**Time and Work Problems**** **– The concept of Time and Work is one of the important topic for the aptitude exams. **Time and work problems** have been appearing regularly over the past decades in most of the aptitude exams like SSC, Banks Exam, UPSC, Railway and other exams. We will explain you some **time and work problems short tricks** here.

Here we are providing few **Mantras to crack Time and Work problems:**

Also read –** How to find out Square root and Cube root of any number**

**Concept #1. – Complete Job :**

The total amount of a complete job = 1, always, unless otherwise specified.

**Concept #2. – 0ne Day Work :**

If a person ‘A’ can do a work in ‘n’ days, then A’s 1 day’s work will be = 1/n

Ex. If a person ‘A’ can do a work in 4 days, then A’s 1 day’s work = ¼

Hence, No. of days = total work / work done in 1 day

**Concept #3. – Part of Work Done :**

If A’s 1 day’s Work = 1/n, then after X days, A’s work = x (1/n)

Ex – If A’s 1 day’s work = 1/6, then after 3 days, A’s work = 3(1/6)

**Concept #4. – Combined 1 Days Work : **

When more than one person are working on the same job, then their combined 1 day’s work = sum of 1 day’s work for each person.

Ex.- If A can do a job in ‘n’ days and B can do it in ‘m’ days and both A and B together can do it in ‘T’ days, then

A’s 1 day’s work = 1/n, B’s 1 days work = 1/m

(A+B)’s combined 1 day’s work = 1/T (concept -2) = A’s 1 day’s work + B’s 1 day’s work

Similarly, if A,B and C are working on a work, then (A+B+C)’s 1 day work = A’s 1 day’s work + B’s 1 day’s work + C’s 1 day’s work.

⇒B’s 1 day’s work = (A+B+C)’s 1 day’s work – A’s 1 day’s work – C’s 1 day’s work.

**Concept #5. – Comparison of Two Worker’s Rate:**

If a person A is ‘n’ time as good workman as another person B, then Complete time by A/ = 1/n

And after any time, A’s work /B’s work = n

**Concept #6. – Chain Rule:**

Hence from the chain rule we can make the following relationship:

- Relationship between Men and Work.

More men ==========⇒ can do ==========⇒ More work

Less men ===========⇒ can do =========⇒ Less work

- Relationship between Work and Time

More work ==========⇒ takes ==========⇒ More Time

Less work ===========⇒ takes ==========⇒ Less Time

- Relationship between Men and Time

More men ===========⇒ can do in =======⇒ Less Time

Less men ============⇒ can do in =======⇒ More Time

**Additional Concepts:**

- If A is twice as good as worker B, then A’s 1 day’s work / B’s 1 day’s work = 2/1, A’s time/B’s time = ½

- If x men can do a job in t1 days and y man in t2 days, then (p men + q women) can do the work in 1/(p/xt1 + q/yt2) days.

- x men or y women can do a work in t days, then (p men + q women) can do the same work in t/(p/x + q/y) days.

- If a person A can do a work in ‘n’ days and A+B together can do it in ‘T’ days, then B alone can finished the work = T * n / n-T days.

Also read – **Problems on Ages – Short Tricks**

**So let’s try few sample questions –**

**Q1**. Dhoni and Raina can do a work in 12 days. Raina alone can do it in 28 days. In how many days can Dhoni alone finish the work?

(A). 16 days (B). 21 days

(C). 18 days (D). 24 days

**Q2**. A can do a work in 12 days. B works 60% more than A, then in how many days B alone would finish this work?

(A). 9 days (B). 8(1/2) days

(C). 7(1/2) days (D). 8 days

**Q3**. If 3 men or 4 women can complete a work in 43 days then in how many days 7 men and 5 women can complete the same work?

(A). 12 days (B). 18 days

(C). 16 days (D). 10 days

**Q4**. If 4 men reap 40 acres in 30 days, how many acres will 18 men reap in 12 days?

(A). 57 Acres (B). 64 Acres

(C). 76 Acres (D). 72 Acres

Answer Key:

Q-1 | Q-2 | Q-3 | Q-4 |

B | C | A | D |

Explanation:

- Ans 1. If T = 12, n = 28, then Required Time = T*n /(n-T) = 28*12/(28-12) = 21 days.
- Ans 2. A’s 1 day’s work = 1/12

B is 60% more fast than A, hence B’s 1 day’s work = 1.6 * 1/12 = 2/15

B can finish alone in = 1/(2/15) = 15/2 = 7.5 days.

- Ans 3. By formula T = t1/ (p/x + q/y)

T = 43/(7/3 + 5/4) = 12 days.

- Ans 4. By formula N1 * D1 / W1 = N2 * D2 / W2

⇒ 4*30 / 40 = 18*12 / W2 ⇒ W2 = 72 acres.

Also read – **How to find out Square of Any Number with short trick.**