Quants Questions : Time And Work Set 4

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1. 6 men and 5 boys can do a piece of work in 10 days while 20men and 45 boys can do the same in 2 days, how much time taken by 13 men and 25 boys in doing the same work ?
   A)2(1/3)days
   B)3(1/3)days
   C)4(1/3)days
   D)2(1/2) days
   
   Answer

   B)3(1/3)days
   Explanation :
   (6m+5b)10 = (20m+45b)2
   60m+50b = 40m + 90b
   20m = 40b
   1m = 2b
   6m+5b =12b+5b = 17b in 10 days
   13m+25b = 26b+25b = 51b in  ? days
   17:10 = 51 :?
   17*10/51 = ? = 3(1/3) days
   
   
   
2. P and Q Working separately can do a piece of work in 6 days and 11 days, if they work alternately beginning with P then the work will be completed in how many days ?
   A)10 days
   B)6 days
   C)8 days
   D)5 days
   
   Answer

   C)8 days
   Explanation :
   Total work = 6*11 = 66
   2 days(P+Q) = 1/6 + 1/11 = (11+6)/66 = 17/66
   6 days(P+Q) = 51/66
   Remaining work = (1-(51/66)) = 15/66
   In 15, 6 done by P remaining done by Q (2 days)
   6+2 = 8 days
   
   
   
3. 3 men and 5 women do a piece of work in 9 days and 2 men 7 children do the same in 6 days. How many women can do as much work as 21 children ?
   A)5
   B)7
   C)8
   D)10
   
   Answer

   D)10
   Explanation :
   3m+5w = 9days…….(1)6m+10w = 18 days
   2m+7c = 6 days…….(2)6m+21c = 18 days
   21c = 10w
   
   
   
4. If 12 persons can complete 3/5 of a work in 10 days, then find the number of persons required to complete the remaining work in 10days ?
   A)7
   B)8
   C)9
   D)10
   
   Answer

   B)8
   Explanation :
   12*10*(3/5) = m *10*(2/5)
   M = 72/4 = 18 men
   
   
   
5. P can complete the work in 16 days. P and Q can complete the work in 12days. In how many days Q alone can complete the same work ?
   A)32
   B)46
   C)48
   D)38
   
   Answer

   C)48
   Explanation :1/12 – 1/16 = (16 – 12)/192 = 4/192 = 1/48
   
   
   
6. A can complete a piece of work in 8 days and B can complete the work in 10 days and C in 12 days. B and C together worked for 3 days, then C left the work and A replaced him. In how many days will the remaining work be completed ?
   A)1
   B)2
   C)3
   D)4
   
   Answer

   B)2
   Explanation :
   (x-3)/8 + (x/10) + (3/12) = 1
   (5x-15+4x)/40 = 1-3/12 = 12-3/12 = 9/12 = ¾
   9x – 15 = 3*40/4 = 30
   X = 45/9 = 5 (3days completed )
   5 -3 = 2 days
   
   
   
7. A can finish a piece of work in 24 days. B is 20% more efficient than A and C is 25% more efficient than B. Find the time B and C will take to finish the work?
   A)7days
   B)6days
   C)8days
   D)9days
   
   Answer

   D)9days
   Explanation :
   A= 1/24
   B = 120/100(1/24) = 1/20
   C= 125/100(1/20) = 1/16
   B+C =(1/20) + (1/16) = 16+20/320 = 36/320 = 8.88 = 9 days
   
   
   
8. Seven men can complete a work in 10 days. They started the work and after 5 days, two men left. In how many days will the work be completed by the remaining men ?
   A)7
   B)6
   C)8
   D)9
   
   Answer

   A)7
   Explanation :
   7 men 1 day’s work will be 1 / 10
   7 men 5 days work will be 5 / 10 = 1/2  remaining work will be (1- 1/ 2) = 1 / 2
   1 man 1 day work will be 1 / (10*7) = 1 / 70
   5 mens 1 day work will be 5 / 70
   (70/5)*( 1 / 2) =  7 days
   
   
   
9. If 40 people can make 60 toys in 8 hrs, if 8 people leave the work, how many toys can make in 12 hrs ?
   A)68
   B)71
   C)72
   D)70
   
   Answer

   C)72
   Explanation :
   (40*8)/60 = (32*12)/x
   X = (32*12*60)/320 = 72 toys
   
   
   
10. 18 Women can complete a work in 10 days. 16 men complete the work in 12 days. The ratio of working capacity of man to that of a woman is
    A)15:16
    B)16:15
    C)15:14
    D)14:15
    
    Answer

    A)15:16
    Explanation :1/(16*12) : 1/(18*10) = 1/192 : 1/180 = 1/16 : 1/15 = 15:16