Breaking

    VEO EXAM PREPARATION    PSC EXAM PROGRAMME 2019     ||        TODAY'S EXAM RESULTS    ||        FINAL ANSWER KEY    ||    FREE STUDY MATERIALS (ALL EXAM)    ||    CURRENT AFFAIRS- 2019
Showing posts with label MATHS (SOLVED IN STEPS). Show all posts
Showing posts with label MATHS (SOLVED IN STEPS). Show all posts

Wednesday, 11 October 2017

MATHS (SOLVED IN STEPS)
22:21

MATHS (SOLVED IN STEPS)


* MATHS (SOLVED IN STEPS ==> Ratio and Proportion
* MATHS (SOLVED IN STEPS ==> Progressions
* MATHS (SOLVED IN STEPS ==> Percentage
* MATHS (SOLVED IN STEPS ==> Surds and Indices
* MATHS (SOLVED IN STEPS ==> Calendar
* MATHS (SOLVED IN STEPS ==> Square and cube
* MATHS (SOLVED IN STEPS ==> Simplification
* MATHS (SOLVED IN STEPS ==> Problems on Average
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> Profit and Loss
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Age 
* MATHS (SOLVED IN STEPS ==> Pipe and Cisterns
* MATHS (SOLVED IN STEPS ==> ODD MAN
* MATHS (SOLVED IN STEPS ==> TIME & WORK




* SCERT KERALA TEXTBOOKS FOR CLASS II, IV, VI, VIII, IX, X, XII – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXTBOOKS FOR ALL CLASSES – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXT BOOKS SOLUTIONS FOR ALL CLASSES ---> Click here
0
By на No comments:
Ярлыки:
MATHS (SOLVED IN STEPS) TIME & WORK - (Page -4)
11:41

MATHS (SOLVED IN STEPS) TIME & WORK - (Page -4)

22. P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How man D. 4 days will be needed if P and R together do it?
A. 3               B. 8                    C. 12             D.14
Answer : Option B
Explanation : Let work done by P in 1 day = p
work done by Q in 1 day =q
Work done by R in 1 day = r
p + q = 1/8 ---(1)
q + r= 1/12 ---(2)
p+ q+ r = 1/6 ---(3)
(3) – (2) => p = 1/6 - 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days


23. P works twice as fast as Q. If Q alone can complete a work in 12 days, P and Q can finish the work in --- days
A. 1                 B. 2                 C. 3              D. 4
Answer : Option D
Explanation : Work done by Q in 1 day = 1/12
Work done by P in 1 day = 2 × (1/12) = 1/6
Work done by P and Q in 1 day = 1/12 + 1/6 = ¼
=> P and Q can finish the work in 4 days

24. A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is
A. 1:3              B. 4:3              C. 2:3               D. 2:1
Answer : Option B
Explanation :Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16×20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×16)
Ratio of the capacity of a man and woman =1/(15×16) :
1/(16×20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3


25. P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
A. 7                B. 8               C. 9             D. 10
Answer : Option D
Explanation : Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10

26. P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
A. Rs.40               B. Rs.70                  C. Rs.90              D. Rs.100
Answer : Option B
Explanation : Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120 ---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
- Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=>Amount Earned by R in 1 day = 70

27. 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
Answer : Option 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


28. There is a group of persons each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?
A. 3 ¼ days                   B. 4⅓ days            C. 5⅙days            D. 6⅕ days
Answer : Option C
Explanation : Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16 …
An easy way to attack such problems is from the choices.
You can see the choices are very close to each other. So just see one by one.
For instance, The first choice given in 3 ¼
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5. Hence
the answer is 5⅙days.    
(Just for your reference, work done in 5 days = 15/16.
Pending work in 6th day = 1 – 15/16 = 1/16.
In 6th day, 6 people are working and work done = 6/16.
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days.
Hence total time required = 5 + 1/6 = 5 ⅙ days)
<Main Page><01, 02, 03, 04 >
* MATHS (SOLVED IN STEPS ==> Main Page
* MATHS (SOLVED IN STEPS ==> Problems on Age
* MATHS (SOLVED IN STEPS ==> ODD MAN  
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Average 
* MATHS (SOLVED IN STEPS ==> PIPES AND CISTERNS 
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> PROFIT AND LOSS 


Related Links
* SCERT KERALA TEXT BOOKS FOR CLASS II, IV, VI, VIII, IX, X, XII – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXT BOOKS FOR ALL CLASSES – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXT BOOKS SOLUTIONS FOR ALL CLASSES ---> Click here
0
By на No comments:
Ярлыки:
MATHS (SOLVED IN STEPS) TIME & WORK - (Page -3)
11:39

MATHS (SOLVED IN STEPS) TIME & WORK - (Page -3)

15. P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in --- days if all of them are working together.
A. 2               B. 3 ³⁄₇              C. 4 ¼              D. 5
Answer : Option B
Explanation : Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/6
Work done by R in 1 day = 1/12
Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24
=> Working together, they will complete the work in 24/7 days = 3 ³⁄₇days


16. 10 men can complete a work in 7 days. But 10 women7 need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
A. 5                  B. 6                 C. 7               D. 8
Answer : Option C
Explanation :Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/ 70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
=> 5 men and 10 women can complete the work in 7 days

17. Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in ----- days.
A.14                       B. 16                 C. 18                     D. 20
Answer : Option B
Explanation :Work done by Kamal in 1 day = 1/20
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days


18. 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
Answer : Option 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

19. P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?
A. 4                     B. 5                    C. 6                D. 7
Answer : Option C
Explanation :Let P takes x days to complete the work
Then Q takes x/2 days and R takes x/3 days to finish the work
Amount of work P does in 1 day = 1/x
Amount of work Q does in 1 day = 2/x
Amount of work R does in 1 day = 3/x
Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x
= 1/x (1 + 2 + 3) = 6/x
6/x = 2
=> x = 12
=> Q takes 12/2 days = 6 days to complete the work


20. P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in --- days.
A. 12                  B. 16                 C. 20               D. 24
Answer : Option A
Explanation : Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 × (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days

21.  P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?
A. 10                  B. 15                  C. 18              D. 22
Answer : Option C
Explanation : Let work done by P in 1 day = p,
Work done by Q in 1 day = q,
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20
= 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8
Remaining work = 1 = 5/8 = 3/8
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18
<Next Page><01, 02, 03, 04 >
* MATHS (SOLVED IN STEPS ==> Main Page
* MATHS (SOLVED IN STEPS ==> Problems on Age
* MATHS (SOLVED IN STEPS ==> ODD MAN  
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Average 
* MATHS (SOLVED IN STEPS ==> PIPES AND CISTERNS 
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> PROFIT AND LOSS 


Related Links
* SCERT KERALA TEXT BOOKS FOR CLASS II, IV, VI, VIII, IX, X, XII – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXT BOOKS FOR ALL CLASSES – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXT BOOKS SOLUTIONS FOR ALL CLASSES ---> Click here
0
By на No comments:
Ярлыки:
MATHS (SOLVED IN STEPS) TIME & WORK - (Page -2)
11:38

MATHS (SOLVED IN STEPS) TIME & WORK - (Page -2)

8. P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. How many days does P alone need to finish the remaining work?
A. 8          B. 5           C. 4              D. 6
Answer : Option D
Explanation :Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6

9. P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
A. 30 days                 B. 25 days                 C. 20 days               D. 15 days
Answer : Option B
Explanation : Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day . Hence the above equation can be written as Work done by P in 1 day × 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days

10. A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
A. 37 ½ days                    B. 22 days               C. 31 days                  D. 22 days
Answer : Option A
Explanation :Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5) / 20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5 (Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days


11. 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?
A. 50                  B. 40               C. 30                         D. 20
Answer : Option B
Explanation : Work done by 4 men and 6 women in 1 day = 1/8
Work done by 3 men and 7 women in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 × (1/
400) = 1/40 Ie, 10 women can complete the work in 40 days

12. A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?
A. 60                   B. 50                C. 40                  D. 30
Answer : Option A
Explanation : Amount of work done by A and B in 1 day = 1/30
Amount of work done by A and B in 20 days = 20 × (1/ 30) = 20/30 = 2/3
Remaining work – 1 – 2/3 = 1/3
A completes 1/3 work in 20 days
Amount of work A can do in 1 day = (1/3)/20 = 1/60
=> A can complete the work in 60 days


13. A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in --days.
A. 5 ⁵⁄₁₁             B. 4 ⁵/₁₁         C. 6 ⁴/₁₁      D. 6 ⁵/₁₁
Answer : Option A
Explanation : A can complete the work in 12 days working 8 hours a day
=> Number of hours A can complete the work = 12×8 = 96 hours
=> Work done by A in 1 hour = 1/96
B can complete the work in 8 days working 10 hours a day
=> Number of hours B can complete the work = 8×10 = 80 hours
=> Work done by B in 1 hour = 1/80
Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480
=> A and B can complete the work in 480/11 hours
A and B works 8 hours a day
Hence total days to complete the work with A and B working together
= (480/11) / (8) = 60/11 days = 5 ⁵⁄₁₁ days

14. 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
Answer : Option 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
<Next Page><01, 02, 03, 04 >
* MATHS (SOLVED IN STEPS ==> Main Page
* MATHS (SOLVED IN STEPS ==> Problems on Age
* MATHS (SOLVED IN STEPS ==> ODD MAN  
* MATHS (SOLVED IN STEPS ==> Problems on Trains 
* MATHS (SOLVED IN STEPS ==> Problems on Average 
* MATHS (SOLVED IN STEPS ==> PIPES AND CISTERNS 
* MATHS (SOLVED IN STEPS ==> HCF & LCM 
* MATHS (SOLVED IN STEPS ==> PROFIT AND LOSS 


Related Links
* SCERT KERALA TEXT BOOKS FOR CLASS II, IV, VI, VIII, IX, X, XII – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXT BOOKS FOR ALL CLASSES – FREE DOWNLOAD ---> Click here
* NCERT & CBSE TEXT BOOKS SOLUTIONS FOR ALL CLASSES ---> Click here
0
By на No comments:
Ярлыки: