New Pattern Time & Work Problems with Solutions for Bank Exams 2019

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New Pattern Time and Work Practice Problems

Directions (1-2) : One day earning of P, Q and R together is Rs.1026 to do a work. ‘P’ earns more than R which is same as ‘R’ earns more than ‘Q’. Efficiency of R and Q is 19 : 18.

1. Find the amount earned by R and P together in 5 days to do the same work?

1. Rs. 3620
2. Rs. 3430
3. Rs. 3510
4. Rs. 3310
5. Rs. 3710

2. S, who’s efficiency is average of efficiency of P and Q, can complete a work in 36 days. If P, Q and R work together, and complete that work then find the total wage of Q

1. Rs. 3888
2. Rs. 4104
   
3. Rs. 4320
4. Rs. 3666
5. Rs. 4520

3. (X+4) men can complete a work in 2X days while (X+12) women can complete same work in (X+8) days. If ratio of efficiency of men to women is 5 : 4 then find in how many days 12 men and 15 women together can complete the same work ?

1. 32 days
2. 16 days
3. 48 days
4. 64 days
5. 80 days

4. A cistern can be filled completely by pipe A and B together in 12 hours. If pipe A works with twice speed while pipe B work with 50% more speed than cistern can be filled completely in 7 hours. Find the capacity of cistern if flow of water through pipe A is 2.5ℓ/ minute.

1. 2800 liter
2. 3150 liter
3. 3300 liter
4. 3650 liter
5. 4200 liter

5. Ratio of efficiency of A and B in completing a work is 3 : 4. Both started to work together but A left after 2 days. Another person C joins B and they together complete the remaining work in 6 days. If A and B together can complete the work in 8 days then C alone can complete the work.

1. 27/4 days
2. 56/3 days
3. 41/3 days
4. 28/3 days
5. 49/3 days

6.Pipe A can fill a tank in 45 hr, pipe B is 50% more efficient than A and pipe C can fill the same tank in 7.5 hr less than B. A and B opened together for X hr and closed after that and pipe C fill remaining tank in (X + 9) hr, if the ratio between tank filled by (A + B) together to tank filled by pipe C is 1 : 2. Find the value of X ?

1. 3 hrs
2. 4 hrs
3. 6 hrs
4. 8 hrs
5. 7 hrs

7. A and B can do a piece of work in 72 days and 64 days respectively. C can do the same work in 2(2/17) more days as A & B take together to complete. If first day A & B work together and second day B & C work together alternatively, then in how many days work will be completed ?

1. 22(13/25) days
2. 27 (13/25) days
3. 32 (13/25) days
4. 25(13/25) days
5. 29(13/25) days

8. Four persons started to do a work together. ‘A’ works only in starting two days after that B, C and D works alternately starting from B. Ratio of time taken by A, B, C and D if they work alone is 4 : 3 : 2 : 5. If the work is completed in 12 days then in how many days A and C can complete the work if they work together ?

1. 6 days
2. 12 days
3. 10 days
4. 8 days
5. 4 days

9. Ratio between efficiency of Arun, Yash and Rana is 6 : 4 : 5. All three starts to work together with same efficiency. But Rana, destroys his 60% of work in every evening, due to which they have to work 20 more days then estimated time. Find the estimated days by them to complete the work.

1. 80
2. 76
3. 84
4. 72
5. 90

Solutions for Time & Work Problems :

(1 & 2)

Let R earns = y
And P earns = y + x
So, Q earns = y – x
ATQ,
y – x + y + y + x = 1026
y = 342
Each person earns according to their efficiencies so
Q earns → (342/19) × 18 = 324
P earns = (342/19) x 20 = 360
Ratio of efficiency of P, R and Q = 20 : 19 : 18
Money per unit work = Rs.18

1) 3
Amount earned by R and P together in 5 days
Work done = (20 + 19) × 5 = 195
Money earned = 195 × 18 = Rs.3510

2) 1
Efficiency of S = (20+18) / 2= 19
Total work → 19 × 36
Days taken by P, Q and R to do that work
⇒(19×36) / (20+19+18) = 12 days
Q’s earning ⇒ 12 × 324 = Rs. 3888

3) 2
(X+4) men can complete work in 2X days
⇒ 1 man can complete same work in 2X(X+4) days
(X+12) women can complete work in (X+8) days
⇒ 1 woman can complete same work in (X+8)(X+12) days
Now ratio of efficiency of men to women is 5 : 4
⇒ Ratio of days taken by men to women is 4 : 5
So, 4/5 = ((2X(X+4)) / ((X+8) (X+12)
⇒ 2(𝑋^2 + 20𝑋 + 96) = 5𝑋(𝑋 + 4)
⇒ 2𝑋^2 + 40𝑋 + 192 = 5𝑋^2 + 20𝑋
⇒ 3𝑋^2− 20𝑋 − 192 = 0
⇒ 3𝑋^2 − 36𝑋 + 16𝑋 − 192 = 0
⇒ 3𝑋(𝑋 − 12) + 16(𝑋 − 12) = 0
⇒ (3𝑋 + 16)(𝑋 − 12) = 0
⇒ 𝑋 = 12,−(16/3)
12 men can complete work in (16×24)/12 = 32 𝑑𝑎𝑦𝑠
15 women can complete work in (24×20)/15 = 32 𝑑𝑎𝑦𝑠
Required time = (32×32) / (32+32) = 16 𝑑𝑎𝑦s

4) 5
Let, pipe A and pipe B alone can fill the tank in x and y hours respectively.
ATQ,
(1/x)+(1/y) = 1/12 … (i)
and, (2/x) + (1.5/y) = 1/7… (ii)
On solving (i) and (ii)
x = 28 hour ⇒ y = 21 hour
Capacity of cistern = 28 × 60 × 2.5 = 4200 liter

5) 2
Let A and B can do 3𝑥 and 4𝑥 unit of work in one day.
So,
Total work = (3𝑥 + 4𝑥) × 8 = 56𝑥
(A + B) two day work = 7𝑥 × 2 = 14𝑥
Remaining work = 42𝑥
In 6 days B will complete = 6 × 4𝑥 = 24𝑥 units
So, remaining 18𝑥 units are completed by C in 6 day So,
56𝑥 unit will be completed in = (56x/18x)/(18x/6) = 56/3 days

6) 3
A = 45 hr
A : B = 100 : 150 = 2 : 3
Total capacity of tank = 45 × 2 = 90 liter
C = (90/3)– 7.5 = 22.5 hr
C efficiency = 90/22.5 = 4ℓ/hr
According to question ⇒ (5x) / (4(X+9)) = 1/2 
⇒ 10X – 4X = 36
X = 6 hr

7) 2
 

C takes = (576/(8+9)) + (36/17) = 612/7 = 36 days 
Efficiency of C = 576/367 = 16 units/days
When First day (A and B) and second day (B and C) work alternatively
Two day work = (A and B) one day work and (B and C) one day work = (8 + 9) + (9 + 16) = 17 + 25 = 42 units
In 26 day = (26/2)× 42 = 546 units
(A and B) on 27th day = 17 units
After 27 days remaining work = (576 – 546 – 17) = 13 units
13 units work done by (B and C) on 28th day = 13/25
Total time = (27 + (13/25)) = 27 13/25 days

8) 4

A, B, C and D worked for 2 days together after that A leave and B, C and D worked alternatively for 10 days starting from B
∴ B worked for 4 days, C for 3 days, and D for 3 days.
Total days A worked = 2
Total days B worked = 4 + 2 = 6
Total days C worked = 3 + 2 = 5
Total days D worked = 3 + 2 = 5
Let, their alone time to complete the work is 4x, 3x, 2x and 5x
respectively.
∴ (2/4x) + (6/3x) + (5/2x) + (5/5x)= 1
⇒ (30+120+150+60) / 60𝑥 = 1
⇒ 𝑥 = 360/60 = 6
‘A’ can complete the work in 4 × 6 = 24 days
‘C’ can complete the work in 2 × 6 = 12 days
Required time = (12×24) / (12+24) = (12×24) /36 = 8 days


9) 1
Ratio of efficiency of Arun, Yash and Rana is 6 : 4 : 5
Total work done by them in 1 day
= (6 + 4 + 5) units = (15) units.
Let they estimate 𝑥 days to complete the work.
Then total work = 15𝑥
But Rana’s 1-day work is only 40%, i.e. (40/100)× 5 = 2 unit
The work done by them in actual
= (6 + 4 + 2) (x + 20) = 12(x + 20)
∴ 15𝑥 = 12𝑥 + 240
3𝑥 = 240
𝑥 = 80
Hence, estimated days are 80.

Shared by Rahul Sankrityan

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