Among four persons Prince, Queen, Raj and Sashi. Prince takes thrice as much time as Queen to complete a piece of work. Queen takes thrice as much time as Raj and Raj takes thrice as much time as Sashi to complete the same work. One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days.

Answer: B From the given information Q is thrice as efficient as P. R is thrice as efficient as Q. S is thrice efficient as R. If work done by P in a day is 'n' units, the work done in a day by Q, R and S would be 3n,9n and 27n units respectively. It can be seem that, P,Q and R working together can do 13n units in a day while P,Q and S working together can do 31n units in a day. Hence, the ratio of times taken to complete the work by the former and later groups is 31:13 P,Q and S take 13 days.

Q. No. 2:

A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 400 nuts per minute and need to be cleared for 15 minutes after production of 2000 nuts. The machine producing only bolts produces 300 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 12000 pairs of bolts and nuts if both machines are operated simultaneously.

Answer: B The nut machine makes 400 nuts per min and 2000 nuts in 5 min. Then it has to be cleared for 15 min To produce 12,000 nuts, time required = 5(20)+ 15 = 105 min The bolt machine makes 300 bolts per min and 3000 bolts in 10 min Then it has to be cleared for 15 min To produce 12000 bolts, time required = 3(25)+ 10 = 85 min In both the cases, we may ignore the time needed for cleaning, after the last lots are produced. We see that the time required is 105 min.

Q. No. 3:

Abhishek starts to paint a fence on one day. On the second day, two more friend of Abhishek join him. On the third day 3 more friends of him join him and so on. If the fence is completely painted this way in exactly 20 days, then find the number of days in which 10 girls painting together can paint the fence completely, given that every girl can paint twice as fast as Abhishek and his friends(Boys)?(Assume that the friends of Abhishek are all boys).

Answer: D The number of boys-days => 1/2[1+ (1+2)+(1+2+3)+.,.................+(1+2+3+....+20)]= 1440 => But , each boy =1/2 girls=> 770 girl-days. 10 girls will take 770/10 = 77 days.

Q. No. 4:

A man takes 20 days to reach the point B under normal circumstances. But, due to the increasingly hostile weather conditions the distance they travel every day reduces by 20%. In how many days would the man reach the point B, taking into consideration weather conditions?

Answer: D Let the total distance to be covered be d On each day under normal weather conditions they travel 'd/20' of the distance. On 1st day they would travel = d/20 On 2nd day they would travel = 0.8 * d/20 On 3rd day they would travel = 0.8* (0.8*d/20) Let he will reach the point B in nth day => d/20 + 0.8d/20 + 0.8^{2}d/20+...................+0.8^{n}d/20 = d => d/20* (-(0.8)^{n}+1)/(-0.8+1) = d => 1- (0.8)^{n} = 4(0.8)^{n} = -3 Since (0.8)^{n} >0, thus it is never equal to -3 The man will never reach the point B.

Q. No. 5:

A work is done by 30 workers not all of them have the same capacity to work. Every day exactly 2 workers, do the work with no pair of workers working together twice. Even after all possible pairs have worked once, all the workers together works for two more days to finish the work. Find the number of days in which all the workers together will finish the whole work?

Answer: A 30 workers work in pairs, with no same pair of workers working together. Each worker will be working with other 29 which means each workers will work for 29 days in pair. Let the time taken by each worker be W1, W2, W3..........W30 respectively According to Question {work done when the workers work in pairs}+{work done when all the woorkers work together for two days}= 1 29[1/W1 + 1/W2 + 1/W3. ....1/W30] + 2[1/W1+ 1/W2+ 1/W3+....1/W30] =1 => [1/W1 + 1/W2 + 1/W3 + .............1/W30] = 1/31. If all the workers work together they will finish the whole work in 31 days.

Q. No. 6:

There are four varieties of pipes Pipe A, Pipe B, Pipe C and Pipe D. Each pipe can be either an inlet pipe or an outlet pipe but cannot be both. there are 5 tanks of equal volume. Tank P is filled by Pipe A and Pipe B Tank Q is filled by Pipe A and Pipe C Tank R is filled by Pipe A and Pipe D Tank S is filled by Pipe B and Pipe C Tank T is filled by Pipe C and Pipe D Time taken for the first 3 tanks(P, Q and R) to get filled are in the ratio 1:2:4 and the time taken for the S and T tanks to be filled are in the ratio 7:10. Find the outlet pipes among the 4 varieties.

Answer: D Let A,B,C and D do a,b,c and d with of work in an hour. Let A and B fill the tank in 1 hour. Then A and C would fill the tank in 2 hours while A and D in 4 hours. a+b =1 ..........(i) a+c=1/2.........(ii) a+d = 1/4.......(iii) Let B and C take 7k hours while c and D take 10k hours to fill the tank => b+c = 1/7k..............(iv) c+d= 1/10k...................(v) a = {(i)+(ii)-(iv)}/(ii) = {(ii) + (iii) - (v)}/(ii) a = {1+1/2-1/7k}/2 = {1/2+1/4-1/10k}/2............(vi) => k= 4/70 On substituting value of k in equation(vi) we get a < 0 => a<0, b>0, c>0 and d>0 Hence only A is the only outlet pipe.