X
X = 30

Putting value of ‘X’ in equation (1), we get
(30 + 6) × 10Y = 7 × (Y + 10) × (30 + 10)
360Y = 280(Y + 10)
9Y = 7(Y + 10)
9Y = 7Y + 70
Y = 35

The value of (2X + Y) = 2 × 30 + 35 = 60 + 35 = 95

Hence, option c.

28. If (X + 20) men can complete the project-‘A’ in (Y – 7) days working ‘H’ hours in a day, then find the value of H.

Correct Answer: (e) 9
Solution:

Project-‘A’:
According to the question,
(X + 6) × 2Y × 5 = (X + 10) × (Y + 10) × 7 ...(1)

Project-‘B’:
According to the question,
(X + 10)(Y – 5) × 9 = 2X × (Y – 5) × 6

3(X + 10) = 4X
3X + 30 = 4X
X = 30

Putting value of ‘X’ in equation (1), we get
(30 + 6) × 10Y = 7 × (Y + 10) × (30 + 10)
360Y = 280(Y + 10)
9Y = 7(Y + 10)
9Y = 7Y + 70
Y = 35

According to the question,
(X + 6) × 2Y × 5 = (X + 20) × (Y – 7) × H

(30 + 6) × 2 × 35 × 5 = (30 + 20) × (35 – 7) × H
36 × 35 × 10 = 50 × 28 × H

H = 9

Hence, option e.

29. Govind and Lakshmi can complete a work in 45 days and 54 days, respectively. Govind and Lakshmi started the work, but Govind and Lakshmi were working with (2/3) and (3/5) of their respective efficiencies. But after some days, they started working with their full efficiency and the whole work gets completed in 30 days. Find the number of days for which they work with their full efficiency.

Correct Answer: (b) 15 days  
Solution:

Let, total work be LCM (45 and 54) = 270 units

Number of units of work done in one day by Govind
= 270 ÷ 45 = 6 units

Number of units of work done in one day by Lakshmi
= 270 ÷ 54 = 5 units

Let, ‘x’ be the number of days for which they work with their full efficiency.

So, {(2/3) × 6 + (3/5) × 5} × (30 – x) + (5 + 6) × x
= 270

(4 + 3)(30 – x) + 11x = 270
210 – 7x + 11x = 270
4x = 270 – 210
4x = 60, x = 60/4 = 15

So, required number of days for which Govind and Lakshmi worked with their full efficiencies = 15 days

Hence, option b.

30. Amitabh, Abhishek and Aishwarya can do a certain piece of work in 45 days, 40 days and 72 days, respectively. All of them started working together but after ___ days, Amitabh and Abhishek left the job and the remaining work is done by Aishwarya 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:

I.) 15, 6   II.) 20, 4   III.) 10, 28

Correct Answer: (c) Only I and III
Solution:

Let the total work = 360 units (LCM of 45, 40 and 72)

Amount of work done by Amitabh alone in one day
= 360/45 = 8 units

Amount of work done by Abhishek alone in one day
= 360/40 = 9 units

Amount of work done by Aishwarya alone in one day
= 360/72 = 5 units

Amount of work done by Amitabh, Abhishek and Aishwarya together in one day = 8 + 9 + 5 = 22 units

For I:
Amount of work done by Amitabh, Abhishek and Aishwarya together in 15 days = 22 × 15 = 330 units

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

Total work done = 330 + 30 = 360 units

So, ‘I’ can be the answer.

For II:
Amount of work done by Amitabh, Abhishek and Aishwarya together in 20 days = 20 × 22 = 440 units > 360

So, ‘II’ can’t be the answer.

For III:
Amount of work done by Amitabh, Abhishek and Aishwarya together in 10 days = 10 × 22 = 220 units

Amount of work done by Aishwarya alone in 28 days
= 28 × 5 = 140 units

Total work done = 220 + 140 = 360 units
So, ‘III’ can be the answer.
Hence, option c.