GATE Questions

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Let M, N and O worked together for x days.

From the given data,
M alone worked for 8 days
M,N,O worked for x days
N, O worked for 1 day

But given that
M alone can complete the work in 18 days
N alone can complete the work in 36 days
O alone can complete the work in 54 days

The total work can be the LCM of 18, 6, 54 = 108 units

M's 1 day work = 108/18 = 6 units
N's 1 day work = 108/36 = 3 units
O's 1 day work = 108/54 = 2 units

Now, the equation is
8 x 6 + 11x + 5 x 1 = 108
48 + 11x + 5 = 108
11x = 103 - 48
11x = 55
x = 5 days.

Hence, all M,N and O together worked for 5 days.

Since T is the brother of Q
Therefore, P is the father of T
but S is the wife of T.
Hence, S is the daughter-in-law of P.

From the given data,

K's profit : L's profit = 7x x 11 : 9x x 7

= 11:9

Therefore, L's profit = 9 x 2460/20 =  Rs. 1107

Reduction in consumption
= P100+P X 100%
= 25100+25 X 100%
= 20%

The Battle of Plassey in the year 1757, victory of British East India company over Nawab of Bengal established British supremacy in India. The victory came under the leadership of Robert Clive.

Average speed = Total distance / Total time.

Total distance traveled by Joel = Distance covered in the first 3 hours + Distance covered in the next 5 hours.

Distance covered in the first 3 hours = 3 x 60 = 180 miles
Distance covered in the next 5 hours = 5 x 24 = 120 miles

Therefore, total distance traveled = 180 + 120 = 300 miles.

Total time taken = 3 + 5 = 8 hours.

Average speed = 300/8 = 37.5 mph.

we know that 1 mile = 1.6 kms

=> 37.5 miles = 37.5 x 1.6 = 60 kms

Average speed in Kmph = 60 kmph.

Given a secret is told to 3 persons in 3 minutes.
And if the process continues with each person saying 3 other persons,
In 30 minutes => the rocess for 10 times because each person time is 3 minutes.
Required number of persons = 3 + 32 + 33 + .... + 39 + 310

Now it forms a geometric progression,

Sum to n terms is S = arn - 1r - 1

Here a = 3, r = 3

 
=> 59048 x 3 /2

= 88572.

what is 70 of 50 means 70% of 50

$$\begin{gathered} ⇒70 x 50100 \\ = 7 x 5 \\ = 35 \end{gathered}$$

Hence, 70 of 50 is 35.