Aptitude and Reasoning Questions

Let, Distance between A and B = d

Distance travelled by P while it meets Q = d + 11

Distance travelled by Q while it meets P = d – 11

Distance travelled by Q while it meets R = d + 9

Distance travelled by R while it meets Q = d – 9

Here the ratio of speeds of P & Q => SP : SQ = d + 11 : d – 11

The ratio of speeds of Q & R => SQ : SR = d + 9 : d – 9

But given Ratio of speeds of P & R => P : R = 3 : 2

 SPSR = SPSQxSQSR = d+11d+9d-11d-9

=> d+11d+9d-11d-9 = 3/2

=>  d = 1, 99

=> d = 99 satisfies.

Therefore, Distance between A and B = 99

      It is a case of shifting as given below:

      1  2  3  4  5                    2  1  3  5  4

      O  F  T  E  N   →  F  O  T  N  E

---------------------------------------------------------------------------

       1  2  3  4  5                   5  4  3  1  2

1.    H  E  A  R  T       →      T  R  A  H  E    

2.    O  P  E  N  S  →  S  N  E  O  P

        1  2  3  4  5         2  1  3  5  4

3.    R  I  S  K  Y  →   I  R  S  Y  K

4.    F  I  R  S  T  →   I  F  R  S  T

Hence option 3 is correct.

We know that,

$$\begin{gathered} i2 = -1 \\ i3 = i2 x i = -1 x i = -i \\ i4 = i2 x i2 = -1 x -1 = 1 \\ Hence, i233 =i4 x 58 + 1 = i232 x i1 = 1 x i = i \end{gathered}$$

$$\begin{gathered} 6.46=6+0.46 \\ =6+4699 \\ 594+4699 \\ =>64099 \end{gathered}$$

The given series follows the rule,
+(11x1), +(11x3), +(11x5), +(11x7), +(11x9),....

So starting from 7, 7 + 11 = 18, 18 + 33 = 51, 51 + 55 = 106, ...
So wrong number is 40 which is to be 51.

Here n(S) = 6 x 6 = 36

E={(1,2),(1,5),(2,1),(2,4),(3,3),(3,6),(4,2),(4,5),(5,1),(5,4),(6,3) ,(6,6),(1,3),(2,2),(2,6),(3,1),(3,5), (4,4),(5,3),(6,2)}

=> n(E)=20

Required Probability n(P) = n(E)/n(S) = 20/36 = 5/9.

1/15 + 1/12 + 1/R = 1/6, we got R = 60 (it means R will take 60 days to complete the work alone)

so ratio of work done by P:Q:R = 1/15 : 1/12 : 1/60 = 5 : 4 : 1

so R share = (1/10) x 1200 = 120.