Time and Work Short Tricks Solved Problems for Competitive Exams

Time and Work Short Tricks Solved Problems

Example 5: 16 men finished one-third work in 6 days. The number of additional men are required to complete the job in next 6 days.

(A) 10

(B) 8

(C) 16

(D) 32

Solution 

M × D = W,

16 × 6 = 1/3 W

Rest work = 2/3 W

For double work in same time 32 men are required to do the work or 16 more men required to do the work.

Shor trick 

2×(16×6) = 6×M → M = 32.

⸫ 16 more men are required.

Example 6: A group of men decided to do a job in 4 days. But since 20 men dropped out every day, the job completed the at the end of the 7^th day. How many men were there at the beginning?

(A) 240

(B) 140

(C) 280

(D) 150

Let n be the initial number of men, then n × 4 = n +(n-20)+(n-40)+…….+(n-120)

→ 4n = 7n – 240 → 3n = 420

⸫ n = 140 men.

Short Tricks

Go through option

140 × 4 = ( 140 + 120 +100+….+20)

560 = 560

Example 7: A is twice as good a workman as B and therefore A takes 6 days less than B to finish the work individually. If A and B working together complete the work in 4 days, then how many days are required by B to complete the work alone?

(A) 12

(B) 18

(C) 8

(D) 6

Solution 

                         A      B

Efficiency  →  2 :     1

Days           →  1 :    2

{Days α 1/Efficiency}

Now, let A requires X days, then B requires 2X days

⸫ Difference in number of days

{=(2X – X) = X = 6 → X = 6

⸫ B requires 2X = 2×6 = 12 days.

Second Method: 

If A takes X days, then B takes ( X+6) days.

Now, A’s 1 day’s work = 1/X.

B’s 1 day’s work = 1/(X+6) ⸫ (1/X)/1/(X+6) = 2/1.

(Since, A does twice the work as B does)

→ X = 6

⸫ B takes 2x = 12 days.

Third Method:

(1/X) + {1/(X+6)} = 1/4.

→ X = 6 and 2X = 12 days (required by B).

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