31. P,Q and R three typists who working simultaneously can type 216 pages in 4 hours.In one hour R can type as many pages more than Q as Q can type more than P.During a period of 5 hours R can type many pages as P can during 7 hours. How many pages does each of them type per hour?

A. 14,17,20 B. 15,17,22 C. 15,18,21 D. 16,18,22

Answer Answer: Option C Explanation: Let the number of pages typed in one hour by P,Q, and R be x,y, and z respectively.
x+y+z = 216/4 = x+y+z = 54 .........(1)
z-y = y-x = 2y = x+z .........(2)
5z = 7x = x = 5/7z .........(3)
solving (1) (2) and (3) we get x = 15; y= 18 ; z = 21

32. 2 men and 3 boys can do a piece of work in 10 days while 3 men and 2 boys can do the same work in 8 days.In how many days can 2 men and 1 boy do the work?

A. 13 1/2 days B. 13 days C. 12 1/2 days D. 10 days

Answer Answer: Option C Explanation: Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y then,
2x+3y = 1/10 and 3x+2y = 1/8
solving we get : x= 7/200 and y = 1/100
(2 men + 1 boy)'s 1 day work = (2*7/200+ 1*1/100) = 16/200 = 2/25
so 2 men and 1 boy together can finish the work in 25/2 = 12 1/2 days.

33. 45 men can complete a work in 16 days. Six days after they started working 30 more men joined them.How many days will they now take to complete the remaining work?

A. 5 days B. 7 days C. 8 days D. 6 days

Answer Answer: Option D Explanation: (45*16) men can complete a work in 1 day
1 man's 1 day's work = 1/720
45 men's 6 day's work =(1/16*6) = 3/8, Remaining work = ( 1- 3/8) = 5/8
75 men's 1 day's work = 75/720 = 5/48
Now 5/48 work is done by them in 1 day
5/8 work is done by them in(48/5*5/8) = 6 days

34. A and B undertake to do a piece of work for Rs.600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C they finish it in 3 days.Find the share of each?

A. Rs.65 B. Rs.68 C. Rs.75 D. Rs.70

Answer Answer: Option C Explanation: C's 1 day's work = 1/3 - (1/6 + 1/ 8) = 1/24
A: B : C = ratio of their 1 day's work = 1/6: 1/8 : 1/24 = 4 : 3: 1
A's share = Rs.(600 * 4/8) = Rs.300, B's share = Rs.(600*3/8) = Rs.225
C's share = Rs.[(600-(300+225)] = Rs.75

35. A can do a piece of work in 80 days.He works at it for 10 days and then B alone finishes the remaining work in 42 days.In how much time will A and B working together finish the work?

A. 25 days B. 30 days C. 32 days D. 26 days

Answer Answer: Option B Explanation: Work done by A in 10 days = (1/80 * 10) =1/8
Remaining work = (1- 1/8) = 7/8
Now 7/8 work is done by B in 42 days
Whole work will be done by B in (42*8/7) = 48 days
A's 1 day's work = 1/80 and B's 1 day's work = 1/48
(A+B)'s 1 day's work = (1/80 + 1/48) = 8/240 = 1/30
Hence both will finish the work in 30 days.