Friday, 29 January 2016

MATHS (SOLVED IN STEPS) TIME & WORK - (Page -1)

MATHS (SOLVED IN STEPS)
TIME & WORK - (Page -1)
1. Praveen is able to do a piece of work in 15 days and Qureshi can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
A. 8/15           B. 7/15            
C. 11/15              D. 2/11
Answer : Option A
Explanation :
Amount of work Praveen can do in 1 day = 1/15
Amount of work Qureshi can do in 1 day = 1/20
Amount of work Praveen and Qureshi can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work Praveen and Qureshi can together do in 4 days = 4 × (7/60) = 7/15
Fraction of work left = 1 – 7/15= 8/15

2. Anil can lay railway track between two stations in 16 days. Subin can do the same job in 12 days. With the help of Jyothi, they completes the job in 4 days. How much days does it take for jyothi alone to complete the work?
A. 9(3/5) days          B. 9(1/5) days          C. 9(2/5) days                D. 10 days
Answer : Option A
Explanation : Amount of work anil can do in 1 day = 1/16
Amount of work subin can do in 1 day = 1/12
Amount of work anil, subin and jyothi can together do in 1 day = 1/4
Amount of work jyothi can do in 1 day = 1/4 - (1/16 + 1/ 12) = 3/16 – 1/12 = 5/48
=> Hence jyothi can do the job on 48/5 days = 9 (3/5) days

3. P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it need to complete the work if P does the work and he is assisted by Q and R on every third day?
A. 10 days              B. 14 days                 C. 15 days             D. 9 days
Answer : Option C
Explanation :Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him Work completed in every three days = 2 × (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 × 1/5 = 1 Ie, the work will be done in 15 days

4. Ajeesh is thrice as good as Binu in work. Ajeesh is able to finish a job in 60 days less than Binu. They can finish the work in - days if they work together
A. 18 days              B. 22 ½ days                    C. 24 days             D. 26 days
Answer : Option B
Explanation : If Ajeesh completes a work in 1 day, Binu completes the same work in 3 days
Hence, if the difference is 2 days, Binu can complete the work in 3 days
=> if the difference is 60 days, Binu can complete the work in 90 days
=> Amount of work Binu can do in 1 day= 1/90
Amount of work Ajeesh can do in 1 day = 3 × (1/90) = 1/30
Amount of work Ajeesh and Binu can together do in 1 day
= 1/90 + 1/30 = 4/90 = 2/45
=> Ajeesh and Binu together can do the work in 45/2 days
= 22 ½ days

5. Ajay can do a particular work in 6 days . Bilal can do the same work in 8 days. Ajay and Bilal signed to do it for Rs. 3200. They completed the work in 3 days with the help of Deepu. How much is to be paid to Deepu?
A. Rs. 380              B. Rs. 600                    C. Rs. 420                D. Rs. 400
Answer : Option D
Explanation : Amount of work Ajay can do in 1 day = 1/6
Amount of work Bilal can do in 1 day = 1/8
Amount of work Ajay + Bilal can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work Ajay + Bilal + Deepu can do = 1/3
Amount of work Deepu can do in 1 day = 1/3 - 7/24 = 1/24
work Ajay can do in 1 day: work Bilal can do in 1 day: work deepu can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to Deepu = 3200 × (1/8) = 400

6. 6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in - days.
A. 4 days                   B. 6 days              C. 2 days                 D. 8 days
Answer : Option A
Explanation : Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
= 15/100 + 20/200 =1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days

7. A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in --- days.
A. 12 hours                  B. 6 hours                     C. 8 hours                 D. 10 hours
Answer : Option A
Explanation :Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = 1/4+1/3 = 7/12

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