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Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

Q11.
A,B,C can do a  work in 36,54 and 72 days respectively.They started work together but A and B left the work 8 and 12 days before completion of the work respectively. Find the total number of days which the work has been completed ?
1) 15 2) 18
3) 24 4) 30
5)None of these
Answer : 24
Explanation : Let,the total numbers of days requires to finish the job is x days.
So, A works for ( x-8) days and B works for (x-12) and C works for x days.
Therefore,
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Q12.
A and B can do a work together  in 12 days while B and C together can do the same work in 15 days. If A is twice good work as C then, in how many days C can alone do the same work ?
1) 30 days 2) 36 days
3) 45 days 4) 60 days
5)None of these
Answer : 60 days
Explanation : Given, A+B can do the work in 1day =1/12 parts --- (I) :
B+C in 1day =1/15 parts ----- (II) 
and also given A = 2C. 
So, putting the value in equation I, we get 2C+B = 12 . 
Then, deducting equation II from equation I , we get, 1/12 - 1/15= c =1/60 i.e 60 days.
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Q13.
6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days. In how many days 15 men and 20 boys can do the same work ? 
1) 4 days 2) 5 days
3) 6 days 4) 7 days
5)None of these
Answer : 4 days
Explanation :
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Q14.
10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work ?
1) 3 2) 5
3) 7 4) Can't be determined
5)None of these
Answer : 7
Explanation :


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Q15.
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it ?
1) 8 hours 2) 10 hours
3) 12 hours 4) 24 hours
5)None of these
Answer : 12 hours
Explanation :
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Q16.
Alok alone can do a piece of work in 6 days and Barun alone in 8 days. Alok and Barun undertook to do it for Rs. 3200. With the help of Chinmay, they completed the work in 3 days. How much is to be paid to Chinmay ?
1) Rs. 375 2) Rs. 400
3) Rs. 600 4) Rs. 800
5)None of these
Answer : Rs. 400
Explanation :
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Q17.
Twelve men complete a work in 9 days. After they have worked for 6 days, 6 more men join them. How many days will they take to complete the remaining work ?
1) 2 days 2) 3 days
3) 4 days 4) 5 days
5)None of these
Answer : 2 days
Explanation : Given, 12 men complete a work in 9 days.
After they have worked for 6 days, remaning days for work = 9 - 6 = 3 days
So, now 12 men can do the work in 3 days .
or 1 men can dothe the work in 12 x 3 = 36 days 
or 12 + 6 = 18 men can do the same work in = 36 /18 = 2 days

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Q18.
A certain number of men can to finish a work in 30 days. If 20 men leave the the work , the work would taken 15 days more. How many men are there originally ?
1) 40 2) 48
3) 50 4) 60
5)None of these
Answer : 60
Explanation : First Method:

Let,  there are 'x' men originally.
'x' men can do a work in 30 days.
or 1 man can do the same work in = 30x days   -------- (1)
Now, 20 men leave .
So, (x-20) men can do the work in (30+15) = 45 days ------ (2)
or 1 man can do the same work in = 45 (x-20) days. 
Therefore, 45 (x-20) = 30x  or 45x - 900 = 30x  or x =  60 men

SHORT-CUT METHOD:
 (60 x 30 ) / (40 x 45 ) = 60  
i.e [People (join/left) x Final numbers of days ] / different numbers of days = Original Strength

  
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Q19.
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:
1) 20 days 2) 22 .5 days
3) 25 days 4) 30 days
5)None of these
Answer : 22 .5 days
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 and B together can do the work in  = (30x90)/(30+90) = 22 .5 days
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Q20.
A fort is provisioned for 32 days for some soldier. After 4 days, a reinforcement of 150 soldiers arrived & the food will now last for 21 days only. How many soldiers were there in the fort in the begining ? 
1) 350 2) 400
3) 450 4) 420
5)None of these
Answer : 450
Explanation :
Shortcut Methods :

 [(People (Join/Left) x Final Numbers of days)]/ Dffrence in days = Original Strength

 i.e. (150 x 21) /(28 - 21) = 450 soldiers
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