## 4 Time & Work Problems To Prepare For Wipro Aptitude Tests

Dear Reader,

Below are four problems based on the concept of time and work.

**Question 1**

Mary and John can do a piece of work in 24 days; John and Vino in 30 days; Vino and Mary in 40 days. If Mary, John and Vino work together they will complete the work in :

a) 10 days b) 20 days c) 17 days d) 15 days

**Answer :** b) 20 days.

Solution :

Given that,

Mary and John take 24 days; i.e., (Mary + John)'s 1 day's work = 1/24

John and Vino take 30 days; i.e., (John + Vino)'s 1 day's work = 1/30

Vino and Mary take 40 days; i.e., (Vino + Mary)'s 1 day's work = 1/40

Adding above 3, we get,

[(Mary + John) + (John + Vino) + (John + Vino)]'s 1 day's work = 1/24 + 1/30 + 1/40

2((Mary + John + Vino)'s 1 days work = 1/24 + 1/30 + 1/40

2(Mary + John + Vino)'s 1 days work = (5 + 4 + 3)/120 = 12/120 = 1/10

Therefore, (Mary + John + Vino)'s 1 days work = 1/20

i.e., Mary, John and Vino together can complete the work in 20 days.

**Question 2**

X and Y can complete a task in 16 days; Y & Z can complete the same task in 24 days and X, Y & Z together can complete in 12 days. The time taken by X & Z together to complete the task is:

a) 24 days b) 16 days c) 18 days d) 20 days

**Answer : **b) 16 days

Solution :

Given that,

X and Y together takes 16 days; then (X+Y)'s 1 day's work = 1/16 ...(1)

Y & Z together takes 24 days; then (Y+Z)'s 1 day's work = 1/24 ...(2)

And, X, Y & Z takes 12 days; then (X+Y+Z)'s 1 day's work = 1/12 ...(3)

Multiplying (3) by 2 and subtracting (1) and (2), we get,

2(X+Y+Z) - (X+Y) - (Y+Z) = 2/12 - 1/24 - 1/16

2X + 2Y + 2Z - X - Y - Y - Z = 1/6 - 1/24 - 1/16

X + Z = (8 - 2 - 3)/48 = 3/48 = 1/16

Therefore, (X+Z)'s 1 day's work = 1/16.

Then, X and Z together take 16 days to complete the task.

**Question 3**

P & Q can draw a picture in 144 hours; Q & R can draw a same picture in 240 hours; P & R can finish it in 180 hours. What will be the time taken by P alone to draw the picture?

a) 280 hours b) 240 hours c) 200 hours d) 300 hours

**Answer :** b) 240 hours

Solution :

Given that, (P+Q) takes 144 hours; i.e., (P+Q)'s 1 hour's work = 1/144

(Q+R) takes 240 hours; i.e., (Q+R)'s 1 hour's work = 1/240

(P+R) takes 180 hours; i.e., (P+R)'s 1 hour's work = 1/180

Adding above 3, we get,

2(P+Q+R)'s 1 hour's work = 1/144 + 1/240 + 1/180 = (5 + 3 + 4)/720 = 12/720 = 1/60

2(P+Q+R)'s 1 hour's work = 1/60

Therefore, (P+Q+R)'s 1 hour's work = 1/120

Now, P's 1 hour's work = (P+Q+R)'s 1 hour's work - (Q+R)'s 1 hour's work

= 1/120 - 1/240 = 1/240

Therefore P alone takes 240 hours.

**Question 4**

Mr.P and Mr.Q can build a wall in 10 days; Mr.Q & Mr.R can take 14 days to build the same wall; and Mr.P and Mr.R can do it in 8 days. Who among them will take more time when they work alone?

a) P b) Q c) R d) data inadequate

**Answer : **b) Q

Solution :

From the given question, we have,

(P+Q)'s 1 day's work = 1/10

(Q+R)'s 1 day's work = 1/14

(P+R)'s 1 day's work = 1/8

Adding above 3, we get,

2(P+Q+R)'s 1 day's work = 1/10 + 1/14 + 1/8 = (28+20+35)/280 = 83/280

i.e., 2(P+Q+R)'s 1 day's work = 83/280

Then, (P+Q+R)'s 1 day's work = 83/560.

Now, P's 1 day's work = (P+Q+R)'s 1 day's work - (Q+R)'s 1 day's work

= 83/560 - 1/14 = (83-40)/560 = 43/560

Q's 1 day's work = (P+Q+R)'s 1 day's work - (P+R)'s 1 day's work

= 83/560 - 1/8 = (83-70)/560 = 13/560

And, R's 1 day's work = (P+Q+R)'s 1 day's work = (Q+P)'s 1 day's work

= 83/560 - 1/10 = (83-56)/560 = 27/560

Therefore, P, alone takes 560/43 days;

Q alone takes 560/13 days;

And R alone takes 560/27 days.

Q takes more time when compared to others since 560/13 is greatest among 560/43, 560/13 and 560/27 .

Hence the answer is option b.

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