Given below are two statements:
Statement (I):
4 boys and 8 girls completed 1/3 of work in 5 days. After that 3 boys and 3 girls increased, and they completed another 1/3 of work in 3 days. If the remaining work is to be completed in 2 days, then the number of girls that should be increased is 32.
Statement (II):
The ratio of time taken by A and C to do a work is 1:2 respectively. B is 166 (2/3)% more efficient than C. Time taken by A to complete 6% of work is 6 days.
Then, the time taken by B and C together to complete the whole work is 54 (6/11) days.
In light of the above statements, choose the most appropriate answer from the options given below.
Given below are two statements:
Statement (I):
4 boys and 8 girls completed 1/3 of work in 5 days. After that 3 boys and 3 girls increased, and they completed another 1/3 of work in 3 days. If the remaining work is to be completed in 2 days, then the number of girls that should be increased is 32.
Statement (II):
The ratio of time taken by A and C to do a work is 1:2 respectively. B is 166 (2/3)% more efficient than C. Time taken by A to complete 6% of work is 6 days.
Then, the time taken by B and C together to complete the whole work is 54 (6/11) days.
In light of the above statements, choose the most appropriate answer from the options given below.
Solution
Statement I:
Initial configuration:
boys + girls = work per day
Complete work in days
So: ...(1)
Second configuration:
boys + girls = work per day
Complete work in days
So: ...(2)
Final requirement:
boys + girls = work per day
Need to complete work in days
So: ...(3)
The proportions don't maintain consistency when solved.
Statement II:
Let's establish relationships:
- A:C = means C's efficiency = × A's efficiency
- B is more efficient than C means B = × C's efficiency
- A takes days for work, so days for full work
For B&C together:
- C does unit work per day
- B does units work per day
- Together they do units per day
- Time taken = days
This checks out mathematically.
Therefore, Statement I is false but Statement II is true.