**TIPS FOR SOLVING QUESTIONS RELATED TO TIME AND WORK:**

**1**. The total work is taken as 1.

**2**. If A can do a piece of work in 'n' days, ,then A's 1 day's work is equal to = **1/n**

**3**. If A's 1 day's work = 1/n, then A can complete the work in 'n' days.

**4**. If A is thrice as good a workman as B, then

Ratio of work done by A and B = 3 : 1.

Ratio of time taken by A and B to finish the work = 1 : 3.

**5**.If ‘M1’ persons can do ‘W1’ work in ‘D1’ days and ‘M2’ persons can do W2 work in D2, days then we have a very general formula in the relationship of **M1 D1 W2 = M2 D2 W1.** The above relationship can be taken as a very basic and all-in-one formula. We also derive

**A)** More men less days and conversely more days less men.

**B)** More men more work and conversely more work more men.

**C)** More days more work and conversely more work more days.

**6.**If we include the working hours (say T1 and T2) for the two groups then the relationship is

**M1 D1 T1 W2 = M2 D2 T2 Q1**

Again, if the efficiency (Say E1 and E2) of the persons in two groups is different then the relationship is

**M1 D1 T1 E1 W2 = M2 D2 T2 E2 W1**

Now, we should go ahead starting with simpler to difficult and more difficult questions.

**Questions on Above Formulaes**

**1.A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?**

A. Rs. 375

B. Rs. 400

C. Rs. 600

D.Rs. 800

**2. Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?**

A. 3 pm

B. 2 pm

C. 1:00 pm

D. 11 am

**3. A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:**

A. 20 days

B. 22 1/2days

C. 25 days

D. 30 days

**4. P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?**

A. 9

B. 11

C. 13

D. 15

**5. If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:**

A. 4 days

B. 5 days

C. 6 days

D. 7 days

**6.40 men can cut 60 trees in 8 hours. If 8 men leave the job how many trees wiil be cut in 12 hours?**

A. 74

B. 82

C. 72

D. 73

**7.A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?**

A. 8 hours

B. 10 hours

C. 12 hours

D. 24 hours

**8. P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?**

A. 5 days

B. 10 days

C. 14 days

D. 22 days

**9. If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600.**

A. 12

B. 14

C. 16

D. 18

**10. Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?**

A. Rs.1104

B. Rs.1000

C. Rs.934

D. Rs.1210

**ANSWERS AND SOLUTION :**

**1(B)Explanation:**

C's 1 day's work = 1/3 - (1/6 + 1/8) = 1/3 - 7/24 = 1/24

A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24 = 4 : 3 : 1.

C's share (for 3 days) = Rs. (3 x 1/24 x 3200) = Rs. 400.

**2(C)Explanation :**

Work done by P in 1 hour = 1/8

Work done by Q in 1 hour = 1/10

Work done by R in 1 hour = 1/12

Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120

Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60

From 9 am to 11 am, all the machines were operating.

Ie, they all operated for 2 hours and work completed = 2 × (37/120) = 37/60

Pending work = 1- 37/60 = 23/60

Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11

which is approximately equal to 2

Hence the work will be completed approximately 2 hours after 11 am ; ie around 1 pm.

**3(B)Explanation:**

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes (3/2 x 60) = 90 days.

So, A takes 30 days to do the work.

A's 1 day's work = 1/30

B's 1 day's work = 1/90

(A + B)'s 1 day's work = (1/30 1/90) = 4/90 = 2/45

So A and B together can do the work in 45/2 = 22 1/2 days.

**4(C)Explanation :**

Work done by P in 1 day = 1/23

Let work done by Q in 1 day = q

q × (130/100) = 1/23

=> q = 100/(23×130) = 10/(23×13)

Work done by P and Q in 1 day = 1/23 + 10/(23×13) = 23/(23×13)= 1/13

=> P and Q together can do the work in 13 days

**5(A)Explanation:**

Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.

Then, 6x + 8y = 1/10 and 26x + 48y = 1/2,.

Solving these two equations, we get : x = 1/100 and y = 1/200 .

(15 men + 20 boy)'s 1 day's work = (15/100 + 20/200) = 1/4

So, 15 men and 20 boys can do the work in 4 days.

**6(C) Explanation**

By basic formula:

M1 = 40, D1 = 8, W1 = 60(cutting of trees is taken as work)

M2 = 40 - 8 = 32, D = 12, W2 = ?

Putting the values in the formula

M1 D1 W2 = M2 D2 W1

We have , 40 x 8 x W2 = 32 x 12 x 60

or, W2 = (32 x 12 x 60)/(40 x 8) = 72

**7(C)Explanation:**

A's 1 hour's work = 1 /4 ;

(B + C)'s 1 hour's work = 1/3 ;

(A + C)'s 1 hour's work = 1/2 .

(A + B + C)'s 1 hour's work = (1/4 + 1/3) = 7/12

B's 1 hour's work = (7/12 - 1/2) = 1/12 .

So, B alone will take 12 hours to do the work.

**8(B)Explanation :**

Work done by P in 1 day = 1/20

Work done by Q in 1 day = 1/12

Work done by P in 4 days = 4 × (1/20) = 1/5

Remaining work = 1 – 1/5 = 4/5

Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15

Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6

Total days = 4 + 6 = 10

**9(C)Explanation :**

Wages of 1 woman for 1 day = (21600)/(40 x 30)

Wages of 1 man for 1 day = (21600×2)/(40×30)

Wages of 1 man for 25 days = (21600×2×25)/(40×30) = 1080000/1200=900

Number of men = 14400/900 =16

**10(A)Explanation :**

Assume that cost of keeping a cow for 1 day = c ,

cost of keeping a goat for 1 day = g

Cost of keeping 20 cows and 40 goats for 10 days = 460

Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46

=> 20c + 40g = 46

=> 10c + 20g = 23 ---(1)

Given that 5g = c

Hence equation (1) can be written as 10c + 4c = 23 => 14c =23

=> c=23/14

cost of keeping 50 cows and 30 goats for 1 day

= 50c + 30g

= 50c + 6c (substituted 5g = c)

= 56 c = 56×23/14

= 92

Cost of keeping 50 cows and 30 goats for 12 days = 12×92 = 1104