Directions: Read the following information to answer the question.
Solution:
Machine I:
Number of nuts produced in one minute = 100
To produce 1000 nuts time required =10 min
Cleaning time for nuts =5 min
Over all time to produce 1000 nuts =15 min.
Over all time to produce 9000=138 min −5 min =133 min -----(1)
Machine II:
To produce 75 bolts time required =1min
To produce 1500 bolts time required =20 min
Cleaning time for bolts =10 min.
Effective time to produce 1500 bolts =30 min
Effective time to produce 9000 bolts =30×6−10=170 min ------ (2)
From (1) and (2)
Minimum time = 170 minutes
Directions: Read the following information to answer the question.
Solution:
Ram takes 24 days to complete the work, if he works alone.
As Krish is twice as efficient as Ram is, Krish will take half the time to complete the work when Krish works alone, i.e., in 12 days.
Ram completes (1/24)th of the work in a day.
Krish completes (1/12)th of the work in a day.
When they work together, they will complete 1/24+1/12=1+2/24=1/8 work in a day.
Therefore, when they work together they will complete the work in 8
Directions: Read the following information to answer the question.
As X started chasing the thief after 15 minutes, the thief had gained (15/60)60 = 15 km over X. the relative speed between the thief and X is 65 - 60 = 5 kmph. So, the time taken by X to catch the thief is 15/5 = 3 hours. As X had started the chase at 12.15 p.m. he caught the thief at 3.15 p.m.
Consider when 4 comes at unit's place.
total number of 4 digit numbers that can be formed
4
2 2 1
= 2 × 2 = 4
Thus, the digit 4 will come at the unit's place 4 times.
Same can be said of digits 1 and 2.
∴ sum of unit's digit column (when all possible numbers of 4 digit using 0, 1, 2 are written one below the
other)
= 4 × 4 + 4 × 2 + 4 × 1 = 28
same will be for hundred's and ten's column.
In case of 1, 2 or 4 coming in thousand's place, total number of numbers that can be formed
⇒
4
3 2 1
= 3 × 2 = 6
in thousand's column, 4 will come 6 times and so will and 2.
We can now write the sum as.
Thousand’s
4 5
6×4
6×2
6×1
Hundred’s
3 1
4×4
4×2
4×1
Ten’s
3 0
4×4
4×2
4×1
One’s
2 8
4×4
4×2
4×1
3 3 2 (note: zeros may
come in any column
any number of
times and still will
not affect the sum)
Thus the answer is 45108.