Question for Practice Questions Level 1: Time & Work - 2
Try yourself:P, Q and R are employed to do a piece of work for Rs. 529. P and R are supposed to finish 19/23 of the work together. How much shall be paid to Q?
Explanation
Work done by Q
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:It was expected that 10 men together would complete a piece of work in 40 days. But after a few days, they increased their efficiency by 25% and completed the work six days earlier. How many days after the start of the work did they increase their efficiency?
Explanation
Assume each man could do 'x' work in 1 day.
So, total work = 10 × 40x = 400x
But they completed the work in 34 days (40 - 6).
Assume after 'd' days, they increased their efficiency.
After increasing the efficiency, they could do 1.25x work in 1 day.
So, 400x = 10 × d × x + 10 (34 - d)1.25x.
⇒ 40 = d + (34 - d)1.25
⇒ 0.25d = 2.5 d = 10
Thus, they increased their efficiency 10 days after the start of the work.
Hence, answer option 4 is correct.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:A swimming pool is filled with water through four pipes, and there is an outlet pipe which can empty the pool in 30 minutes. The first pipe can fill the pool in 40 minutes; the second and third pipes can fill it in 15 minutes; the second and fourth pipes can fill it in 25 minutes; and the third and fourth pipes can fill it in 12 minutes. In what time will the pool be filled if all the five pipes are working simultaneously?
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Raju can do 25% of a piece of work in 5 days. How many days will he take to complete the work ten times?
Explanation
He will complete the work in 20 days. Hence, he will complete ten times the work in 200 days.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:A can do a piece of work in 20 days and B can do it in 15 days. How long will they take if both work together?
Explanation
A’s one day work will be 5%, while B will do 6.66 % of the work in one day. Hence, their total work will be 11.66% in a day.
In 8 days they will complete → 11.66 x 8 = 93.33%
This will leave 6.66% of the work. This will correspond to 4/7 of the ninth day since in 6.66/11.66 both the numerator and the denominator are divisible by 1.66.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Nishu and Archana can do a piece of work in 10 days and Nishu alone can do it in 12 days. In how many days can Archana do it alone?
Explanation
N + A = 10%
N = 8.33%
Hence A = 1.66% → 60 days.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?
Explanation
24 man days + 18 women days = 20 man days + 28 woman days
→ 4 man days = 10 woman days.
→ 1 man day = 2.5 woman days
Total work = 24 man days + 18 woman days = 60 woman days + 18 woman days = 78 woman days.
Hence, 1 man + 1 woman = 3.5 women can do it in 78/3.5 = 156/7 = 22(2/7) days.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:A can do a piece of work in 10 days and B can do the same work in 20 days. With the help of C, they finish the work in 5 days. How long will it take for C alone to finish the work?
Explanation
A = 10%, B = 5% and Combined work is 20%. Hence, C’s work is 5% and will require 20 days.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:A and B undertake to do a piece of work for ₹ 100. A can do it in 5 days and B can do it in 10 days. With the help of C, they finish it in 2 days. How much should C be paid for his contribution?
Explanation
A = 20%, B = 10% and A + B + C = 50%. Hence, C = 20%. Thus, in two days, C contributes 40% of the total work and should be paid 40% of the total amount.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Arun and Vinay together can do a piece of work in 7 days. If Arun does twice as much work as Vinay in a given time, how long will Arun alone take to do the work.
Explanation
Let the time taken by Arun be ‘t’ days. Then, time taken by Vinay = 2t days. 1/t + 1/2t = 1/7 → t = 10.5
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:X number of men can finish a piece of work in 30 days. If there were 6 men more, the work could be finished in 10 days less. What is the original number of men?
Explanation
30X = 20 (X + 6) → 10X = 120 → X = 12.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Raju can do a piece of work in 10 days, Vicky in 12 days and Tinku in 15 days. They all start the work together, but Raju leaves after 2 days and Vicky leaves 3 days before the work is completed. In how many days is the work completed?
Explanation
Raju = 10%, Vicky = 8.33% and Tinku = 6.66%. Hence, total work for a day if all three work = 25%.
In 2 days they will complete, 50% work. On the third day onwards Raju doesn’t work. The rate of work will become 15%. Also, since Vicky leaves 3 days before the actual completion of the work, Tinku works alone for the last 3 days (and must have done the last 6.66 x 3 = 20% work alone). This would mean that Vicky leaves after 80% work is done. Thus, Vicky and Tinku must be doing 30% work together over two days.
Hence, total time required = 2 days (all three) + 2
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Manoj takes twice as much time as Anjay and thrice as much as Vijay to finish a piece of work. Together they finish the work in 1 day. What is the time taken by Manoj to finish the work?
Explanation
Let Anjay take 3t days, Vijay take 2t days and Manoj take 6t days in order to complete the work. Then we get: 1/3t +
1/2t + 1/6t = 1 → t = 1. Thus, Manoj would take 6t = 6 days to complete the work.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Apurva can do a piece of work in 12 days. Apurva and Amit complete the work together and were paid ₹ 54 and ₹ 81 respectively. How many days must they have taken to complete the work together?
Explanation
Since the ratio of money given to Apurva and Amit is 2:3, their work done would also be in the same ratio. Thus, their time ratio would be 3:2 (inverse of 2:3). So, if Apurva takes 12 days, Amit would take 8 days and the total number of days required (t) would be given by the equation:
(1/12 + 1/8)t = 1 → t = 24/5 = 4.8 days
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:In a company XYZ Ltd. a certain number of engineers can develop a design in 40 days. If there were 5 more engineers, it could be finished in 10 days less. How many engineers were there in the beginning?
Explanation
40n = 30 (n + 5) → n = 15
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:A can do a work in 10 days and B can do the same work in 20 days. They work together for 5 days and then A goes away. In how many more days will B finish the work?
Explanation
A’s rate of working is 10 per cent per day while B’s rate of working is 5 per cent per day. In 5 days they will complete 75 per cent work. Thus the last 25 per cent would be done by B alone. Working at the rate of 5 per cent per day, B would do the work in 5 days.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Ajay and Vijay undertake to do a piece of work for ₹ 200. Ajay alone can do it in 24 days while Vijay alone can do it in 30 days. With the help of Pradeep, they finish the work in 12 days. How much should Pradeep get for his work?
Explanation
Ajay’s daily work = 4.1666%, Vijay’s daily work = 3.33% and the daily work of all the three together is 8.33%. Hence, Pradeep’s daily work will be 0.8333%. Hence, he will end up doing 10% of the total work in 12 days. This will mean that he will be paid ₹ 20.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Ajay, Vijay and Sanjay are employed to do a piece of work for ₹ 529. Ajay and Vijay together are supposed to do 19/23 of the work and Vijay and Sanjay together 8/23 of the work. How much should Ajay be paid?
Explanation
A + V + S = 1 (1)
A + V = 19/23
V + S = 8/23
→ A + 2V + S = 27/23 (2)
(2)–(1) gives us: V = 4/23.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:In a fort there was sufficient food for 200 soldiers for 31 days. After 27 days 120 soldiers left the fort. For how many extra days will the rest of the food last for the remaining soldiers?
Explanation
After 27 days, food left = 4 x 200 = 800 soldier days worth of food. Since, now there are only 80 soldiers, this food would last for 800/80 = 10 days.
Number of extra days for which the food lasts = 10 – 4 = 6 days.
Question for Practice Questions Level 1: Time & Work - 2
Try yourself:Ajay and Vijay can do a piece of work in 28 days. With the help of Manoj, they can finish it in 21 days. How long will Manoj take to finish the work all alone?
Explanation
Ajay + Vijay = 1/28 and Ajay + Vijay + Manoj = 1/21.
Hence, Manoj = 1/21 – 1/28 = 1/84.
Hence, Manoj will take 84 days to do the work.