One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.

First , we select 13 persons out of 24 persons in ²⁴ C₁₃ ways.
Now, these 13 persons can be seated in 12! ways around a table .

So required number of ways = ²⁴ C₁₃ x 12!
= [24! / {13!(24 - 13)!}] x 12!
= [24! / {13! x 11!}] x 12!
= 24! / (13 x 11!)

Total ways = 52
There is one queen of club and one king of heart favourable ways = 1 + 1 = 2.
? Required probability = 2/52 = 1/26

If the sum be ? P, then
(2240 - P) = (P x 4 x 3)/100
? 2240 = 12P/100 + P
? 2240 = 112P/100
? P = (2240 x 100)/112 = ? 2000

Now, required interest,
SI = PRT/100 = [{2000 x (7/2) x (1/2)} /100]
= ? 35

Length of train = 264 m

Time taken to cross the pole = 12 sec

Speed of the train, in m/sec = Length of the train/ Time taken to cross the pole

Therefore, speed in m/sec= (264 / 12) m/sec = 22 m /sec

Calculating speed in km/ hour = (22 m/sec ) x 18/5 = 396/5 km/hr = 79.2 km/ hour

8⁵⁷ = (2³)⁵⁷ = 2¹⁷¹
? Required answer = (171 log₁₀ 2 + 1 )
= [171 x 0.3010] + 1 = [51.4710] +1
= 51+1 =52

A leap year must be divisible by 4 as every 4th year is a leap year..

Let the speed of man and current be U and V km/h, respectively.
Speed upstream = (U - V) km/h
Speed down stream = (U + V) km/h
According to the question,
(3 x 60)/(4 x 15) = U - V
? U - V = 3 ......(i)

and (3/4) x (60/10) = U + V
? U + V = 9/2 ...(ii)

On adding Eqs. (i) and (ii), we get
2U = 3 + 9/2
? U = 15/4

On putting the value of U in Eq. (ii), we get
15/4 + V = 9/2
V = 9/2 - 15/4 = 18 - 15/4
? V = 3/4

Hence, speed of man U = 15/4 and
Speed of current V = 3/4
Hence, required ratio = 15/4 : 3/4 = 5 : 1

Suppose that the man takes H hours to cover 4 km downstream and H house to cover 3 km upstream.
Then, 48H/4 + 48H/3 = 14
? H = 1/2
? Rate upstream = 3/(1/2)= 6 km/hr
and rate downstream = 4/(1/2) = 8 km/hr
? Rate of the stream = (8 - 6)/2 = 1 km/hr .