Time and work formulas with examples for SSC and Bank Exams

Time and work formulas for Competitive Exams:

Formula with examples: 

1. If ‘M₁’ person can do ‘W₁’ work in ‘D₁’ days working T₁h in a day and 'M_2' person can do' W₂ ' work in 'D₂ 'days working T₂h in a day then we have a very basic and all in one relationship as M₁D₁T₁W₂=M₂D₂T₂W₁.

Ex. 16 men can do a piece of work in 10 days. How many men are needed to complete the work in 20 days ?

(A) 4

(B) 7

(C) 8

(D) 6

Solution: 

Here, M1 = 16, D1=10, W1=W2=1,D2=20, M2=?

According to the formula, M₁D₁W₂=M₂D₂W₁.

→ 16 × 10 × 1 = M2 × 20 × 1

$$∴M2 =\left({16×10\over20}\right)=\left({160\over20}\right)= 8 men $$

2. If ‘A’ can do a piece of work in ‘x’ days and ‘B’ can do the same work in ‘y’ days, then (A+B)’s 1 day’s work =  inverse of (A +B)’s 1 day’s work = Time taken by (A+B) to complete the work

Ex. A can do a piece of work in 10 days and B can do the same work in 12 days. How long they take to finish the work together 

$$(A)\ 7{1\over3}days$$

 $$(B)\ 2{1\over3}days$$

 $$(C)\ 10\ days$$

 $$(D)\ 5{5\over11}days$$

Solution:

A’s 1 day’s work = 1\10, B’s 1 day’s work = 1/12

(A+B)’s 1 day’s work = $${1\over10}+{1\over12}={6+5\over60}days={11\over60}$$

∴ (A+B) complete the whole work in   

3. If A and B can do a piece of work in x days, B and C can do the same work in y days and A and C can do it in z days, then working together, A, B and C can do that work in 

Ex. A and B can do piece of work in 3 days. B and C can do the same work in 9, while C and A can do it in 12 days. Find the time in which A, B and C can finish the work, working together.

$$ (a)\ 3{15\over19}days\ (b)\ 2{21\over20}days\ (c)\ 4{1\over3}days\ (d)\ 4{15\over19}days $$

Solution:

According to the formula,

Required time taken by A,B and C can do that work in  

$$={2×3×9×12\over3×9+9×12+3×12}={2×3×9×12\over27+108+36}={72\over19}=3{15\over19}days$$

4. If ‘x’ takes ‘a’ days more to complete a work, then the time taken by (x+y) to do same work and ‘y’ takes ‘b’ days more than the time taken (x+y) to do the same work, then (x+y) do the work in  days.

Ex. When A alone does a piece of work, he takes 16 days more than the time taken by (A+B) to complete the work while B alone takes 9 days more than the time taken by (A+B) to finish the work. What time A and B together will take to finish this work ?

(a) 10 days         (b) 12 days               (c) 8 days                (d) 5 days

Solution: 

According to the formula

$$Required\ time = { \sqrt{ab} }.$$ where a=16, b=9

  $$∴Required\ time = { \sqrt{16×9}=4×3=12 \ days }.$$

5. A and B, each alone can do a piece of work in ‘a’ days and ‘b’ days, respectively. Both begin together and if

(i) A leaves the work ‘x’ days before its completion, then total time taken for completion of work will be given as T = 

(ii) B leaves the work ‘x’ days before its completion, then total time taken for completion of work will be given as T=

Ex. A can do a piece of work in 10 days while B can do it in 15 days. They begin together but 5 days before the completion of the work, B leaves off. Find the total number of days for the work to be completed.

(a) 5 days  (b) 3 days (c) 7 days (d) 8 days

Solution:

Here a = 10 days, b = 15 days, x= 5, T = ?

According to the formula,

$$ Required\ time =   {(b+x)a\over(a+b)} = {(15+10)10\over10+15}={20+10\over25}=4×2=8 \ days $$

Q.6 A and B do a piece of work in ‘a’ days and ‘b’ days respectively. Both begin together but after some days, A leaves off and the remaining work is completed by B in ‘x’ days. Then, the time after which A left, is given by T=.

Ex. A and B can do a piece of work in 40 days and 50 days, respectively. Both begin together but after a certain time, A leaves off. In this case B finishes the remaining work in 20 days. After how many days did A leave?

Solution:

Given that, a = 40 days, b= 50 days, x = 20, T= ?

$$∴  Required\ time =  {(b-x)a\over(a+b)} = {(1520)×40\over(40+50)}={30×40\over90}={40\over3}=  13{1\over3} \ days $$

These are the important six time and work formulas with examples which will help you in your competitive exams. You can ask me in the comment section if you have any problem regarding time and work formulas for ssc and bank exams.

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