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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?**

- Rs. 3620
- Rs. 3430
- Rs. 3510
- Rs. 3310
- 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**

- Rs. 3888
- Rs. 4104
- Rs. 4320
- Rs. 3666
- 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 ?**

**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.**

- 2800 liter
- 3150 liter
- 3300 liter
- 3650 liter
- 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.**

- 27/4 days
- 56/3 days
- 41/3 days
- 28/3 days
- 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 ?**

- 3 hrs
- 4 hrs
- 6 hrs
- 8 hrs
- 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 ?**

- 22(13/25) days
- 27 (13/25) days
- 32 (13/25) days
- 25(13/25) days
- 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 ?**

- 6 days
- 12 days
- 10 days
- 8 days
- 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.**

- 80
- 76
- 84
- 72
- 90

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**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

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

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.

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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