1.Arun can do a piece of work in 40 days, but Bala can do the same work in 5 days less, than Arun, when working alone. Arun and Bala both started the work together but Bala left after some days and Arun finished the remaining work in 30 days with half of his efficiency but he did the work with Bala with his complete efficiency. For how many days they had worked together?
A. 25/3 days
B. 31/3 days
C. 35/3 days
D. 38/3 days
E. None of these
Answer & Explanation
Answer – C. 35/3 days
Explanation :
1 day work of Arun and Bala = 1/40 + 1/35 = 15/280
Arun finished the remaining work in 30 days = 30 * 1/40 * 2 = 3/8
Remaining work done by Arun and Bala = 5/8
Worked together = (5/8)/(15/280) = 35/3 days.
2.Kiran can do a work in 20 days, while Karan can do the same work in 25 days. They started the work jointly. Few days later Suman also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.1000. What is the share of Suman?
A. 200
B. 400
C. 100
D. 300
E. 500
Answer & Explanation
Answer – C. 100
Explanation :
Efficiency of Kiran = 5%
Efficiency of Karan = 4%
They will complete only 90% of the work = [(5+4)*10] =90
Remaining work done by Suman = 10%.
Share of Suman = 10/100 * 1000 = 100
3.7 Indian and 4 American finish a job in 6 days. 7 African and 3 American finish the same job in 8 days. The efficiency of each person of a particular nationality is same but different from others. One Indian One American and One African will complete the work in:
A. 10 days
B. 12 days
C. 24 days
D. 36 days
E. None of these
Answer & Explanation
Answer – C. 24 days
Explanation :
Explanation:
7I + 4Am = 1/6
7Af + 4Am = 1/8
7I + 7Af + 7Am = 7/24
1I + 1Af + 1Am = 1/24
4.One Indian One American and One African will complete the work in – 24 days.
Chitra is twice efficient as Arun. Bala takes thrice as many days as Chitra. Arun takes 12 days to finish the work alone. If they work in pairs(i.e Arun-Bala, Bala-Chitra, Chitra-Arun) starting with Arun – Bala on the first day, Bala – Chitra on the second day and Chitra – Arun on the third day and so on, then how many days are required to finish the work?
A. 26/9 days
B. 46/9 days
C. 16/9 days
D. 56/9 days
E. None of these
Answer & Explanation
Answer – B. 9 days
Explanation :
No of days taken by Arun = 12 days
No of days(Arun:Bala:Chitra) = 2:3:1
1 day work of (Arun+Bala) = 5/36
1 day work of (Bala+Chitra) = 8/36
1 day work of (Chitra+Arun) = 9/36
5 days total work – 35/36
1/36 is done by Arun-Chitra
Number of days taken by Arun-Chitra for the rest of the work = (1/36)/(9/36) = 1/9
Total time taken to complete the work = 5 + 1/9 = 46/9 days
5.A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for six more days to finish the work. Find the number of days in which all the workers together will finish the work?
A. 22 days
B. 20 days
C. 24 days
D. 35 days
E. 32 days
Answer & Explanation
Answer – D. 35 days
Explanation :
30 workers work in pairs, with no same pair of workers working together twice
29[1/w1 + 1/w2 ….. + 1/w30] + 6[1/w1 + 1/w2 ….. + 1/w30] = 1
[1/w1 + 1/w2 ….. + 1/w30] = 1/35
35 days.
6.Arun can do a piece of work in 10 days, Bala 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. 5000 as wages for the whole work, what are the daily wages of Arun, Bala and Chitra respectively (in Rs)?
A. 600, 400, 500
B. 200, 300, 400
C. 500, 300, 400
D. 600, 500, 300
E. 400, 300, 200
Answer & Explanation
Answer – A. 600, 400, 500
Explanation :
A’s 5 days work = 50%
B’s 5 days work = 33.33%
C’s 2 days work = 16.66%[100- (50+33.33)] Ratio of contribution of work of Arun, Bala and Chitra = 3 : 2 : 1
Arun’s total share = Rs. 3000
Bala’s total share = Rs. 2000
Chitra’s total share = Rs. 1000
Arun’s one day’s earning = Rs.600
Bala’s one day’s earning = Rs.400
Chitra’s one day’s earning = Rs.500
7.A Contractor employed a certain number of workers to finish constructing a building in a certain scheduled time. Some time later, when a part of work had been completed, he realized that the work would get delayed by half of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the building on the scheduled time. How much work he had been completed, before increasing the number of workers?
A. 200/3 %
B. 100/3 %
C. 300/3 %
D. Can’t be determined
E. None of these
Answer & Explanation
Answer – B. 100/3 %
Explanation :
Explanation:
D * x +(100- D) * 2x= 150x
=> D= 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
8.(x-2) person can do a work in x days and (x+7) person can do 75% of the same work in (x-10)days. Then in how many days can (x+10) person finish the work?
A. 27 days
B. 12 days
C. 25 days
D. 18 days
E. None of these
Answer & Explanation
Answer – B. 12 days
Explanation :
3/4 * (x-2)x = (x+7)(x-10)
x – 6x – 280 = 0
x = 20; x = -14
(x-2)x = 18 * 20 = 360
360 = 30 * y
y = 12 days
9.The ratio of efficiency of Arun is to Chitra is 5:3. The ratio of number of days taken by Bala is to Chitra is 2:3. Arun takes 6 days less than Chitra, when Arun and Chitra complete the work individually. Bala and Chitra started the work and left after 2 days. The number of days taken by Arun to finish the remaining work is?
A. 4 days
B. 5 days
C. 6 days
D. 9 days
E. None of these
Answer & Explanation
Answer – C. 6 days
Explanation :
Ratio of number of days = 9:10:15
Work done By B and C in first two days = 2*1/6 = 1/3
Rest of the work = 2/3
Number of days = (2/3)/(1/9) = 6 days
10.Arun is twice efficient as Bala and together they do the same work in as much time as Chitra and David together. If Chitra and David can complete the work in 20 and 30 days respectively, working alone, then in how many days A can complete the work individually?
A. 12 days
B. 18 days
C. 24 days
D. 30 days
E. None of these
Answer & Explanation
Answer – B. 18 days
Explanation :
1/x + 1/2x = 1/20 + 1/30
3/2x = 1/12
Number of days taken by Arun = 18 days
A. 25/3 days
B. 31/3 days
C. 35/3 days
D. 38/3 days
E. None of these
Answer & Explanation
Answer – C. 35/3 days
Explanation :
1 day work of Arun and Bala = 1/40 + 1/35 = 15/280
Arun finished the remaining work in 30 days = 30 * 1/40 * 2 = 3/8
Remaining work done by Arun and Bala = 5/8
Worked together = (5/8)/(15/280) = 35/3 days.
2.Kiran can do a work in 20 days, while Karan can do the same work in 25 days. They started the work jointly. Few days later Suman also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.1000. What is the share of Suman?
A. 200
B. 400
C. 100
D. 300
E. 500
Answer & Explanation
Answer – C. 100
Explanation :
Efficiency of Kiran = 5%
Efficiency of Karan = 4%
They will complete only 90% of the work = [(5+4)*10] =90
Remaining work done by Suman = 10%.
Share of Suman = 10/100 * 1000 = 100
3.7 Indian and 4 American finish a job in 6 days. 7 African and 3 American finish the same job in 8 days. The efficiency of each person of a particular nationality is same but different from others. One Indian One American and One African will complete the work in:
A. 10 days
B. 12 days
C. 24 days
D. 36 days
E. None of these
Answer & Explanation
Answer – C. 24 days
Explanation :
Explanation:
7I + 4Am = 1/6
7Af + 4Am = 1/8
7I + 7Af + 7Am = 7/24
1I + 1Af + 1Am = 1/24
4.One Indian One American and One African will complete the work in – 24 days.
Chitra is twice efficient as Arun. Bala takes thrice as many days as Chitra. Arun takes 12 days to finish the work alone. If they work in pairs(i.e Arun-Bala, Bala-Chitra, Chitra-Arun) starting with Arun – Bala on the first day, Bala – Chitra on the second day and Chitra – Arun on the third day and so on, then how many days are required to finish the work?
A. 26/9 days
B. 46/9 days
C. 16/9 days
D. 56/9 days
E. None of these
Answer & Explanation
Answer – B. 9 days
Explanation :
No of days taken by Arun = 12 days
No of days(Arun:Bala:Chitra) = 2:3:1
1 day work of (Arun+Bala) = 5/36
1 day work of (Bala+Chitra) = 8/36
1 day work of (Chitra+Arun) = 9/36
5 days total work – 35/36
1/36 is done by Arun-Chitra
Number of days taken by Arun-Chitra for the rest of the work = (1/36)/(9/36) = 1/9
Total time taken to complete the work = 5 + 1/9 = 46/9 days
5.A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for six more days to finish the work. Find the number of days in which all the workers together will finish the work?
A. 22 days
B. 20 days
C. 24 days
D. 35 days
E. 32 days
Answer & Explanation
Answer – D. 35 days
Explanation :
30 workers work in pairs, with no same pair of workers working together twice
29[1/w1 + 1/w2 ….. + 1/w30] + 6[1/w1 + 1/w2 ….. + 1/w30] = 1
[1/w1 + 1/w2 ….. + 1/w30] = 1/35
35 days.
6.Arun can do a piece of work in 10 days, Bala 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. 5000 as wages for the whole work, what are the daily wages of Arun, Bala and Chitra respectively (in Rs)?
A. 600, 400, 500
B. 200, 300, 400
C. 500, 300, 400
D. 600, 500, 300
E. 400, 300, 200
Answer & Explanation
Answer – A. 600, 400, 500
Explanation :
A’s 5 days work = 50%
B’s 5 days work = 33.33%
C’s 2 days work = 16.66%[100- (50+33.33)] Ratio of contribution of work of Arun, Bala and Chitra = 3 : 2 : 1
Arun’s total share = Rs. 3000
Bala’s total share = Rs. 2000
Chitra’s total share = Rs. 1000
Arun’s one day’s earning = Rs.600
Bala’s one day’s earning = Rs.400
Chitra’s one day’s earning = Rs.500
7.A Contractor employed a certain number of workers to finish constructing a building in a certain scheduled time. Some time later, when a part of work had been completed, he realized that the work would get delayed by half of the scheduled time, so he at once doubled the no of workers and thus he managed to finish the building on the scheduled time. How much work he had been completed, before increasing the number of workers?
A. 200/3 %
B. 100/3 %
C. 300/3 %
D. Can’t be determined
E. None of these
Answer & Explanation
Answer – B. 100/3 %
Explanation :
Explanation:
D * x +(100- D) * 2x= 150x
=> D= 50 days
work done in 50 days = 50x
Total work = 150x
50x/150x * 100 = 100/3
8.(x-2) person can do a work in x days and (x+7) person can do 75% of the same work in (x-10)days. Then in how many days can (x+10) person finish the work?
A. 27 days
B. 12 days
C. 25 days
D. 18 days
E. None of these
Answer & Explanation
Answer – B. 12 days
Explanation :
3/4 * (x-2)x = (x+7)(x-10)
x – 6x – 280 = 0
x = 20; x = -14
(x-2)x = 18 * 20 = 360
360 = 30 * y
y = 12 days
9.The ratio of efficiency of Arun is to Chitra is 5:3. The ratio of number of days taken by Bala is to Chitra is 2:3. Arun takes 6 days less than Chitra, when Arun and Chitra complete the work individually. Bala and Chitra started the work and left after 2 days. The number of days taken by Arun to finish the remaining work is?
A. 4 days
B. 5 days
C. 6 days
D. 9 days
E. None of these
Answer & Explanation
Answer – C. 6 days
Explanation :
Ratio of number of days = 9:10:15
Work done By B and C in first two days = 2*1/6 = 1/3
Rest of the work = 2/3
Number of days = (2/3)/(1/9) = 6 days
10.Arun is twice efficient as Bala and together they do the same work in as much time as Chitra and David together. If Chitra and David can complete the work in 20 and 30 days respectively, working alone, then in how many days A can complete the work individually?
A. 12 days
B. 18 days
C. 24 days
D. 30 days
E. None of these
Answer & Explanation
Answer – B. 18 days
Explanation :
1/x + 1/2x = 1/20 + 1/30
3/2x = 1/12
Number of days taken by Arun = 18 days