### TIME AND WORK QUIZ 001

- 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 1/2 days **

(c) 25 days

(d) 30 days

(e) None of these

*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’s and B’s one day work = 1/30 + 1/90 = 2/45.

Therefore, A and B together can do the work in = 45/2 = 22(1/2) days.

- A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days. The number of days after which A left the work was?

(a) 12

(b) 11

(c) 10

**(d) 9**

(e) None of these

*Explanation:*

Let the total units of work to be done be 360.

The units of work done by A in a single day = 8

Similarly, the units of work done by B in a single day = 9.

A and B’s one day work = 17 units

A and B worked together for some days = 17X ( Assume)

B’s work alone for 23 days = 23 x 9 = 207

So, the work done by A and B together = (360 – 207) = 153 units

Therefore, 17X = 153

=> 9 units

Therefore, the number of days after which A left the work was 9 days.

- A can do a piece of work in 10 days, B in 15 days. They work for 5 days. The rest of work finished by C in 2 days. If they get Rs 1500 for the whole work, the daily wages of B and C are?

(a) 275

(b) 250

**(c) 225 **

(d) 300

(e) None of these

*Explanation:*

Part of work done by A = 5/10 = 1/2

Part of work done by B = 1/3

Part of work done by C = (1- (1/2 + 1/3)) = 1/6

A’s share : B’s share : C’s share = 1/2 : 1/3 : 1/6 = 3 : 2 : 1.

A’s share = (3/6) x 1500 = 750

B’s share = (2/6) x 1500 = 500

C’s share = (1/6) x 1500 = 250

A’s daily wages = 750/5 = 150/-

B’s daily wages = 500/5 = 100/-

C’s daily wages = 250/2 = 125/-

Daily wages of B & C = 100 + 125 = 225/-

- A is twice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B. In how many days they can complete the whole work; working together?

**(a) 20 days**

(b) 22.5 days

(c) 25 days

(d) 35 days

(e) 40 days

*Explanation:*

Ratio of times taken by A and B = 1 : 2.

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

If difference of time is 1 day, B takes 2 days.

If difference of time is 30 days, B takes 2 x 30 = 60 days.

So, A takes 30 days to do the work.

A’s 1 day’s work = 1/30

B’s 1 day’s work = 1/60

(A + B)’s 1 day’s work = 1/30 + 1/60 = 1/20

A and B together can do the work in 20 days.

- Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. What is the ratio between the capacity of a man and a woman?

**(a) 4:3**

(b) 5:6

(c) 7:9

(d) 8:9

(e) 2:3

*Explanation:*

(20 x 16) women can complete the work in 1 day.

1 woman’s 1 day’s work = 1/320 .

(16 x 15) men can complete the work in 1 day.

1 man’s 1 day’s work = 1/240

So, required ratio

= 1/240 : 1/320

= 240 : 320

= 1/3 : 1/4

= 4 : 3 (cross multiplied)

- A and B can do a job together in 7 days. A is 13/4 times as efficient as B. The same job can be done by A alone in:

(a) 9 (1/3)

(b) 2 (5/6)

**(c) 11**

(d) 5 (2/8)

(e) 4 (6/8)

*Explanation:*

(A’s 1 day’s work) : (B’s 1 day’s work) = 7 /4: 1 = 7 : 4.

Let A’s and B’s 1 day’s work be 7x and 4x respectively.

Then, 7x + 4x = 1 => 11x = 1/7 => x =1/77

Therefore A’s 1 day’s work = ( 1/77 x 7 ) = 1/11 .

- A can do a piece of work in 8 days which B can destroy in 3 days. A has worked for 6 days, during the last 2 days of which B has been destroying. How many days must A now work alone to complete the work?

(a) 7 days

**(b) 7(1/3) days**

(c) 7(2/3) days

(d) 8 days

(e) None of these

*Explanation:*

In 6 days part of the work done by

A = 6/8 = ¾ during 2 days, part of the work destroyed by B = 2/3

- A can complete a piece of work in 10 days, B in 15 days and C in 20 days. A and C worked together for two days and then A was replaced by B. In how many days, altogether, was the work completed?

(a) 12

(b) 10

(c) 6

**(d) 8**

*Explanation:*

- A can do a piece of work in 20 days. He works at it for 5 days and then B finishes it in 10 more days. In how many days will A and B together finish the work?

**(a) 8 days**

(b) 10 days

(c) 12 days

(d) 6 days

(e) 16 days

*Explanation:*

- A and B can do a piece of work in 30 days while B and C do the same work in 24 days and C and A in 20 days. They work for 10 days after that B and C left. How many days more A takes to finish the work?

(a) 15 days

**(b) 18 days**

(c) 14 days

(d) 12 days

(e) None of these

*Explanation:*

- A group of 30 men, working 4 hours a day can do a piece of work in 10 days. Find the number of days in which another group of 45 men working 8 hrs a day can do twice the work. Assume that 2 men of the first group do as much work in 2 hours as 4 men of the second group do in 1 hr.

(a) 6(1/3) days

**(b) 6(2/3) days**

(c) 5(5/6) days

(d) 3(1/6) days

(e) None of these

*Explanation:*

Let the first group is man can do x unit in one hour and second group’s man can do y unit in one hour

2 × x × 2 = 4 × y × 1

x = y

2 × 30 × 4 × 10 = 45 × 8 × t

t = 6 (2/3) days

- P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together. working 8 hours a day. in how many days can they complete the work?

**(a) 5 (5/11)**

(b) 5 (6/11)

(c) 6 (8/11)

(d) 6 (6/11)

(e) None of these

*Explanation:*

- If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn for 30 days are ₹

(a) 12

(b) 14

**(c) 16**

(d) 18

(e) 20

*Explanation:*

- A telecom service provider engages male and female operators for answering 1000 calls per day. A male operator can handle 40 calls per day whereas a female operator can handle 50 calls per day. The male and the female operators get a fixed wage of ₹ 250 and ₹ 300 per day respectively. In addition, a male operator gets ₹ 15 per call he answers and female operator gets ₹ 10 per call she answers. To minimize the total cost, how many male operators should the service provider employ assuming he has to employ more than 7 and maximum 12 number of the females?

(a) 15

(b) 14

(c) 12

**(d) 10**

(e) None of these

*Explanation:*

Let us form both equations first:

40m + 50f = 1000

250 m + 300 f + 40 × 15 m + 50 × 10 × f = A

850m + 8000 f = A

When M and F are the number of Males and Females and A is the amount paid by the service provider.

Then the possible values of F are 8, 9, 10, 11, 12

If F = 8, then, M = 15

If F = 9, 10, 11 then M will not be an integer while F = 12 then M will be 10.

By putting F = 8 and M = 15, A = 18800. When F = 12 and M = 10, then A = 18100.

Hence the number of males will be 10.

- Published in TIME AND WORK