Quantitative Aptitude - Arithmetic Ability Questions

Let the required number be 'p'.

From the given data,

p + 12 = 160 x 1/p

=> p + 12 = 160/p

=> p(p + 12) = 160

=> P^2 + 12p - 160 = 0

=> p^2 + 20p - 8p - 160 = 0

=> P(p + 20) - 8(p + 20) = 0

=> (p + 20)(p - 8) = 0

=> p = -20 or p = 8

As, given the number is a natural number, so it can't be negative.

Hence, the required number p = 8.

The 7 letters word 'POVERTY' be arranged in 7P7 ways = 7! = 5040 ways.

Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) =( C37×C24 ) = 210.

Number of groups, each having 3 consonants and 2 vowels =210

Each group contains 5 letters.

Number of ways of arranging 5 letters among themselves = 5! = 120. 

Required number of words = (210 x 120) = 25200.

$$\begin{gathered} 3 \\ 32 + 3 = 12 \\ 5 \\ 52 + 5 = 30 \end{gathered}$$

Out of 9 persons,4 can be choosen in 9C4 ways =126.

Favourable events for given condition = 2C2*7C2= 21.

So,required probability = 21/126 =1/6.

Ans. 
Distance covered by 1st train in 4 hours = 80*4 = 320 km
Relative speed of 2nd train = 120-80 = 40 km
It will overtake another train in 320/40 = 8 hours
Distance between overtake point and station A = 8*120 = 960 km

i=j/m