Aptitude Questions : Chain Rule Set 2

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1. 50 people went on picnic along with taking food for 10 days. After 4 days 10 people left the picnic. For how many days the food will last now?
   A) 7 1/2
   B) 15 1/2
   C) 8
   D) 6
   E) 6 1/2
   

   Answer & Explanation

   A) 7 1/2
   Explanation:
   After 4 days, there is (10-4) = 6 days food for 50 people. But 10 people left, so there are 40 people left, and let now the same food is for x days for 40 people. So
   M1*D1 = M2*D2
   50*6 = 40*x
   Solve, x = 15/2
   
   
   
2. 50 people can do 1/4th of work in 20 days working 4 hrs each day. How many people need to be joined in order to complete the work in 40 days working same number of hours as before?
   A) 75
   B) 50
   C) 20
   D) 25
   E) None of these
   

   Answer & Explanation

   D) 25
   Explanation:
   M1*D1*H1*W2 = M2*D2*H2*W1
   50*20*4*(3/4) = (50+x)*40*4*(1/4)
   Solve x = 25
   
   
3. 2 men and 3 women are employed to type 100 pages on computer. They completed the work in 5 hours. If one man can do twice work in one hour as compared to one woman, find the number of hours to type 200 pages by 10 women.
   A) 12
   B) 7
   C) 6
   D) 8.5
   E) 10
   

   Answer & Explanation

   B) 7
   Explanation:
   Given 1 m = 2 w. So 2 m = 4w
   2m+3w 100 pages in 5 hrs, so 4w+3w = 7 women 100 pages in 5 hours. So
   M1*H1*W2 = M2*D2*H2*W1
   7*5*200 = 10*H2*100
   Solve H2 = 7
   
   
   
4. Fruits were purchased for Rs 350. 9 boys ate 3/5th of them in 2 hours. 6 boys feel their stomach as full so do not eat further. In how many hours the remaining fruits will get finished by remaining boys?
   A) 2 hours
   B) 3 hours
   C) 5 hours
   D) 4 hours
   E) 6 hours
   

   Answer & Explanation

   D) 4 hours
   Explanation:
   Remaining boys = 3, remaining fruits = 2/5th
   Eating is work here. So
   M1*H1*W2 = M2*H2*W1
   9*2*(2/5) = 3*H2*(3/5)
   Solve, H2 = 4
   
   
   
5. 100 men were to complete a piece of work in 20 days. After they worked for 10 days, 60 more men were employed to complete the work on time. If additional men were not employed, then how many days behind schedule the work would be finished?
   A) 12
   B) 8
   C) 10
   D) 6
   E) None of these
   

   Answer & Explanation

   D) 6
   Explanation:
   Let 100 men complete x work in 10 days after which (100+60) = 160 men complete the remaining (1-x) work in remaining 10 days [Total work to be completed in 20 days]
   So, M1*D1*W2 = M2*D2*W1
   100*10*(1-x) = 160*10*x
   Solve, x= 5/13
   This means that initially employed 100 men can finish 5/13th of work in 10 days, so let they will complete 1 whole work in x days.
   M1*D1*W2 = M2*D2*W1
   100*10*1 = 100*x*(5/13)
   Solve, x = 26
   This means extra (26-20) = 6 days will be required if additional men are not employed after 10 days.
   
   
6. If 2 men or 5 women can complete a work in 15 days, then in how many days 4 men and 5 women will complete the same work?
   A) 7
   B) 12
   C) 8
   D) 5
   E) 10
   

   Answer & Explanation

   D) 5
   Explanation:
   2 m or 5 w
   4m + 5w
   Cross multiply and put in denominator
   Days = 15*2*5/ [2*5 +5*4]
   
   
   
7. To do a certain work in 9 days, some men were employed. All came on the first day, but after seeing that there is too much labor for the work, 6 men left the work after 1 day. If the work is now completed in 6 days more than the scheduled time, how many men were initially employed?
   A) 14
   B) 15
   C) 20
   D) 18
   E) 12
   

   Answer & Explanation

   A) 14
   Explanation:
   After 1 day, x men were to work for 8 days, but 6 men left, now (x-6) men will complete the same remaining work in (8+6) = 14days.
   So x*8 = (x-6)*14
   Solve, x = 14
   
   
   
8. A pipe filled 4/5th of a cistern in 10 minutes. How much more time will it take to fill the rest?
   A) 2 minutes
   B) 2.5 minutes
   C) 3 minutes
   D) 3.5 minutes
   E) 2 minutes
   

   Answer & Explanation

   B) 2.5 minutes
   Explanation:
   1/5 * 10 = (4/5) * x
   x = 5/2
   
   
9. 30 women complete the 2/5th work in 40 days working 6 hours each day. If 10 women leave, in how many days the remaining work will get completed if now they work for 10 hours each day?
   A) 62
   B) 58
   C) 54
   D) 70
   E) 45
   

   Answer & Explanation

   C) 54
   Explanation:
   30*40*6*(3/5) = 20*D2*8*(2/5)
   D2 = 54
   
   
10. In a refugee camp, 20 people are provided food which was given for 5 days. 10 people left this group after 2 days, and it was found that the remaining food lasted for 3 days for remaining people. If the people would not have left, how many days the food would have been lasted?
    A) 4 days
    B) 3.5 days
    C) 3 days
    D) 4.5 days
    E) None of these
    

    Answer & Explanation

    B) 3.5 days
    Explanation:
    After 2 days, let x food was left, which means that 10 people ate x food for 3 days, so let us find the number of days for which x food has lasted for 20 people.
    Eating burgers will be considered as a work. So
    M1*D1*W2 = M2*D2*W1
    10*3*x = 20*D2*x
    Solve D2 = 3/2
    So 20 people first ate the food for 2 days, after it the remaining food they would have eaten in 3/2 days more so total (2 + 3/2) days