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QUESTION: 1

Kiran can do a work in 25 days, while Ravi can do the same work in 50 days. They started the work jointly. Few days later Sumit also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.600. What is the Share of Sumit?

Solution:

Efficiency of Kiran = 4%

Efficiency of Ravi = 2%

[(4+2)*10] = 60%

The remaining work done by Sumit = 40%.

40% of 600 = 240

QUESTION: 2

Working together Bala and Chitra take 50% more number of days than Angel, Bala and Chitra together take and Angel and Bala working together, take 8/3 more number of days than Angel, Bala and Chitra take together. If Angel, Bala and Chitra all have worked together till the completion of the work and Bala has received Rs.120 out of total earnings of Rs. 480 then in how many days did Angel, Bala and Chitra together complete the whole work?

Solution:

The days ratio of (Angel + Bala + Chitra) : (Bala + Chitra) = X:3X/2 = 2X:3x;

Efficiency ratio = 3X:2X

Efficiency of Angel = x.

(480/3X) = Rs.160

Amount received by Bala = Rs.120 & Chitra = 200

160:120:200 =4:3:5

1/4:1/3:1/5= 15:20:12;

(1/15+1/12+1/20)*Y = 1

Y = 5 days

QUESTION: 3

Angel can do a piece of work in 10 days, Balu in 15 days. They work together for 5 days, the rest of the work is finished by Chitra in two more days. If they get Rs. 6000 as wages for the whole work, what are the daily wages of Angel, Bala and Chitra respectively?

Solution:

Angel’s 5 days work = 50%

Balu’s 5 days work = 33.33%

Chitra’s 2 days work = 16.66%

[100- (50+33.33)]

Ratio of work of Angel, Balu and Chitra = 3: 2: 1

Angel’s total share = Rs. 3000

Balu’s total share = Rs. 2000

Chitra’s total share = Rs. 1000

Angel’s one day’s wage = Rs.600

Balu’s one day’s wage = Rs.400

Chitra’s one day’s wage = Rs.500

QUESTION: 4

Ravi can do a piece of work in 16 days. Rakesh can do the same work in 64/5 days, while Geeta can do it in 32 days. All of them started to work together but Ravi leaves after 4 days. Rakesh leaves the job 3 days before the completion of the work. How long would the work last?

Solution:

Let the work lasted for x days,

Ravi’s 4 day’s work + Rakesh (x – 3) day’s work + Geeta’s x day’s work = 1

⇒ (4/16) + (x – 3) / (64/5) + x/32 = 1

⇒ 5(x – 3)/64 + x/32 = 1 – 1/4

⇒ [5(x – 3) + 2x] / 64 = 3/4

⇒ 7x – 15 = 48

∴ x = (48 + 15)/7 = 63/7 = 9 days

QUESTION: 5

Ramu, Hari and Sanjay are three typists, who working simultaneously, can type 228 pages in four hours. In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ramu. During a period of five hours, Sanjay can type as many passages as Ramu can, during seven hours. How many pages does each of them type per hour?

Solution:

Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h. Therefore, they together can type 4(x + y + z) pages in 4 h

∴ 4(x + y + z) = 228

⇒ x + y + z = 57 …..(i)

Also, z – y = y – x

i.e., 2y = x + z ……(ii)

5z = 7x ……(iii)

From Eqs. (i) and (ii), we get

3y = 57

⇒ y = 19

From Eq. (ii), x + z = 38

x = 16 and z = 22

QUESTION: 6

Efficiency of A is 25% more then B and B takes 25 days to complete a piece of work. A started a work alone and then B joined her 5 days before actual completion of the work. For how many days A worked alone?

Solution:

Efficiency (A : B) = 5 : 4

Number of days(A : B) = 4x : 5x = 4x : 25

∴ Number of days required by A to finish the work alone = 4x

= 4 x 5 = 20.

A and B work together for last 5 days = 5 x 9 = 45%

Efficiency of A = 5% and B’s efficiency = 4%

∴ No. of days taken by A to complete 55% work = 55/5 = 11days

QUESTION: 7

In a cucumber factory, there are equal number of women and children. Women work for 8 h a day and children for 6 h a day. During festival time, the work load goes up by 50%. The government rule does not allow children to work for more than 8 h a day. If they are equally efficient and the extra work is done by women, then extra hours of work put in by women every day are?

Solution:

Let extra hours a day are x.

According to the formula,

(M1D1T1) / W1 = (M2D2T2) / W2

⇒ [1 x 1 x (8 + 6)] / 1 = [1 x 1 x (8 + 8 + x)] / 3/2

⇒ (3/2) x 14 = 16 + x

⇒ 21= 16 + x

∴ x = 21 – 16 = 5

QUESTION: 8

A building contractor undertook to finish a certain work in 162 days and employed 150 men. After 72 days, he found that he had already done 2/3 of the work. How many men can be discharged now, so that the work finish in time?

Solution:

M1 = 150, M2 = 150 – n, D1 = 72, D2 = 90

W1= 2/3 and W2 = 1/3

According to the formula,

(M1D1) / W1 = (M2D2) / W2

⇒ [150 x 72] / 2 = [(150 – n) x 90] / 1

⇒ (150 x 72) / (2 x 60) = (150 – n)

⇒ (150 – n) = 60

∴ n = 150 – 60 = 90

QUESTION: 9

Sanjay can do a piece of work in 50 days. He started the work and left after some days, when 25% work was done. After it Ajit joined and completed it working for 25 days. In how many days Sanjay and Ajit can do the complete work, working together?

Solution:

Efficiency of Sanjay = (100/50) = 2%

Rest work = 75%

∴ Efficiency of Ajit = 75/25 = 3%

∴ Combined efficiency of Sanjay and Ajit = 5%

∴ Number of days required by Sonu and Abhijeet, to work together = 100/5 = 20 days.

QUESTION: 10

Kiran can do a piece of work in 9 days and Kumar can do the same work in 18 days. They started the work. After 3 days Sanjay joined them, who can complete alone the same whole work in 3 days. What is the total number of days in which they had completed the work?

Solution:

Efficiency of Kiran and Kumar = 11.11 + 5.55 = 16.66%

Work done in 3 days = 3 x 16.66 = 50%

Rest work done by Kiran, Kumar and Sanjay = 50/50 = 1 day

Work can be completed in 4 days.

QUESTION: 11

Mohan can do a work in 15 days. After working for 3 days he is joined by Vinod. If they complete the remaining work in 3 more days, in how many days can Vinod alone complete the work?

Solution:

Total days Mohan worked = 3+3 = 6

6/15 = 2/5

So 3/5 = 3/x

x = 5

QUESTION: 12

Arun can do a certain work in the same time in which Bipasha and Rahul together can do it. If Arun and Bipasha together could do it in 10 days and Rahul alone in 50 days, then Bipasha alone could do it in:

Solution:

Arun, Bipasha and rahul’s 1 day work = 1/10 + 1/50 = 6/50 = 3/25

Arun’s 1 day work = Bipasha + Rahul ‘s 1 day work

2*(Arun’s 1 day work) = 3/25

Arun’s 1 day work = 3/50

Bipasha’s 1 day work = 1/10 – 3/50 = 2/50 = 1/25

QUESTION: 13

Sekar, Pradeep and Sandeep can do a piece of work in 15 days. After all the three worked for 2 days, sekar left. Pradeep and Sandeep worked for 10 more days and Pradeep left. Sandeep worked for another 40 days and completed the work. In how many days can sekar alone complete the work if sandeep can complete it in 75 days?

Solution:

Assume the total work to be 600 units. (LCM of all the numbers) Then Sandeep’s 1 day work = 8 units.

All three’s 1 day work = 40 units.All work together in the first 2 days

Work done in the first 2 days = 40 × 2 = 80 units

Sandeep alone works during the last 40 days

Work done in the last 40 days = 40 × 8 = 320 units

Remaining work = 600 – (320 + 80) = 200 units

This work is done by pradeep and sandeep in 10 days.

Pradeep and Sandeep together’s 1 day work = 20 units

Sekar’s 1 day work = All three 1 day work – Pradeep and Sandeep together’s 1 day

work = 40 units – 20 units = 20 units

Sekar can do the work of 600 units in 30 days.

QUESTION: 14

Dinesh does 80% of a work in 20 days. He then calls in Gokul and theytogether finish the remaining work in 3 days. How long Gokul alone would take to do the whole work?

Solution:

Dinesh work done = 20*5/4 = 25 days

1/5 workdone by Dinesh and gokul in 3days.

Whole work done = 15 days

Dinesh 1 days work = 1/25

Dinesh and gokul’s 1 day work = 1/15

Gokul’s 1 day work = 1/15 – 1/25 = 2/75

Gokul alone in 75/2 days or 37 ½ days.

QUESTION: 15

Hari and Vijay can together finish a work in 30 days. They worked together for 20 days and then Vijay left. After another 20 days, hari finished the remaining work. In how many days hari alone can finish the work?

Solution:

Hari + vijay 20 days work = 1/30 *20 = 2/3

Remaining work = 1/3

1/3 work in 20 days so whole work in 60 days.

QUESTION: 16

Madhavan can finish a work in 5 hours. He invites Manohar and Manjima who can work 3/4th as fast as he can to join him. He also invites Mani and Mohan who can work only 1/5th as fast as he can to join him. If the five person team works the same job and they start together, how long will it take for them to finish the job?

Solution:

Let the work be 100 units.

Madhavan’s 1 hour work = 100/5 = 20 units

Manohar and Manjima’s 1 day work = 3/4 × 20 = 15 units.

Mohan and Mani’s 1 day work = 1/5 × 20 = 4 units.

In one day all five of them can do = 20 + 15 + 15 + 4 + 4 = 58 units of work. Hence they can complete the work in 100/58 days.

QUESTION: 17

A typing work is done by three person P, Q and R. P alone takes 10 hours to type a single booklet but B and C working together takes 4 hours, for the completion of the same booklet. If all of them worked together and completed 14 booklets, then how many hours have they worked?

Solution:

1/P = 1/10

1/P + 1/Q + 1/R = 1/10 + ¼ = 7/20

In 20 hours, working together, they will complete 7 booklets.

Thus, in 40 hours they will complete 14 booklets.

QUESTION: 18

Nakul and Ram are working on aproduction company. Nakul takes 6 hours to make 32 products, while Ram takes 5 hours to make 40 products. How much time will they take, working together to make 110 products?

Solution:

Number of products made by Nakul in 1 hour = 32/6 = 16/3

Number of products made by Ram in 1 hour = 40/5 = 8

Number of products made by both in 1 hour = 16/3 + 8 = 40/3

Time taken by both to make 110 products = 110* 3/40 = 8 ¼ hrs

QUESTION: 19

Gopal does a work in 90 days, Vikash in 40 days and Santhosh in 12 days. They work one after another for a day each, starting with Gopal followed by Vikash and then by Santhosh. If the total wages received are Rs 360 and Gopal, Vikash, Santhosh share them in the ratio of the work done, find their respective individual wages.

Solution:

Assume there are 360 units of work (LCM of 90, 40 and 12).

Hence, they can do 4,9 and 30 units per day or together 43 units every 3 days.

So In 24 days, 43×8=344 units of work is completed.

In the next 2 days, 13 unitsare completed and on 27th day,Santhosh takes 1/10 thof a day to finish the rest.

So, gopal and vikash worked for 9 days each and have hence put in 36 and 81 units respectively, and the rest of the 243 units is put in by santhosh.

The wages shall also be distributed in the same ratio as: Rs 36, Rs 81 and Rs 243.

QUESTION: 20

When Ashok and Karthik are working alone, they can complete a piece of work in 25 days and 30 days respectively. On day 1, Karthik started the work and Ashok joined B from day 3 on-wards. Find approximately after how many days will the work be completed?

Solution:

Fraction of work completed by Karthik on day 1 and day 2 = 2* 1/30 = 1/15

Fraction of work left after 2 days = 14/15

Fraction of work completed by Both = 1/25 + 1/30 = 11/150

Number of days after day 2 to complete work = 14*150/15*11 = 13 days

So after 2+13 = 15 days works will be completed

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