Quantitative Aptitude - Arithmetic Ability Questions

Clearly total persons are increased in  28/35 :: 52/65 = 4:5.

As time is inversely proportional to men, so total time will decrease in the ratio 5:4.

Hence, 22.5 x 4/5 = 18 days.

$$\begin{gathered} 112 × 54 \\ 112 × 1024 \\ = 112 × 1000024 \\ = 1120000/16 \end{gathered}$$

= 70,000.

63.5% of 8924.2 +? % of 5324.4 = 6827.5862

=> 63.5% of 8925 + ? % of 5325 = 6830

=> 6830 ~= 5320 + ?(5325)/100

=> ? ~= 22

 $$\begin{gathered} = log 33 + log 23+ log 103log10×3×22 \\ \end{gathered}$$ 

=log33 12+log 23+log 10312log(10×3×22)  

=12log 33+3 log 2+12 log103log10+log3+log22  

=32log 3 + 2 log 2 + log 10log 3 + 2 log 2 + log 10 = 32  

 Given A = log321875 and B = log2432187

B = log352187 = log321875

=> A

Therefore, A = B

Let the length of the 1st train = L mts

Speed of 1st train = 48 kmph

Now the length of the 2nd train = L/2 mts

Speed of 2nd train = 42 kmph

Let the length of the bridge = D mts

Distance = L + L/2 = 3L/2

Relative speed = 48 + 42 = 90 kmph = 90 x 5/18 = 25 m/s(opposite)

Time = 12 sec

=> 3L/2x25 = 12

=> L = 200 mts

Now it covers the bridge in 45 sec

=> distance = D + 200

Time = 45 sec

Speed = 48 x5/18 = 40/3 m/s

=> D + 200/(40/3) = 45

=> D = 600 - 200 = 400 mts

Hence, the length of the bridge = 400 mts.

Total number of alphabets = 10

so ways to arrange them = 10! 

Then there will be duplicates because 1st S is no different than 2nd S.

we have 4 Is 3 S and 2 Ps 

Hence number of arrangements = 10!/4! x 3! x 2! = 12600