Time and work formulas with examples for SSC and Bank Exams

Time and work formulas for Competitive Exams:

Formula with examples: 

Example.1. Worker A takes 8 hours to do a job. Worker B takes 10 hours to do the same job. How long should it take both A and B, working together but independently, to do the same job?

$$ (A) \ 4{1\over3} \ $$ 

$$ (B) \ 4{4\over9}\ $$ 

$$ (C) \ 5{1\over4} $$ 

$$ (D) \ 5{1\over2}\ $$

$$ A's \   1 \  hour's \ work \ = {1\over8}$$

$$ B's \   1 \  hour's \ work \ = {1\over10}$$

$$ (A+B)'s \  1 \   hour's \ work \ = \left({1\over8}+ {1\over10} \right)={1\over40} $$

$$ ⸫ \ Both \ A\ and\ B\ will\ finish\ the\ work\ in {40\over9}= 4{4\over9} $$

Example.2. A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work?

(A) 6

(B) 10 

(C) 12

(D) 14

$$ (A+B)'s \  1 \   days's \ work \ = {1\over4}, $$

$$ A's \  1 \  day's \ work \ = {1\over12}$$

$$ ∴ \  B's \  1 \   day's \ work \ = \left({1\over4} - {1\over12} \right) = {1\over6} $$

Hence, B alone can complete the work in 6 days. 

Example.3. A can do piece of work in 7 days of 9 hours each and B can do it in 6 days of 7 hours each. How long will they take to do it, working together  hours a day?

(A) 2

(B) 8 

(C) 5

(D) 3

A can complete the work in (7×9) = 63 hours.

B can complete the work in (6×7) = 42 hours.

$$ A's \   1 \  hour's \ work \ = {1\over63}$$

$$ and \ B's \  1 \   hour's \ work \ = {1\over42};$$

$$ (A+B)'s \  1 \   hour's \ work \ = \left({1\over63}+ {1\over42} \right)={5\over126} $$

$$ ∴ Both \ will \ finish \ the \ work\ in\ \left({126\over5} \right) hrs$$

$$ Number\ of\ days\ of\ 8{2\over5}\ hrs \ each\ = \left({126\over5}× {5\over42}\right)= 3 \ days $$.

Ex.4. A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work?

(A) 20

(B)  25 

(C) 27

(D) 30

$$ (A+B)'s \  1 \   day's \ work \ = {1\over18}$$

$$ Divide \ {1\over18}\ in\ the\ ratio \ 2 : 1. $$

$$ ∴ A's \  1 \  hour's \ work \ = \left({1\over18}× {2\over3} \right)= {1\over27} $$

Hence, A alone can finish the work in 27 days.

Ex.5. A can do a certain job in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?

$$ (A) \ 7{1\over2} \ $$ 

$$ (B) \ 4{3\over9}\ $$ 

$$ (C) \ 5{5\over4} $$ 

$$ (D) \ 7{1\over5}\ $$

Ration of times taken by A and B = 160 : 100 = 8 : 5.

Suppose B alone takes x days to do the job.

Then, 8 : 5 : : 12 : x 

→ 8x = 5 × 12

 →  $$ x = 7{1\over2}\ days $$.
 

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