Directions: Each question below contains a statement followed by Quan...
Quantity I: Ram can do a piece of work in 20 days. If the efficiency of Ram is 66.67% of the efficiency of Mohan and the efficiency of Mohan is 25% less than the efficiency of Prakash, then how long will Prakash take to do the same piece of work?
Quantity II: A person can type 50 pages in 10 hours. How many days will he take to type a book of 1320 pages? [Assume the person works continuously for 24 hours/day]
To solve this problem, we need to calculate the efficiency of Ram, Mohan, and Prakash and then find the time taken by Prakash to complete the work.
Let's analyze Quantity I first:
Quantity I: Ram can do a piece of work in 20 days.
This means that Ram's work rate is 1/20 of the work per day.
Now, let's find the efficiency of Mohan:
Ram's efficiency is 66.67% of Mohan's efficiency.
So, Mohan's efficiency is 100% (100/66.67) times Ram's efficiency.
Therefore, Mohan's efficiency is (100/66.67) * (1/20) = 0.075 of the work per day.
Next, let's find the efficiency of Prakash:
Mohan's efficiency is 25% less than Prakash's efficiency.
So, Prakash's efficiency is 100% (100/75) times Mohan's efficiency.
Therefore, Prakash's efficiency is (100/75) * 0.075 = 0.1 of the work per day.
To find the time taken by Prakash to do the same piece of work:
Prakash's work rate is 0.1 of the work per day.
So, Prakash will take 1 / 0.1 = 10 days to do the same piece of work.
Now, let's analyze Quantity II:
Quantity II: A person can type 50 pages in 10 hours.
This means that the person's work rate is 50/10 = 5 pages per hour.
To find the time taken by the person to type a book of 1320 pages:
The person's work rate is 5 pages per hour.
So, the person will take 1320 / 5 = 264 hours to type the book.
Since we assumed that the person works continuously for 24 hours/day, the person will take 264 / 24 = 11 days to type the book.
Comparing Quantity I and Quantity II:
Quantity I = 10 days
Quantity II = 11 days
Therefore, Quantity I < quantity="" />
Hence, the correct answer is option 'A' (Quantity I > Quantity II).
Directions: Each question below contains a statement followed by Quan...
Quantity I:
Ram can do a work in 20 days.
Efficiency of Ram = 66.67% of efficiency of Mohan
So Mohan can do the same work in 20 x (3/2) days = 30 days
Now, Efficiency of Mohan = 75% of efficiency of Prakash
So Prakash can do the same work in 30 x 100/75 = 40 days.
Quantity II:
A person can type 50 pages in 10 hours.
So, a person can type 50/10 pages in 1 hour = 5 pages
Hence, a person a type (5 x 24) in 1 day (24 hours) = 120 pages
120 pages can be typed in 24 hours or 1 day
Similarly, 1320 pages can be typed in = (1/120) x 1320 = 11 days
Hence, Quantity I > Quantity II