Practice Test: Time & Work - 1 - CAT MCQ

Since P to R is double the distance of P to Q,
Therefore, it is evident that the time taken from P to R and back would be double the time taken from P to Q and back (i.e. double of 6.5 hours = 13 hours).

Since going from P to R takes 9 hours, coming back from R to P would take 4 hours i.e. 13- 9 = 4

So Option A is correct

Given:

A and B together can do a piece of work in 50 days.

A is 40% less efficient than B

Concept used:

Total work = Efficiency of the workers × time taken by them

Calculation:

Let the efficiency of B be 5a

So, efficiency of A = 5a × 60%

⇒ 3a

So, total efficiency of them = 8a

Total work = 8a × 50

⇒ 400a

Now,

60% of the work = 400a × 60%

⇒ 240a

Now,

Required time = 240a/3a

⇒ 80 days

∴ A can complete 60% of the work working alone in 80 days.

Let Entire work be W
Now Anil worked for 24 days
Bimal worked for 14 days and Charu worked for 14 days .
Now Anil Completes W in 60 days
so in 24 days he completed 0.4W
Bimal completes W in 84 Days
So in 14 Days Bimal completes = W/6
Therefore work done by charu 
Therefore proportion of Charu = 13/30 x 21000 = 9100

Since time taken to finish work is in the ratio 5:8:10

So efficiency will be in the ratio 40/5:40/8:40/10 = 8:5:4

So, Anu does 8 units per hour, Tanu does 5 and Manu does 4.

Total work = 4*8*(8+5+4) = 544

Work done by Anu and Tanu =  6*6.67*(8+5) = 520

Work remaining = 544 – 520 = 24

Time taken by Manu to complete = 24/4 = 6 hours

• X’s five day work = 5/20 = 1/4. Remaining work = 1 – 1/4 = 3/4.
• This work was done by Y in 15 days. Y does 3/4th of the work in 15 days, he will finish the work in 15 × 4/3 = 20 days.  
• X & Y together would take 1/20 + 1/20 = 2/20 = 1/10 i.e. 10 days to complete the work.

So Option C is correct

As machine B's effciency is twice as of A's, Hence, it will complete its work in 30 hours.

And C's effciency is putting A and B together i.e. = 20 hours ((1/60 + 1/30)^-1)

Now if all three work together, then it will be completed in x (say) days.

or x = 10 hours

Money will be distributed in the ratio of work done in an hour.
i.e. 1/6 : 1/8 : 1/15
or 20:15:8
Hence part of A will be = 20/43 × 94.6 = 44
part of B will be = 15/43 ×  94.6 = 33
part of C will be = 8/43 × 94.6 = 17.60

Now Anil Paints in 12 Days
Barun paints in 16 Days
Now together Arun , Barun and Chandu painted in 6 Days
Now let total work be W
Now each worked for 6 days
So Anil's work = 0.5W
Barun's work = 6W/16 = 3W/8
Therefore Charu's work = W/2 - 3W/8 = W/8
Therefore proportion of charu = 24000/8 = 3000

Let the total amount of work in filling a cistern be 24 units. (LCM of 3, 4 and 8)

Work done by pipe 1 in 1 hour = 24/3 = 8 units.

Work done by pipe 2 in 1 hour = 24/4 = 6 units.

Work done by pipe 3 in 1 hour = 24/ (-8) = -3 units

Total work done in 1 hour = 8 + 6 – 3 = 11 units

The time required to complete 11/12^th of the work = 11/12 × 24/ 11 = 2 hours

∴ The correct answer is 2 hours.

Let the time taken by the outlet pipe to empty = x hours
Then,

=> x+ 40
Hence time taken by the outlet pipe to make the tank half-full = 40/2 = 20 hour