1. George and Mark can paint 720 boxes in 20 days, Mark and Harry in 24 days and Harry and George in 15 days. George works for 4 days, Mark for 8 days and Harry for 8 days. The total number of boxes painted by them is
Capacities of these people as followes
G + M = 720/20 = 36
M + H = 720/24 = 30
H + G = 720/15 = 48
Adding all above we get 2(G + M + H ) = 114 ⇒ G + M + H = 114/2 = 57
Now individual capacities are given below
G = 27 ; M = 9; H = 21
So 27 × 4 + 9 × 8 + 21 × 8 = 348
2. 4 men can check exam papers in 8 days working 5 hours regularly. What is the total hours when 2 men will check the double of the papers in 20 days?
Explaination: Let a man can do 1 unit of work in 1 hour.
Total units of work = 4 x 8 x 5 = 160 units.
Now work = 2 x 160 = 320 units.
Now 2 men work for 20 days. Let in x hours they have to work per day.
Now total work = 2×x×20 = 40 x
40x = 320 So x = 320/40 = 8 hours.
3.Tony alone can paint a wall in 7 days and his friend Roy alone can paint the same wall in 9 days. In how many days they can paint the wall working together? Round off the answer to the nearest integer.
Answer: Option B
Sol. use formula (xy / x+y)
So nearest value for 3.93 = 4
4.Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in
a. 96 days
b. 48 days
c. 32 days
d. 24 days
Answer : b
Explanation: Simple one. Let the total work to be done is 48 meters. Now Jake can dig 3 mts, Paul can dig 2 mts a day. Now all of them combined dug in 8 days so per day they dug 48/8 = 6 mts. So Of these 8 mts, Hari capacity is 1 mt.
So he takes 48 /1 = 48 days to complete the digging job.
5.Rajiv can do a piece of work in 10 days , Venky in 12 days and Ravi in 15 days. They all start the work together, but Rajiv leaves after 2 days and Venky leaves 3 days before the work is completed. In how many days is the work completed ?
Explanation: Let the work be 60 units. If venky leave 3 days before the work, Last 3 days must be worked by Ravi. So the remaining days of work be x days, total days to complete the work be x + 3 days.
Now Capacities of Rajiv is 60/10 = 6, Venky is 5, Ravi is 4.
(6 + 5 + 4) 2 + (5 + 4) (x – 3) + 4 x 3 = 60.
30 + 9x – 27 + 12 = 60
9x – 15 =30
9x = 45
x = 5
So total days to complete the work = 2 + 5 = 7 days.
6.A man has a job, which requires him to work 8 straight days and rest on the ninth day. If he started work on Monday, find the day of the week on which he gets his 12th rest day.
He works for 8 days and takes rest on the 9th day. So On the 12th rest day, there are 9 x 12 = 108 days passed. Number of odd days = (108 – 1) / 7 = 107 / 7 = 2. So the 12th rest day is wednesday.
7.B alone can do piece of work in 10 days. A alone can do it in 15 days. If the total wages for the work is Rs 5000, how much should B be paid if they work together for the entire duration of the work?
Explaination:Time taken by A and B is in the ratio of = 3:2
Ratio of the Work = 2 : 3 (since, time and work are inversely proportional)
Total money is divided in the ratio of 2 : 3 and B gets Rs.3000
8.If twenty four men and sixteen women work on a day, the total wages to be paid is 11,600. If twelve men and thirty seven women work on a day, the total wages to be paid remains the same. What is the wages paid to a man for a day’s work?
Explaination: Let man daily wages and woman daily wages be M and W respectively
solving the above equations gives M=350 and W=200
9.The water from one outlet, flowing at a constant rate, can fill the swimming pool in 9 hours. The water from second outlet, flowing at a constant rate can fill up the same pool in approximately in 5 hours. If both the outlets are used at the same time, approximately what is the number of hours required to fill the pool?
Explaination: Assume tank capacity is 45 Litres. Given that the first pipe fills the tank in 9 hours. So its capacity is 45 / 9 = 5 Litres/ Hour. Second pipe fills the tank in 5 hours. So its capacity is 45 / 5 = 9 Litres/Hour. If both pipes are opened together, then combined capacity is 14 litres/hour. To fill a tank of capacity 45 litres, Both pipes takes 45 / 14 = 3.21 Hours.
10.J can dig a well in 16 days. P can dig a well in 24 days. J, P, H dig in 8 days. H alone can dig the well in How many days?
Answer: bAssume the total work = 48 units.
Explaination: Capacity fo J = 48 / 16 = 3 units / day
Capacity of P = 48 / 24 = 2 units / day
Capacity of J, P, H = 48 / 8 = 6 units / day
From the above capacity of H = 6 – 2 – 3 = 1
So H takes 48 / 1 days = 48 days to dig the well