Time & Work- 1 - Free MCQ Practice Test with solutions, GATE ME General

He will complete the work in 20 days. Hence, he will complete ten times the work in 200 days.

N + A = 10%
N = 8.33%
Hence A = 1.66% Æ 60 days.

The data is insufficient, since we only know that the work gets completed in 200 boy days and 300 women days.

In 5 days, A would do 25% of the work. Since, B finishes the remaining 75% work in 10 days, we
can conclude that B’s work in a day = 7.5%
Thus, (A + B) = 12.5% per day.
Together they would take 100/12.5 = 8 days.

Total man days required = 600 man days. If 5 workers leave the job after ‘n’ days, the total work
would be done in 35 days. We have to find the value of ‘n’ to satisfy:
20 × n + (35 – n) × 15 = 600.
Solving for n, we get
20n – 15n + 35 × 15 = 600
5n = 75
n = 15.

Subhash can copy 200 pages in 40 hours (reaction to the first sentence). Hence, Prakash can copy
100 pages in 40 hours. Thus, he can copy 30 pages in 30% of the time: i.e. 12 hours.

Sashi = 4%, Rishi = 5%. In five days, they do a total of 45% work. Rishi will finish the remaining
55% work in 11 more days.

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 Æ t = 1. Thus, Manoj would take 6t = 6 days to complete the work.

Raju being twice as good a workman as Vijay, you can solve the following equation to get the
required answer:
1/R + 1/2R = 1/14.
Solving will give you that Vijay takes 42 days.

12 × 5 man days + 16 × 5 Boy days
= 13 × 4 man days + 24 × 4 Boy days
Æ 8 man days = 16 Boy days
1 man day = 2 Boy days.
Required ratio of man’s work to boy’s work = 2 : 1.

Work equivalence method:
30 × 5 × 16 = 20 × 6 × n
Gives the value of n as 20 days

Total work = 15 × 210 = 3150 man days.
After 100 days, work done = 15 × 100 = 1500 man days.
Work left = 3150 – 1500 = 1650 man days.
This work has to be done with 30 men working each day.
The number of days (more) required = 1650/30 = 55 days.

After 27 days, food left = 4 × 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.

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.

A + V = 16.66% and A = 10% Æ V = 6.66%. Consequently Vijay would require 100/6.66 = 15
days to do it alone.