Time and Work - Aptitude test, questions, shortcuts, solved example videos

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Time & Work

Work is always considered as an entire value or one. There exists an analogy between the time-speed-distance problems and work. Work based problems are more or less related to time speed and distance.

Important Formulae:

1) Work from days:
If a person can do a work in 'n' days, then person's 1 day work = 1 / n

2) Days from work:
If a person's 1 day work is equal to 1/n , then the person can finish the work in 'n' days.

3) Numer of Days =	Total Work
	Work Done in 1 Day

Quick Tricks & Tips:

1) Ratio:

If 'A' is 'x' times as good a workman as 'B', then
a) Ratio of work done by A & B in equal time = x: 1
b) Ratio of time taken by A & B to complete the work = 1: x. This means that 'A' takes (1/x^th) time as that of 'B' to finish same amount of work.

For example,
if A is twice good a workman as B, then it means that

a) A does twice as much work as done by B in equal time i.e. A:B = 2:1
b) A finishes his work in half the time as B

2) Combined Work:

a) If 'A' and 'B' can finish the work in 'x' & 'y' days respectively, then

A's one day work =	1
	x

B's one day work =	1
	y

(A + B)'s one day work =	1	+	1	=	(x + y)
	x		y		xy

Together, they finish the work in	xy	days.
	(x + y)

b) If 'A', 'B' & 'C' can complete the work in x, y & z days respectively, then

(A + B+ C) 's 1 day work =	1	+	1	+	1	=	(xy + yz + xz)
	x		y		z		xyz

Together, they complete the work in	xyz	days.
	xy + yz + xz

c) If A can do a work in 'x' days and if the same amount of work is done by A & B together in 'y' days, then

A's one day work =	1
	x

(A+B)'s one day work =	1
	y

B's one day work =	1	–	1	=	x – y
	y		x		xy

So, 'B' alone will take	xy	days.
	x – y

d) If A & B together perform some part of work in 'x' days, B & C together perform it in 'y' days and C & A together perform it in 'z' days, then

(A + B)'s one day work =	1
	x

(B + C)'s one day work =	1
	y

(C + A)'s one day work =	1
	z

1	+	1	+	1	= 2(A+B+C)'s 1 one day work
x		y		z

Now, we have at hand (A + B + C)'s one day work =	1 + 1 + 1 x y z
	2

(A+ B+ C) will together complete the work in		days
	2
	1 + 1 + 1 x y z

If A works alone, then deduct A's work from the total work of B & C to find the time taken by A alone.

For A working alone, time required =A's work - (A+B+C)'s combined work

=
	2
	1 – 1 + 1 x y z

=	2xyz	days
	[xy + yz – zx]

Similarly,

- If B works alone, then time required =	2xyz
	(– xy + yz + zx)

- If C works alone, then time required =	2xyz
	(xy – yz + zx)

3) Man -Work -Hour related problems:

Remember that	M D H	= Constant
	W

where,
M: Number of Men
D: Number of Days
H: Number of Hours
W: Amount of Work done

If men are fixed, work is proportional to time. If work is fixed , time is inversely proportional to men. Thus,

M1 x T1	=	M2 x T2
W1		W2

Once you have understood the following simple things, this chapter will become extremely easy for you.

a) Work and time are directly proportional to each other
b) Number of men and time are inversely proportional to each other
c) And, work can be divided into equal parts i.e. if a task is finished in 10 days, in one day you will finish (1/10^th) part of the work.

Questions Variety:

Examples:

Q 1. Reema can complete a piece of work in 12 days while Seema can the same work in 18 days. If they both work together, then how many days will be required to finish the work?

a. 6 days
b. 7.2 days
c. 9.5 days
d. 12 days
View solution
Q 2. If 'A' completes a piece of work in 3 days, which 'B' completes it in 5 days and 'C' takes 10 days to complete the same work. How long will they take to complete the work , if they work together?
a. 1.5 days
b. 4.5 days
c. 7 days
d. 9.8 days
View solution

Examples:

Q 3. Two painters 'P₁' & 'P₂' paint the bungalow in 3 days. If P₁ alone can paint the bungalow in 12 days, in how many days can 'P₂'' alone complete the same paint work?

a. 4 days
b. 6 days
c. 9 days
d. 12 days
View solution
Q 4. A & B can make paintings in 6 days, B & C can can make those paintings in 10 days. If A, B & C together can finish the work in 4 days, then A & C together will do it in ________ days.

a. 4 (2/7) days
b. 1/ 8 days
c. 2 (2/5) days
d. 6 (3/ 8) days
View solution

Examples:

Q 5. Pooja is twice as efficient as Aarti and takes 90 days less than Aarti to complete the job. Find the time in which they can finish the job together.

a. 30 days
b. 45 days
c. 60 days
d. 90 days
View solution
Q 6. Monika is twice as good as Sonika and together they complete a piece of work in 20 days. In how many days will Monika alone will finish the work?

a. 22 days
b. 30 days
c. 37 days
d. 52 days
View solution

Examples:

Q 7. 6 men can pack 12 boxes in 7 days by working for 7 hours a day. In how many days can 14 men pack 18 boxes if they work for 9 hours a day?
a. 3.5 days
b. 5 days
c. 7.5 days
d. 12 days
View solution
Q 8. 4 men and 5 boys can do a piece of work in 20 days while 5 men and 4 boys can do the same work in 16 days. In how many days can 4 men and 3 boys do the same work?

a. 10 days
b. 15 days
c. 20 days
d. 25 days
View solution
Practice questions on Time and Work

• Time and work (30 questions)
• Time and work (20 questions)